A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids

Advances in Colloid and Interface Science 302 (2022) 102620 Available online 3 March 2022 0001-8686/© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Historical Perspective A broad perspective to particle-laden fluid interfaces systems: from chemically homogeneous particles to active colloids Eduardo Guzm´ an a , b , * , Fernando Martínez-Pedrero a , ** , Carles Calero c , d , Armando Maestro e , f , Francisco Ortega a , b , Ram´ on G. Rubio a , b , * a Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain b Unidad de Materia Condensada, Instituto Pluridisciplinar, Universidad Complutense de Madrid, Paseo Juan XXIII 1, 28040 Madrid, Spain c Departament de Física de la Mat` eria Condensada, Facultat de Física, Universitat de Barcelona, Avenida Diagonal 647, 08028 Barcelona, Spain d Institut de Nanoci` encia i Nanotecnologia, IN2UB, Universitat de Barcelona, Avenida, Diagonal 647, 08028 Barcelona, Spain e Centro de Fısica de Materiales (CSIC, UPV/EHU)-Materials Physics Center MPC, Paseo Manuel de Lardizabal 5, 20018 San Sebasti´ an, Spain f IKERBASQUE—Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain ARTICLE INFO Keywords: Particle fluid interfaces contact angle dynamics active particles rheology ABSTRACT Particles adsorbed to fluid interfaces are ubiquitous in industry, nature or life. The wide range of properties arising from the assembly of particles at fluid interface has stimulated an intense research activity on shed light to the most fundamental physico-chemical aspects of these systems. These include the mechanisms driving the equilibration of the interfacial layers, trapping energy, specific inter-particle interactions and the response of the particle-laden interface to mechanical perturbations and flows. The understanding of the physico-chemistry of particle-laden interfaces becomes essential for taking advantage of the particle capacity to stabilize interfaces for the preparation of different dispersed systems (emulsions, foams or colloidosomes) and the fabrication of new reconfigurable interface-dominated devices. This review presents a detailed overview of the physico-chemical aspects that determine the behavior of particles trapped at fluid interfaces. This has been combined with some examples of real and potential applications of these systems in technological and industrial fields. It is expected that this information can provide a general perspective of the topic that can be exploited for researchers and technologist non-specialized in the study of particle-laden interfaces, or for experienced researcher seeking new questions to solve. 1. Introduction Adsorption and self-assembly of nanoparticles and microparticles at fluid interfaces are widely exploited phenomena on different technological and industrial purposes. This may be understood considering that fluid interfaces provide a suitable environment for the quasi-2D confinement of particles, which results extremely useful for guiding the fabrication of soft and reconfigurable interface-dominated devices [1,2]. In fact, particle-laden interface has been used as support of novel applications which range from the stabilization the stabilization of dispersed systems, including emulsions (Pickering emulsions or bijels), foams, liquid marbles or colloidosomes, to the production of novel nanoporous membranes for filtration or encapsulation [3–6] and the fabrication of functional materials with different electrical, optical, or magnetic properties [7–9]. The accumulation, and quasi-2D confinement, of colloids at fluid interfaces leads to the emergence of completely new behaviors and properties, e.g., intriguing 2D phase transitions or anomalous rheological responses. These cannot be easily explained in terms of the physico-chemical concepts traditionally used in the description of their 3D counterparts, and require to consider thermodynamics aspects acting at the molecular scale with mechanical ones operating at the microscale or even larger distances, which are strongly determined by the characteristics of the particles and the nature of the fluids composing the interface [10,11]. The distinctive features of particle-laden interfaces with respect to those stabilized with surfactants, can be understood considering that: (i) particles are frequently * Corresponding author at: Departamento de Química Física, Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Ciudad Universitaria s/n, 28040 Madrid, Spain. ** Corresponding author. E-mail addresses: [email protected] (E. Guzm´ an), [email protected] (F. Martínez-Pedrero), [email protected] (R.G. Rubio). Contents lists available at ScienceDirect Advances in Colloid and Interface Science journal homepage: www.elsevier.com/locate/cis https://doi.org/10.1016/j.cis.2022.102620 Received 4 December 2021; Received in revised form 22 February 2022; Accepted 23 February 2022 Advances in Colloid and Interface Science 302 (2022) 102620 2 chemically isotropic objects (Janus particles and patchy colloids are exceptions that introduce some specificities); (ii) particles do not tend to aggregate in bulk to form well-defined supramolecular systems such as micelles, and (iii) most of the adsorbed partices hardly undergo desorption or bending processes [12–15]. The above aspects, together with the effect of colloidal interactions between particles, some of them arising specifically at interfaces, or between the particles and the interfaces, determine the adsorption kinetics and self-organization of adsorbed particles [16–18]. The understanding of phenomena involving the interactions of particles with fluid interfaces has advanced significantly since the seminal studies of Ramsdem [19] and Pickering [20], in which some of the most fundamental aspects underlying the physico-chemistry of particle-laden fluid interfaces were introduced. Nowadays, the development of new synthesis routes, which have enabled the controlled fabrication of many types of particles that differ in shape, size (ranging from a few nanometers to several micrometers) or surface chemistry has opened new avenues on the understanding of the physico-chemical behavior of particle-laden interfaces [21]. Controlling the physicochemical and structural characteristics of particles also greatly expands the phenomena arising from adsorption and particle assembly at fluid interfaces, while allowing the behavior of particle-laden fluid interfaces to be modulated almost at will [16]. On the other hand, in the last years that the understanding the fundamental aspects of particle adsorption/ desorption at fluid interfaces, such as the dynamics of binding, requires experiments that monitor the motion of controllable particles during the process [22]. Nevertheless, there are many aspects of the behavior of particle-charged fluid interfaces that remain unclear, which continues to stimulate the research aimed to the understanding of the processes of particle adsorption at fluid interfaces and the physico-chemical properties of the resulting layers, such as their response against mechanical stresses. The last decade has been fruitful in advancing the knowledge of particle-laden interfaces, as reflected in the numerous published reviews on specific aspects of this type of systems, e.g., contact angle [23–25], mechanical response [11,26–35], the dynamics of particles trapped at fluid interfaces [36,37], active and externally actuated particles [8,38], the interaction of particle layers with biological interfaces [39,40] or the development of particular applications (stabilization of emulsions and foams, interface-dominated devices or prevention of coffee-ring effect) [1,2,5,14,15,18,41]. This review attempts to provide an integrative view of the behavior of particle-laden fluid interfaces that may help researchers and technologists in the understanding of fundamental and applicative aspects of this type of systems. 2. A brief approach to the adsorption and self-organization of particles at fluid interfaces This section tries to provide a description of the two processes that are indispensable in the formation of any particle-laden fluid interface, regardless of the specific nature of the colloidal objects or the fluid interface: (i) the transport of colloidal particles to the interface, and (ii) the breach of the interface as a result of particle protrusion. As soon as the particles enter into contact with the interface, their penetration into the interface is mainly driven by the reduction of contact area between the two fluid phases, which leads to the minimization of the unfavorable fluid/fluid interactions and the reduction of the total free energy of the system [13]. This energy reduction in turn contributes to guarantee the interfacial stabilization. 2.1. Interaction between particles and the interface Particle-interface interactions can be expected to be relevant as soon as the particle is transported to the vicinity of the interface. Since most of the particles of interest hold surface charges that lead to the emergence of electrical double layer forces, and both the water/vapor and water/ non-polar fluid interfaces exhibit a negative effective charge [42], the adsorption of negative charged particles at the fluid interface is expected to occur very slowly, or does not occur [43], while the adsorption of positively charged particles is usually strongly favored, although the diffusion process can be very slow. Furthermore, as the particles approach the interface made up of fluid with different dielectric constant, they experience repulsive image charge repulsions and other confinement effects, that distort the electrical double layer of the particles near the interface [43–45]. In fact, when a charged colloidal particle approaches to the interface between fluids having very different values of dielectric constants, a new type of electrostatic interaction emerges. This can be rationalized considering that a particle with a defined charge close to the interface (at a distance d) perceives a force equivalent to that what would be expected for its interaction with a similar particle placed in the other phase at similar distance to the interface, i.e., the particle and the image particle are separated by a distance 2d [46]. For charged particles suspended in water near an interface with air or oil, the image charge interactions are always repulsive, independently of the sign of the particle charge. This allows modulating the adsorption by varying the ionic strength of the dispersion [47], because the increase of the electrolyte concentration screens the electrostatic repulsion between the particles and the interface. On the other side, when the sign of the image charge is opposite to that of the particle, the interaction results attractive. Moreover, short range van der Waals particle-interface interactions arise from the combination of three different contributions (i) interactions between permanent dipoles (Keesom interactions); (ii) interactions between permanent and induced dipoles (Debye interactions), and (iii) interactions involving fluctuating dipoles (London interactions). The overall interaction can be parameterized in terms of the Hamaker constants of the three materials, i.e., those that compose the particle and the two fluids. Thus, for a smooth and chemically homogeneous spherical particle of radius R completely immersed in one of the fluids (fluid 1), but placed very close to the fluid interface, it is possible to define the Hamaker constant for the interaction between the solid particle and the second fluid (fluid 2) through a very thin layer of fluid 1, A P12 , as follows [47] AP12 ≈( APP √− A11 √)(  A22 √− A11 √)(1) where A PP , A 11 and A 22 are the Hamaker constants of the particles, and fluids 1 and 2, respectively. Note that A P12 is always positive, so the van der Waals particle-interface interactions are always attractive [48]. The different contributions to the Hamaker constant A P12 can be related, using Lifshitz’s theory, to the dielectric permittivity ε and refractive indices of the two fluid and the particles [49]. Considering dielectric media with identical adsorption frequency ( ν e ), it is possible to obtain the following approximate expression, AP12 ≈3 4kBT( ε P− ε 1 ε P+ ε 1)( ε 2− ε 1 ε 2+ ε 1)+3h ν e 8 2 √(n2 P−n2 1)(n2 2−n2 1)  n2 P+n2 1 √  n2 2+n2 1 √( n2 P+n2 1 √+ n2 2+n2 1 √)(2) E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 3 where h is the Planck’s constant; and ε i and n i are, respectively, the static (zero-frequency) dielectric constants, and the refractive indices in the visible range, and k B and T the Boltzmann constant and the absolute temperature, respectively. Here, the sub-indexes P, 1 and 2 refer to the particle and the fluids 1 and 2. In Equation 2, the first term accounts for the Keesom and Debye contribution, and are always lower than ¾k B T [48,49], while the second term incorporates the contribution of London interactions, which is commonly the most significant. 2.2. Adsorption dynamics of particles to the fluid interface The different transport mechanisms that promote the approach of micron-sized particles from a bulk phase to the fluid interface can be classified into (i) spontaneous (including Brownian diffusion, sedimentation or flotation) or (ii) externally triggered (field-induced or hydrodynamically guided) [35,36,50–52]. When diffusion is the main mechanism, gravity often plays an important role due to the particle density. In the dilute regime, where interactions between particles can be neglected, the terminal velocity of particle settling is determined by a balance between the gravitational and viscous forces. According to the Stokes' law [53], the terminal velocity of the falling particles is given by vSt =2R( ρ p− ρ 1)g 9 η (3) where ρ p and ρ 1 are the densities of the particles and the fluid phase, respectively, g is the gravitational acceleration and η the dynamic viscosity. The competition between gravity and diffusion is evaluated by means of the P´ eclet number, a dimensionless number which evaluates the ratio of convective to diffusive transport defined as Pe =RvSt D(4) Here, D is the bulk diffusion coefficient of the particles. P´ eclet number assumes values about 0.1 for silica particles of 1 μ m suspended in water, whereas particles of 10 μ m presents a P´ eclet number almost 4 orders of magnitude higher. Therefore, it is clear that the increase of the particle size may favor the ballistic movement of the particles over diffusive transport [29]. If gravitational forces can be neglected, Pe <<1, and diffusion occurs in the absence of adsorption barriers and external flow fields, particles transport to the interface can be described by a Fickian-like diffusion law, in a similar manner to the description of molecular surfactant adsorption developed by Ward-Tordai [45]. Thus, the mass transport rate is given by ∂ c(x,t) ∂ t=D ∂ 2c(x,t) ∂ x2(5) with c(t, x) being the bulk concentration, x the distance to the fluid interface and t the diffusion time, respectively. Assuming an initially homogeneous particle bulk concentration c(x, 0) =c ∞ , then the boundary condition for the adsorption kinetics is given by ∂ Γ ∂ t=D[ ∂ c(x,t) ∂ x]x=0 (6) where Γ(t) is defined as the time-dependent interfacial excess of particles adsorbed at the interface, and Γ(0) =0. Thus, taking the WardTordai approach under conditions of irreversible adsorption and without the presence of any adsorption barrier, and considering a complete depletion of the particles contained in the sublayer and small change of the bulk concentration, i.e., c(∞, t) → c ∞ , the combination of Equations (5) and (6) leads to [45] Γ(t) = 2c∞ Dt π √(7) However, the presence of electrostatic barriers between the particles in the bulk phase and the fluid interface is very common and requires an extension of the framework described above (see Fig. 1). The effect of the electrostatic barrier on the time evolution of the surface concentration can be approximate by including an effective diffusivity [54] Γ(t) = − 2c∞ΔEp Deff t π √(8) where ΔE p is the reduction in interfacial energy associated with the screening of the fluid–fluid interface and D eff is the effective diffusion coefficient, defined as Deff =Dexp(−ΔEbarrier kBT)(9) with ΔE barrier being the height of the energy barrier of the energetic landscape emerging for adsorption of a particle to a fluid interface [54]. On the other hand, Schwenke et al. [50] found that the adsorption kinetics is also slowed down with the increase of interfacial coverage in agreement with the results by Deshmukh et al. [35]. The latter reported the existence of two distinct regimes in the time evolution of the adsorption of microgel particles at water/vapor interfaces: (i) a shortterm regime, where adsorption is controlled by diffusion, and (ii) a long-term slower regime, limited by the increase in coverage and the associated steric barrier. This is similar to what was found for the adsorption of several surface active water-soluble polymers, where a first initial fast diffusion of the molecules from the solution to the subsurface is followed by a reorganization of the molecules, which is limited by the steric hindrance induced by the adsorbed molecules and drives the equilibration of the interfacial layer [55]. 2.3. The meaning of the interfacial tension for particle-laden interfaces Fluid interfaces are commonly considered to be in the molecular scale, with their density profile being analytically described by a hyperbolic-tangent function [56,57]. However, in most of the cases, the size of the particles is much bigger than the interface width, which does not allow one to use the classical microscopic description for explaining the decrease of the interfacial tension of clean fluid/fluid interface γ 12 as result of the particle trapping at the interface [2]. Instead, it is usually described in terms of the decrease of the free energy associated with the reduction of the contact area between the two fluid phases [58–61]. Considering a particle constituted by a material having the same interfacial tension with both fluid phases, it is expected that its adsorption at the interface occurs because it leads to a decrease of the direct contact Fig. 1. Simplified representation of the energetic landscape emerging for adsorption of a particle to a fluid interface. The energy barrier ΔE barrier usually increases with the interfacial coverage due to the increase of the electrical potential and, thus the Debye length. Reprinted from Deshmukh et al. [35], Copyright (2015), with permission from Elsevier. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 4 between the two fluids, without any additional energetic costs due to the contact of the particles with the fluids [40]. The above picture requires a description of the interfacial tension using a macroscopic perspective, which considers that the surface tension of a particle-laden interface is not truly a thermodynamic magnitude, and should be defined as an effective one [2,13]. Thus, the reduction of the effective interfacial tension is due to the emergence of a 2D lateral pressure Π, originated from an intricate balance between the entropy and inter-particle interactions, which counteracts the contraction of the interfacial area associated with the interfacial tension. This leads to a decrease of the interfacial tension γ=γ 12 -Π, as the interfacial packing of the particle-laden interface increases, which is measurable using some of the common methodological approaches used for interfacial tension evaluation [2,13,61–65]. Further analysis of the change of the interfacial tension with the trapping of particles point out that the reduction of the area between the two fluids is directly correlated to the interfacial excess of particles, Γ, and, consequently, to the total number of particles, N, which leads to a definition of the effective interfacial tension for a particle-laden interface as γ=( ∂ Gγ ∂ A)Γ=( ∂ Gγ ∂ A)N,T,p (10) The trapping of a particle to a fluid/fluid interface is associated with an energy change ΔE p , which leads to a reduction of the interfacial tension ΔE p /A. Therefore, the effective interfacial tension of the particle-laden fluid/fluid interface in absence of any contribution of the inter-particle interactions, i.e., at low interfacial excess concentration, is defined by [66] γ=γ12 −Π(Γ)(11) with Π(Γ) =Γ|ΔE p |. 2.3.1. Thermodynamics model for describing particle-laden fluid interfaces The definition of the interfacial tension for a particle-laden interface as an effective magnitude makes it difficult to obtain a physically insightful thermodynamic description of such systems. The definition of the interfacial tension for a particle-laden interface as an effective magnitude makes it difficult to obtain a physicaly insightful thermodynamic description of such systems. This makes it necessary to consider the role of the interactions between the particles trapped at the interface and between the particles and the interface, together with the wetting and the chemical potential of the particles [2,31,32]. However, this is not trivial for particle trapped at fluid interfaces, because, unlike molecular species, the particle size is very different from that of the solvent molecules [67], so, a new thermodynamic framework is needed. Henderson [68] proposed the first thermodynamic description of particle-laden fluid interface, considering that the interfacial film was composed of a 2D colloidal fluid of hard disc-shaped particles, in which only the role of the volume interactions was considered. However, this model did not provide a realistic picture because it did not include the changes on the surface pressure at low interfacial coverage due to longrange electrostatic inter-particle repulsions. The simplification adopted in the previous model was partially overcome by the one introduced by Binks [68], who combined Volmer and van der Waals equations were combined. This model accounts for the absence of lateral interactions between particles at low packing density and short-range lateral interactions between them at high packing density, respectively. Besides, it includes two additional assumptions: (i) the behavior of the particles is reminiscent of that expected for a surfactant molecule, and (ii) the area occupied by the adsorbed particle at the fluid interface is the area projected by the adsorbed particle on the fluid interface, i.e., its geometrical area. However, this model did still not consider the role of interactions between particles at long separation distances, so it continued to provide unrealistic predictions on the dependence of the interfacial tension with the packing density. Finally, the different length-scales involved in particle-laden and surfactant-laden interfaces were an additional contribution to the failure of the model, that predicted changes in the surface pressure only at high values of the interfacial coverage (50-70% of the total interfacial area when the monolayer was composed of small particles, diameter <1nm). A more realistic thermodynamic description of particle-laden fluid interfaces was proposed by the group of Miller [69,70]. They extended their previous work on the thermodynamic description of protein-laden fluid interfaces [71] by including specific aspects enabling for a description of the behavior of particles trapped at the fluid interface. According to this model, the interfacial pressure of the particle-laden interface is given by Π=kBT ω 0[ln(1− ω A)+( ω A)]−Πcoh (12) where ω /A and ω 0 are the fraction of area covers by particles and the area of a single particle, respectively, and Π coh is the cohesion pressure, a parameter that accounts for the contribution of the inter-particle interactions to the packing of the particle-laden interface. Application of the above model provides a suitable description of the change in interfacial tension with packing density, regardless of the chemical nature and dimensions of the particles in question, even when the interfacial coverages is far from a close-packed state. More recently, Hua et al. [72] introduced an alternative model that accounts for: (i) the impact of the reduction of the contact line between the two fluid phases on the interfacial tension, and (ii) the inter-particle interactions. The contribution of the reduction of the contact line on the surface pressure due to particle adsorption, Π p , was obtained in terms of the particle density at the fluid interface, whereas the contribution associated with the inter-particle interactions, Π p-p , was assessed, assuming a linear additivity Π =Π p +Π p-p , by evaluating the change of the interfacial pressure of the 2D particle-laden interface. Thus, combining these contributions with the Frumkim model [57], which considers the non-ideality of the interactions, and assuming thermodynamic equilibrium, where the Gibbs relationship is fulfilled, the interfacial pressure is given by the following expression [73] Π= − kBTΓ∞[ln(1−ϑ)− 0.5Kϑ2](13) where Γ ∞ and K are the interfacial excess concentration for a closepacked particle-laden interface and an inter-particle interaction constant, respectively. Here, ϑ=Γ/Γ ∞ represents the interfacial coverage, i. e., the affinity of the particles for the interface. Finally, Groot and Stoyanov [74] proposed a model that introduces the dependence of the inter-particle interactions on the interfacial coverage density in the estimation of the interfacial pressure. According to this model, the latter is described by Π=4kBT π d2[byZ λ−b2ϑ2](14) where d accounts for the range of the long-range interactions, Z is the compressibility factor [74], (λ) 1/2  λ √is the effective diameter of the particles, and b and b 2 are parameters accounting for the inter-particle interactions. This model has been successfully applied on the description of the collective behavior of soft particles adsorbed at fluid interfaces [75]. 2.4. Wettability of particles at a fluid interface The chemical anisotropy of surfactants, i.e., the existence of two moieties with different polarities and different affinity for fluid phases, is the main driving force for their attachment to fluid interfaces. The entropic penalty associated with the reduction of the degree of freedom in the orientation of the surfactant molecules, is counterbalanced by a E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 5 favorable enthalpic contribution, thus reducing the Gibbs free energy of the system. However for describing the entrapment of smooth, spherical and chemically isotropic particles at a fluid interface, particle wettability plays the essential role [29]. Entrapment of a particle at a fluid interface is only possible when the difference between the energies of the particle dispersed in one of the bulk phases and that of the particle trapped at the fluid interface exceeds the energy associated with thermal agitation k B T. Assuming that the particle is small enough to neglect gravitational forces, the energy of a particle, whose center is located at an arbitrary distance z of the interface, is given by [1,25] E(z) = π R2γ12[(z R)2+2(γP2−γP1 γ12 )(z R)+2(γP2+γP1 γ12 )−1](15) where γ P1 and γ P2 are the interfacial tensions between the solid particles and the two fluid phases. Fig. 2 shows the dependence of the energy of a particle as a function of z 0 =z/R, with z 0 =1 and z 0 =-1 corresponding to a particle completely immersed in the fluid 1 and 2, respectively, and z 0 =0 to a particle placed in the interfacial plane. The equilibrium position z 0min , which corresponds to a particle mostly immersed in fluid 1 (0<z 0min <1) or 2 (−1 <z 0min <0), is placed at the distance where the free energy is minimized, i.e., ∂ E/ ∂ z =0, and is given by [76] zmin 0=γP1−γP2 γ12 R(16) At this point, the equilibrium condition of the forces acting at the contact line can be defined in terms of the three characteristic interfacial tensions, the interaction between the particle and both fluids and between the two fluid phases, simplifies to the Young-Dupre equation 0=γP1−γP2−γ12cosθ (17) Here, the contact angle, θ, is defined as the angle between the plane tangent to the particle’s surface and the interface at the line where the interface meets the solid, as shown in Fig. 3 [77]. Under these conditions, the equilibrium contact angle is completely determined by the three surface tensions cosθ =γP1−γP2 γ12 (18) From the previous equation, it follows that the particle adsorbs at the fluid interface only when the following inequality is met [13,25] |γP2−γP1|<γ12 (19) Hence, the contact angle plays the same role as the hydrophiliclipophilic balance (HLB) of molecular surfactants [12,23], i.e., a parameter that provides information on the preferential partitioning of particles between the two fluid phases, and results from the different interaction of the particles with the two fluid phases [10,12,78]. It is possible to describe the trapping of colloidal particles at a fluid interface in terms of the intricate balance of interactions, e.g., van der Waals, polar and electrostatic interactions, and hydrodynamics forces that contribute to interfacial equilibrium [48,49]. For example, in charged particles the free energy per unit of area, associated with the formation of the electric double layer, ΔF DL , leads to a change of the surface free energy γ 1P =γ 1P,0 +ΔF DL [79], where γ 1P,0 is the surface tension at the point of zero net charge. Introducing the above correction into Equation (18), the following expression is obtained cosθ =cosθ0−ΔFDL γ12 (20) Considering that in most cases the double layer forms spontaneously, ΔF DL <0. Therefore, a smaller partitioning of the charged particles between the two media is expected than for an uncharged particle. If one of the fluids is water, particles are considered as hydrophilic when θ < 90◦, and they remain mainly submerged in water, while particles are considered hydrophobic when θ >90◦, and they are predominantly submerged in the non-aqueous phase. The case in which the particles show a similar preference for both fluid phases is the so-called neutral wetting and is characterized by a contact angle of 90◦(see Fig. 4). For spherical and perfectly smooth particles, it is possible to find a simple geometrical relation connecting the contact angle and the protrusion height h of the particle into the less polar phase, Fig. 2. Free energy of a spherical colloidal particle (R =50 nm) as a function of its center relative to the hexadecane/water interface. The interfacial tensions are γ 12 =53.5 mN/m, γ P1 =28.5 mN/m and γ P2 =14.2 mN/m. Reprinted from Ballard et al. [25], Copyright (2019), with permission from The Royal Society of Chemistry. Fig. 3. Idealized representation of the position of a particle trapped at an arbitrary fluid/fluid interface. θ and R represent the contact angle, or relative wettability of the particle by the interface, and particle radius, respectively; γ P1 and γ P2 are the interfacial tensions between the solid particle and the two fluid phases, and γ 12 the interfacial tensions corresponding to the fluid interface. Adapted from Davies et al. [77], Copyright (2014), with permission from American Institute of Physics. Fig. 4. Schematic showing the relative position of a colloidal particle in relation to the interfacial plane as a function of its contact angle. Reprinted from Maestro et al. [80], Copyright (2019), with permission from The Royal Society of Chemistry. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 6 θ=cos−1[1−h/R](21) From equation (15), the energy change associated with the transference of a particle from a fluid phase to its equilibrium position, i.e. the so-called trapping energy, is given by [81] ΔEp= − π R2 γ12 (γ12 − (γP1−γP2))2(22) which for spherical particles can also be defined in terms of the contact angle as ΔEp= − π R2γ12(1±cosθ)2(23) where the ±signs in the bracket indicate the position of the particles in relation to the interfacial plane. According to Equation (23) particle trapping at fluid interfaces strongly depends on size. Fig. 5 shows the dependence of the entrapment energy on the contact angle, calculated with Equation (23), for two colloidal particles with different sizes, 10 nm and 1 μ m, at an arbitrary fluid interface with γ 12 =50 mN/m. The energetic landscape, resulting from the analysis of the contact angle and size dependences of the trapping energy, shows that the latter largely exceeds the thermal energy k B T in most of the cases [82]. Therefore, the adsorption of micron-sized particles to a fluid interface can be considered as an irreversible process, with typical trapping energy values in the range between 10 6 k B T and 10 7 k B T. For the mentioned microparticles, adsorption is reversible only at very low values of the fluid/fluid interfacial tension γ 12, and/or for cosθ ~ 1. On the other hand, in particles with sizes smaller than 10 nm the trapping energy is of the order of several k B T. This suggests that for particles with a very small size, the low value of the trapping energy can lead to a thermal-activated escape of the particles from the interface. Hence, small nanoparticles exhibit an adsorption-desorption equilibrium like that found in conventional molecular surfactants, polymers and proteins [83]. Fig. 6 shows the dependence of the detachment energy (-ΔE p ) on the particle radius for the trapping of colloidal particles at an oil/water interface with γ 12 =50 mN/m, and a fixed value of θ =90◦. The residence time of particles at the fluid interface is reduced with the decrease of the characteristic size of the adsorbed particles, which explains the facilitated displacement of small nanoparticles from the interface by the adsorption of particles with bigger size [84]. In most cases, micro-sized particles are irreversibly adsorbed, so that the particles can only move freely within the interfacial plane. The existence of lateral mobility of the particles allows their rearrangement in a diffusive manner or after the application of external stimuli, which lays the foundation for the fabrication of new materials that can be reconfigured by adjusting the particle interactions/organization at the fluid interface [17,37]. This scenario largely differs from the one stablished when particles are set on liquid/solid interfaces [16], or even when particles are in the vicinity of a fluid interface but without actually being adsorbed [85]. The position of particles trapped at fluid interfaces undergoes fluctuations relative to the interfacial plane, when the interfacial and thermal energies are comparable, and deformations induced by interface capillary waves [84,86]. However, the motion of adsorbed particles along the direction perpendicular to the fluid interface induces the emergence of capillary forces that promote the reestablishment of the equilibrium position [87]. The entrapment of a colloidal particle in the interfacial plane separating two fluid phases requires that the interfacial tension forces can overcome the action of gravity [81]. The balance between these two contributions is typically defined in terms of the Bond or E¨ otvos number Bo =Δ ρ g2R γ(24) where Δ ρ denotes the difference between the density of the particle and the fluid. It should be noted that the gravitational contribution only is relevant for particles of several micrometers. For particles smaller than 10 μ m, Bo assumes values well below unity, and hence the contribution of interfacial tension forces becomes dominant [88,89]. It should be noted that the reversible/irreversible character of the attachment of particles to the fluid interface, together with the value of the contact angle have an important impact on different physicochemical aspects associated with potential applications of particle-laden interfaces. Among them, the organization of the particles at the interface, the strength and nature of the interparticle interactions, the friction coefficient values in microrheology experiments, or the response of particle-laden fluid interfaces to external mechanical deformations, that govern the ability of particles to stabilize emulsions and foams [27,64,78,80,86,90–93]. 2.4.1. Effect of line tension and particle roughness in the wetting of particles for fluid interfaces The contributions of the particle roughness and/or the line tension to the wetting properties of the particles limit the applicability of Equation (18) to provide an appropriate description of particle entrapment at fluid interfaces [94]. The line tension is caused by the imbalance Fig. 5. Trapping energy for two colloidal particles with R =1 μ m (a) and R = 10 nm (b), at a fluid interface with γ 12 =50 mN/m, as function of the contact angle. Please, note the differences on the energy scales. Reprinted from Guzm´ an et al. [34], Copyright (2021), with permission from Institute of Physics. Fig. 6. Dependence of the detachment energy at 298 K for a particle adsorbed at a planar oil/water interface (γ 12 =50 mN/m) at a fixed contact angle θ = 90◦. Note the low energies for particles with radii smaller than 0.5 nm (close to that of molecular surfactants). Adapted from Binks [12], Copyright (2002), with permission from Elsevier. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 7 between the intermolecular forces that operate within the three-phase contact line [95], and can be positive or negative, with a magnitude in the range between 1-100 pN [25]. The relative importance of its contribution can be assessed in terms of a dimensionless number defined as Li = τ γ12L(25) where τ and L are the line tension and the length of the contact line, respectively [96]. The role of the line tension in the wetting of particles can be included by modifying the Young’s equation with the correction proposed by Bresme and Quirke [97], who introduced a dependence between both interfacial and line tensions on the contact angle of spherical smooth particles as follows γP1−γP2 cosθ −γ12 = − τ Rsinθ (26) It follows from the above expression that the line tension influences the wettability of particles only for sizes below 20 nm [10,18,98–100]. Following arguments analogous to those developed in section 2.4, but including the contribution associated with the line tension, the energy change associated with the entrapment of a particle at the fluid interface can be defined as ΔEp=γ12cosθ∞2 π R2(1−cosθ)+2 τπ Rsinθ − π R2γ12cos2θ(27) where θ ∞ is the contact angle provided by the Equation (18). When particles are in conditions of mechanical and thermal equilibrium, with ( ∂ ΔE P / ∂ θ) T =0, they are in the position dictated by the contact angle cosθ =cosθ∞[1− τ Rγ12]−1 (28) It should be noted that the minimization of the line tensionmodifies the wettability of non-spherical particles and their orientation at the interface [88,89,96]. For θ → 90◦, i.e., intermediate wetting conditions, it is possible to neglect the role of line tension, and Equation (28) becomes Equation (18). In such conditions, the line tension applies almost tangentially to the interface, and therefore its impact on the position of the particles in relation to the interficail plane becomes almost negligible [13,25]. When the contact angle differs significantly from 90◦, the perpendicular component of the line tension assumes a relatively high value, becoming maximum for θ → 0◦and θ → 180◦[101], which leads to a positive contribution to the energy change associated with the trapping of the particle. The assymetry of the shape and roughness of the particles increase the ratio between the contact line and the characteristic dimension of the particles [98], also modifying the wetting properties of colloidal particles by fluid interfaces [61,102], especially when the roughness of the particles is high and their size is small [103]. This modifications were studied theoretically by Nonomura and Komura [103] using the Cassie–Baxter model, associated to the emergence of pinning–depinning of the interface along the contact line. 2.4.2. Tuning the contact angle of particles at a fluid interface The interfacial organization of the particles within the interface can be modulated by altering the wettability of the particles (see Fig. 7), and consequently the interparticle interactions. Many physical and chemical tools are currently available to modify the wettability of colloidal particles and tune their interfacial organization. The most widespread strategy to modify the ability of particles to remain trapped at the fluid interface is the addition of different chemical additives, e.g., surfactants, polymers, salts or even low molecular weight compounds (e.g., alcohols), to the particle dispersion. These molecular species can decorate the particle surface through non-electrostatic, e.g., hydrogen bonds, electrostatic or van der Waals interactions [51,58,60,61,102,104–108]. For instance, due to a complex interplay between hydrophobic and non-covalent electrostatic interactions, it is possible to modify the wettability of the particles in situ by modifying the amount of surfactant added in the dispersion containing the colloidal particles, or in the second fluid [109]. The gradual addition of surfactants usually results in the appearance of different surfactant structures and the progressive increase in particle hydrophobicity. The maximum degree of particle hydrophobization is usually found for surfactant concentrations high enough to ensure neutralization of the surface charge of the particles. Any further increase of the surfactant concentration beyond the isoelectric point usually leads to rehydration of the particles. The decrease in contact angle is usually due to the formation of a surfactant bilayer on the surface of the particles through hydrophobic interactions between the alkyl tails of the surfactant molecules. This approach was explored by Maestro et al. [80] and Binks et al. [110], who added two different types of alkyltrimethylammonium bromide surfactants (hexadecyltrimethylammonium bromide, CTAB and dodecyltrimethylammonium bromide, DTAB) to dispersions containing silica nanoparticles to tune the assembly of silica nanoparticles at the water/steam interface. Binks et al. [111] extended the possibility of modifying the wettability of silica particles by the addition of a two tails surfactant (didecyldimethylammonium bromide). Obviously, the impact of the addition of surfactants on the wettability of particles is determined by the chemical nature of the particles. Deleurence et al. [112] studied the modification of hydrophobic anionic polystyrene and hydrophilic silica particles with a cationic surfactant. They found that polystyrene particles underwent a Fig. 7. Sketch showing the effect of the wettability of the particles on their organization at a fluid interface. Reprinted from Garbin et al. [93], Copyright (2012), with permission from Elsevier. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 8 strong change in their contact angle. However, the contact angle of silica particles was not significantly modified, although there was a strong modification of the particle charge. Another example of the strong impact of the additives on the interfacial properties of particles can be found in the work by Perrin et al. [113]. They demonstrated that the addition of diethylene glycol monobutyl ether to silver nanoparticles leads to a strong modification of the ability of particles for adsorption at both fluid/fluid and fluid/solid interfaces, which can be exploited in the fabrication of electronic devices by ink-jet printing [114]. On the other hand, it is also possible to obtain a well-controlled modification of particle wettability by irreversible covalent bonding of specific coating ligands to the particle surface [115]. For instance, silanization of silicon dioxide particles, with a reduction in the percentage of surface free silanol groups from 34% to 20%, leads to an increase in the value of the particle contact angle at the water/vapor interface by a factor of two. [116] Thus, particles with the highest hydrophobicity (those with 20% of free silanol groups) present a contact angle of 113◦, whereas this decreases for hydrophilic particles (those with 34% of free silanol groups) down to 55◦. Similarly, grafting poly (glycerol-monomethacrylate) chains onto the surface of polystyrene latex particles modifies their contact angle at the fluid interface [117]. The particle wettability control developed in recent years has stimulated significant research efforts on the rational design of wettabilitycontrolled particles, and in particular for the design of colloidal particles with asymmetric wetting properties, e.g., Janus particles and patchy colloids [29,118,119]. 2.4.3. Experimental methods for the evaluation of the contact angle of particles trapped at fluid interfaces Since there is no standard approach to determine the contact angle of particles at fluid interfaces, regardless of their dimensions, shape and morphology, its determination remains a challenge [120–122]. At present, there are different experimental techniques designed for a direct or indirect determination of the contact angle of isolated particles adsorbed at the interface of the fluid (or its assemblies). These methods are usually classified into three different groups: (i) indirect measurements; (ii) direct measurements of multiple particles (ensemble methods); and (iii) direct measurements of individual particles, in which the position of the particle centre is resolved relative to the interfacial plane [23,24,123,124]. Indirect methods the mean value of the contact angle of the particle trapped in a fluid interface by measuring a property associated with it. In single particle methods, colloids are directly visualized by different types of microscopies (optical, electron, atomic force...), so the minimum particle size that can be observed depends on the specific technique. These methods are usually free of assumptions and allow the detection of any interface heterogeneity. However, they require imaging of a large number of particles to ensure good statistics for contact angle determination. On the other hand, ensemble approaches allow determining a very accurate mean contact angle, with very good statistics, by measuring the macroscopic properties of the system, even in smaller objects. However, the use of this type of methods does not give directly information about the possible heterogeneity of the particle contact angle, i.e., the possible variation of the contact angle between individual adsorbed particles resulting from subtle changes on their chemistry, size or morphology (shape and roughness). 2.4.3.1. Indirect methods. The analysis of the profile of a sessile droplet deposited on the surface of a flat substrate, that has the same chemical nature as the particles trapped at the fluid interface, is an indirect method commonly used to estimate the contact angle [125]. However, the assumption that this angle coincides with the particle contact angle fails in most cases because it does not consider the role of curvature, roughness and line tension. The particle contact angle at the fluid interface can also be determined through the analysis of interfacial pressure-area isotherms (Π-A) of particle-laden fluid interfaces. Two different methods have been described for such purpose: (i) the analysis of the area exclusion induced by the particles in a second component, usually a surfactant, and (ii) the evaluation of the isotherm collapse pressure. The first method is based on the analysis of the area displacement exhibited by the Π-A isotherms of an insoluble surfactant when colloidal particles are adsorbed simultaneously. In this case, the contact angle is estimated by assuming both that the wettability of the particles does not change with the presence of the surfactant, and that such displacement occurs because the particles occupy part of the interfacial area. The latter assumption implies the absence of interactions between particles and surfactant molecules. Otherwise, the area shift could mask the expansion or contraction of available area associated with the interactions [126,127]. The second method, exploited for a long time, calculates the contact angle by surface pressure measurements and geometrical considerations, assuming that once the system reaches the collapse pressure, Π c , identified by a kink or flat region in the Π–A isotherm,the particles adopt a close packing configuration organized in ideal coplanarity [52,128–131]. On the other hand, if compression provides enough energy to force desorption of the particles the collapse pressure and desorption energy can be correlated as follows [128] ΔEp=Πc Γc (29) where Γ c is the surface concentration at the collapse point. The pendant drop tensiometer is also a technique often used to measure the binding energy of particles trapped at a fluid interface. This technique monitors the time evolution of the interfacial tension of a droplet of the particle suspension during the spontaneous adsorption of the particles at the fluid interface [66]. Thus, neglecting the existence of interparticle interactions at the interface, and assuming that the maximum packing of the particles at the interface corresponds to a perfect 2D hexagonal array, the saturation of the interfacial tension is related to the adsorption free energy as ΔF= − (γ12 −γ) π R2/ η (30) with η =0.91 for a close-packed interface. A very popular alternative approach for indirect contact angle determination is based on the measurement of the upward velocity of a fluid, pushed by capillary pressure, which is contained in a capillary column filled by a packed bed of particles [132,133]. This method, exploited to determine the contact angle of particles with a wide range of sizes, shapes and chemical nature, assumes that particles form a bundle of capillary tubes, of circular cross-section and radius R eq . In this method, the contact angle is assessed using the Washburn equation [134] h2 L=γ12Reqcosθ 2 η t(31) where h L , t and η are the height of the liquid column, the time and the viscosity of the rising liquid, respectively. According to Equation (31) h L is defined as a function of the experimental time. However, this method is limited to the determination of the contact angle of rather monodisperse particles, which form bundles where the porosity of the bed of particles is well defined. Furthermore, the Washburn method only provides information of the advancing contact angle, which can be far from the true equilibrium situation due to the wetting dynamics. As alternative to the Washburn method, Diggins et al. [135] introduced another approach based on the determination of the equilibrium capillary pressure of a packed bed of particles, ΔP, which can be defined as the pressure required for hindering the fluid motion through the packed particles. The latter is related to the contact angle through the Laplace-White equation [136] E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 9 ΔP=γ12Aϕcosθ 1−ϕ(32) The main advantage of this approach is that only depends on experimentally accesible parameters, such as the specific surface area A, the volume fraction of powder ϕ and the fluid/fluid interfacial tension γ 12 . The use of a force tensiometer can also help on the evaluation of the wettability of powders. This evaluation is possible by loading a packed bed of particles, hunged from a precision balance and then dipped into the liquid. Thus, it is possible to determine the contact angle from the change detected in the mass when the liquid progressively penetrates through the bed, as follows cosθ(t) = m2 η C ρ 2γ12t(33) where C is a constant characteristic of the material and m the variation of the mass at a given embedding time t [137]. It is should be stressed that the different approaches introduced for replacing the conventional Washburn method can be only used for obtaining the advancing contact angle. Another approach used to determine the contact angle is based on the use of a heat-flow calorimeter to measure the energy changeassociated with the mixing of solid particles and a liquid [138]. In this method, the contact angle is related to the enthalpy of immersion, through thermodynamic consideration, as follows cosθ =−KT −hi γ12 (34) where K is given by the temperature change associated with the immersion of the particles in the fluid phase, and h i is the change of enthalpy associated with such immersion. This approach requires the use of two calorimetric cells: the first one filled with dried powder, and the second empty one used as reference. The experimental evaluation of the contact angle relies of the equilibration of both chambers with liquid, and the determination of the differences on the changes of thermal energy during the wetting process. This method is commonly used for particle trapped at liquid/vapor interfaces, with the contact angle for particles at liquid/liquid interfaces being obtained by combination of the data obtained for the individual liquid/vapor interfaces. However, the required assumptions to link immersion enthalpy and contact angle have limited the applicability of this approach. A last indirect alternative used to determine the contact angle relies on the use of the Atomic Force Microscope (AFM). In this method, the contact angle is estimated by measuring the force-distance curve due to the interaction between a colloidal probe and a liquid bubble [139]. This is possible because during attachment and detachment of the colloidal particle from the interface, it is possible to obtain information of different parameters, including the jump-in and detachment position, the detachment force and the work adhesion, which allows estimating both the advancing and receding contact angles of particles bigger than 2–3 μ m. The use of AFM for determining the contact angle is a extremely sensitive methodology which is affected by specific details of the particle surface, e.g. surface topography and chemistry, which can result in displacements of the contact line or local pinning. Furthermore, the complexity of the methodology makes it difficult to obtain a detailed statistical analysis from AFM measurements, even though this technique provides important information related to the mechanics of the wetting of particles. 2.4.3.2. Direct methods for particle ensembles 2.4.3.2.1. Immobilization methodologies. A very popular approach for determining the contact angle of particles trapped at fluid interfaces relies on the immobilization of particles at the interface, commonly by freezing [122] or gelling [140], followed by an analysis of the immobilized surfaces by using a high-resolution microscopy (electron microscopy or AFM). Currently, there is a broad range of immobilization strategies that allow obtaining information on the contact angle of particles at fluid interfaces, with their main advantages arising from the possibility to evaluate many particles from a single measurement. Nevertheless, their application appears limited by the significant interface manipulation, which may modify the locations of the particles, induce particle deformations or change the composition of the system. The first and probably most popular methodology based on particle immobilization is the so-called gel trapping technique (GTT). It was originally designed for the evaluation of the contact angle of microparticles at a fluid/fluid interface by their transference to a solid matrix, allowing their direct visualization by using Scanning Electron Microscopy (SEM) [140]. It was quickly extended to the determination of the contact angles of nanoparticles trapped at fluid interfaces by using AFM for imaging [99,120]. In the GTT, a particle film is prepared at the interface between a fluid and an aqueous solution of a gellan, maintained at a temperature above its gelling temperature. The temperature is then reduced to force the gelation and the particles are trapped in their fixed position at the interface. This allows the monolayer to be transferred to a poly(dimethylsiloxane) (PDMS) replica, where the relative position of the adsorbed particles can be directly determined by microscopy. From the images it is possible to estimate the contact angle by a simple geometrical analysis. Thus, it is possible to determine the contact angle of particles with sizes in the range 100 nm-100 μ m, trapped at both liquid/vapor and liquid/liquid interfaces [102,120,140]. Despite its apparent simplicity and accuracy (contact angle can be determined with a variability of 3-5◦), the use of GTT appears limited due to the different aspects. First, the gellan is a nonsurfactant active molecule with a characteristic length of 10 nm. This can lead to trapping heterogeneities which makes difficulty to provide a definition of the contact line when particles with a diameter below 100 nm are considered. Furthermore, the aplication of high temperatures limits the applicability of GTT to non-volatile fluids, and can induce deformation on the particles [141]. Vogel et al. [142] introduced an alternative to conventional GTT based on the addition of butylcyanoacrylate to the interface through the vapour phase. The formation of a poly(butylcyanoacrylate) matrix, via an anionic polymerization process that starts upon the contact of the precursor butylcyanoacrylate with the aqueous phases promotes the trapping of the colloids at the water/vapour interface. This approach also creates a solid replica of the interface that can be used for the evaluation of the equilibrium positions of the colloids, using high resolution microscopy. A more sophisticated immobilization methodology combines freezefracture (FreSCa) and shadow-casting cryo-Scanning Electron Microscopy (SEM) [122]. This method relies on the immobilization of the particles at the fluid interface by a fast vitrification, helped by the action of propane jet freezer, that traps the particles at the fluid interface without any significant thermal contraction. The obtained sample are later fractured and uni-directionally coated with a metal layer at a welldefined tilt angle α , and then the contact angle of the particles is determined from the images obtained using cryo-SEM, using simple geometrical assumptions [111,122,143]. This is possible because the presence of a particle-laden layer at a flat interface appears as a weak fracture plane, and allows the exposure of the immobilized particles. Thus, the oblique metal deposition casts the shadow of the particle protruding from the interface. The measurement of the length of the shadow and the projected height make it possible the calculation of the protruding height h, and consequently the contact angle, knowing the value of the shadowing angle α and the geometry of the particles [144]. The use of the FreSCa coupled with cryo-SEM imaging allows evaluating relatively large regions of particle-laden interfaces, which allows an accurate evaluation of the existence of wetting heterogeneities at the interface. Furthermore, this method offers a high accuracy and flexibility for the determination of contact angles of particles at water/oil E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 16 interfacial plane, is mainly defined by the wetting properties of the particles [206]. However, their adsorption can lead to local deformations of the fluid interface around the particles, thus leading to long-range capillary immersion forces. Roughness and/or chemical heterogeneities on the surface of the adsorbed particles surface promote the formation of a non-smooth, wavy or irregularly shaped, three phase contact lines, deformed enough to promote strong capillary interactions [10,40,207]. The capillary interaction between two identical neighboring spherical colloids can be expressed through an effective potential [207] Ecapillary(R) = − 12 π γ12Κ2ζr4 R4(56) where ζ is a factor that defines the dependence of the capillary interaction on the particle orientation and K a function accounting for the deformation amplitude of the interface. The deformation of the interface, and thus the strength and dominant mode of capillary forces, can be modified by the application of electric or magnetic fields [208], or the addition of different additives (salts, surfactants, or polymers), that allow fine-tuning of particle wettability and interfacial tensions. The adsorption of charged colloids at a fluid interface between non-polar and polar fluids promotes extra interfacial deformations. These deformations are produced by the vertical interfacial electric force directed towards the fluid with higher dielectric constant, resulting from the combination of any external vertical force acting on the colloid and an inhomogeneous stress field. The latter presents different components of the above and below the fluid interface, which are induced by the electric dipolar field of the particles, and can be described in terms of the Maxwell pressure tensor [10]. These conditions lead to the electrodipping and electrocapillary forces that involve multiple or single particles, respectively [18,205]. It should be noted that electrocapillary and electrodipping forces can induce interfacial deformations that are often comparable to those resulting from the action of gravity on interfaces laden with large particles [78]. When the capillary interactions engage a larger number of particles, they can induce self-assembly through the so-called “Cheerios” effect, similar to that what is observed in cereal bowls [88]. Therefore, the control of capillary interactions, by adjusting the shape or wetting properties of the particles, can be used in the fabrication of complex interfacial structures [188]. If the apparent weight of the adsorbed species becomes larger than the interfacial forces, which is often the case of monolayers with a high interfacial coverage, the collective effects may modify the simple pairwise interactions, determining the deformation of the surrounding interface. This affects the organization of particles at the interface such that the entire aggregate sinks to the heavier phase (“collective sinking mechanism”) [192,209]. 4.2.2. Hydrodynamic interactions Capillary forces are not the only contribution to the energetic landscape emerging in particle-laden fluid interfaces appearing as result of the presence of the interface, with the hydrodynamic interactions, stimulated by the motion of the particles through the viscous media, being strongly distorted by the particle adsorption. The adsorbed particles move in an overdamped regime, in which the applied forces and torques are constantly balanced by their viscous counterparts. The flow generated by the random or directed motion of the adsorbed particles, which can be modified by the possible presence of other particles or objects and surfaces, transports energy through the two media and can be described by the linearised Stokes equations. Therefore, apart from other possible direct interactions, the particles always exhibit solventmediated forces which, unlike the interactions described above, cannot be described by a potential. Complex and indirect hydrodynamic interactions have a tensor character, as they are strongly determined by the shape, orientation and relative velocity of the agents involved. These interface-mediated hydrodynamic interactions control the steering of swimmers along defined trajectories [210], their attraction towards the interface [211], the circular path found in the motion of Escherichia coli [212], can be exploited on the transport of cargos along fluid interfaces [9], or the rectification of rotation into translational motion [213], where the local flow induced by the slip boundary condition imposed by the liquid-air interface differed from the one generated by the stick boundary condition characteristic of a solid wall. On the other hand, the balance between attractive interactions and hydrodynamic repulsive interactions emerging between rotating disks, floating at a liquid/air interface, leads to the assembly of dynamic lattices [214]. The relative importance of the hydrodynamic interactions is given by the capillary number Ca = η vp γ12 (57) where v p is the particle velocity. It is commonly accepted that for Ca <1, the role of the hydrodynamics interactions may be neglected [40,208]. 4.3. Externally actuated interactions The adsorption of particles at a fluid interface is associated with a restriction of their mobility with respect to the interfacial plane. However, in-plane mobility is not limited, and in principle particles are free to move within the interfacial plane [215]. This motion can be boosted by the mechanical deformation of the interface, which can induce changes on the interfacial area (dilatational deformations) or shape (shear deformations). So, these perturbations can be exploited in the control of the interfacial assembly or the modulation of 2D phase transitions, which allows to adjust almost at will different mechanical, optical or electronic properties [104,216,217]. The application of magnetic or electric fields leads to similar effects when considering assemblies of responsive particles and is also a very powerful tool for tuning the assembly of colloids at fluid interfaces [7,208,218]. When adsorbed particles respond appreciably to the application of a magnetic field, while dispersive fluids do not show a strong response, the presence of the interface has essentially no effect on the nature of the magnetic interaction between the particles. However, the mobility constraints imposed by the high adsorption energy force the particles to restrict their motion to the adsorption plane. Consequently, the angle of application of the external field becomes a fundamental parameter determining the response of the particle monolayer. Alternatively, the applied field can be used only to force the rotation of the particles along the axes parallel to the confining surface, which is strongly hampered by the occurrence of interfacial pairs. The induced rotation can be used to change the extent and nature of capillary interactions at will [10,97]. An alternative way to modulate the interactions between particles, and thus the organization of particle assemblies at fluid interfaces, is by modifying the environmental conditions (pH, temperature or ionic strength). For example, changing environmental conditions has proven to be a very powerful tool for controlling the assembly of microgel particles at fluid interfaces [35,75,182]. 5. Chemically isotropic particles at fluid interfaces As developed previously, the surface chemistry of particles influences the self-assembly of particles at the fluid interfaces [75]. This results from the specific wetting properties of the particles [117], the shape of the contact line and/or the inter-particle interactions operating between the adsorbed particles [219]. In particular, chemical heterogeneities on the particle surface can lead to an undulated contact line. Furthermore, the presence of surface charges on the particles may modify the electrostatic and capillary contributions to the inter-particle interactions [219], and consequently the self-assembly of particles at the fluid interfaces. Therefore, the importance of the surface chemistry on the control of the properties of particle-laden fluid interfaces makes E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 17 necessary to distinguish between at least three different situations: (i) chemically isotropic particles; (ii) particles capped with ligands, and (iii) chemically anisotropic particles. This section focuses on the interfacial behavior of chemically isotropic particles. 5.1. Hard particles at fluid interfaces Colloidal hard particles are a category including a broad range of particles with different chemical nature (polymeric, metallic, metal oxide compounds or ceramic), which present as main characteristic that their maximum deformation upon trapping at the interface remains on a length scale much smaller than their diameter, and hence they behave at the interface as solid-impenetrable objects for neighboring particles. This property determines the maximum packing that these particles can achieve at the fluid interface. 5.1.1. Spherical particles The equilibrium trapping of chemically isotropic spherical particles at fluid interfaces is characterized by the existence of a single energy minimum, determined by the interfacial tension, particle size and contact angle, which also rule on the organization and properties of the adsorbed assemblies. 5.1.1.1. Interfacial organization. The understanding of the organization and self-assembly of colloidal particles at fluid interfaces requires to consider both the distribution of the particles within the quasi-2D fluid interface, and the position of the particles with respect to the interfacial plane, i.e., contact angle of the particles or immersion height. Both aspects are strongly correlated to the complex interactions that occur between particles both through the bulk and the fluid interface [220]. For instance, Zang et al. [221] reported that the change in the wettability of the adsorbed nanoparticles allows tuning the packing of the structures formed at the fluid interface, and consequently the interfacial morphology, in agreement with studies by different authors [64,80]. In a different work, the increase of the hydrophobicity of particles was described as the driving force for to a transition from loose-packed to close-packed arrays of particles [61], which appears strongly correlated to the complex interplay of interactions occurring between particles both in the bulk and upon trapping at the fluid interface [220]. Bonales et al. [222] studied the self-assembly of polystyrene sulfate latex particles, with a broad range of diameters (in the range 1.0-5.7 μ m) at water/oil interfaces (in particular at water/octane interfaces). They found that the increase of the interfacial coverage drove the emergence of transitions between phases with different degree of ordering as was also found for nanoparticles [221]. It should be noted that the transitions between the different phases were not find independent of the particle dimensions, and only a shift of the critical density for the onset on a specific phase was observed with the change of the particle size. These finding were in accordance with the results obtained by Parolini et al [223] in a similar work. Fig. 10 reports a set of optical microscopy images corresponding to polystyrene sulfate latex particles microparticles of different sizes trapped at the water/octane interface, at different surface densities, together with the corresponding Fast Fourier Transform (FFT) of the images. The images obtained using an optical microscope shows that the increase of the density of the particles trapped at the fluid interface enhances the order within the monolayer, in such a way that should be considered as reminiscent to that what happens in traditional 3D systems. The increase of the interfacial order is also reflected in the FFT images (see insets in the optical microscope images). The fluid phases, both gas-like and liquid-like films, are characterized by a random distribution of points in the FFT images. The hexatic phase, and more clearly the solid one, shows the formation of well-defined hexagonal arrays of dots in the FFT images as the monolayer density increases. The authors obtained further information related to the organization of the particles at the fluid interface by calculating the structure factor. Thus, at low interfacial coverage, the gas-like character of the monolayer was evidenced from an initial increase of the value of the structural factor from 0 to 1, followed for a region of constant value. The increase of the interfacial coverage pushes the monolayers to the onset on the liquidlike phase. This presents a structure factor characterized for the presence of a few oscillations which undergo an exponential damping with the increase of the separation between particles. This may be considered the result of the weakening of the positional order with the increase of the separation between particles. Therefore, the gas-like and liquid-like monolayers are characterized by the absence of orientational and positional order. The order in hexagonal 2D solid is evidenced by the presence of a narrow and intense peaks followed by another set of peaks, which appears at the position expected for a hexagonal array. The hexagonal 2D arrays present positional and orientational orders. On the other side, the hexatic phase presents only orientational order, appearing as an intermediate state between a liquid-like system and a perfectly order solid-like one as is predicted for the KTHNY theory [224]. Bonales et al. [225] also explored the interfacial organization of mixtures monolayers composed of particles having different sizes. They found that independently of the size difference between the particles the inclusion of particles of different size promotes disorder, and the stoichiometry in the mixture determines the emergence of arrested glassy states or polycrystalline regions, leading to an interfacial organization which appears as intermediate between those what correspond to each individual set of particles. Rahman et al. [226] analyzed the possible correlations existing between the inter-particle interactions and the different phases emerging in particle-laden interfaces as the coverage increases. They found that the order at the interface is dependent on the strength of the interactions. Weakly repulsive or strongly attractive interactions promote the formation of disordered phases, whereas the emergence of a strong repulsion between the particles at the interface is associated with the formation of a highly ordered hexagonal array. The formation of the hexatic phase occurs when the repulsive and attractive forces are counter-balanced. The important role of the interactions in the organization of particles Fig. 10. Images and FFT images for charged polystyrene sulfate latex microparticles trapped at the water/octane interface. From left to right: microparticles with diameter of 2.9 μ m; microparticles with diameter of 5.7 μ m; microparticles with diameter of 1.6 μ m, and microparticles with diameter of 1.0 μ m. Adapted from Bonales et al. [222], Copyright (2011), with permission from American Chemical Society. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 18 at fluid interfaces was also revealed by the results obtained by Reynaert et al. [227]. They found that the modulation of the electrostatic and capillary interactions, by adding electrolyte or surfactant, may induce the aggregation or percolation of perfectly ordered monolayers formed by polystyrene sulfonate latex microparticles adsorbed at the water/ decane interface. Thus, under conditions characterized by strong capillary and/or hydrodynamics interactions, percolation can occur, resulting in the formation of networks formed by particles formin chains that span the boundaries of the interface [130]. The emergence of percolation in particle-laden interfaces offers a very interesting tool for modulating the mechanical resistance of the film [228]. 5.1.1.2. Interfacial rheology. The adsorption of particles to fluid interfaces is widely used in the design and optimization of new materials and technological processes [65,70,183,229], e.g., phase transfer catalysis, encapsulation, enhanced oil recovery or emulsification and foaming [230]. In particular, these systems can be introduced to control the thicknesses of films in coating flows [231,232], the dispersion of surface waves [30,233], the dynamics and thicknesses of spreading films [113,234] and the lifetime of foams and emulsions [235–237]. The latter occurs because the adsorbed particles induce an additional energetic barrier to the coalescence of droplets and bubbles, due to electrostatic or steric repulsions, which slow or stop the thinning of liquid films. [238]. These processes are also governed by the dynamics of the system, since the particles advected by film thinning introduce gradients (Marangoni stresses) that oppose film drainage [239]. On the other hand, particles trapped at fluid interfaces can induce excess surface viscosity, elasticity or viscoelasticity that delays or modifies the film thinning [235]. Therefore, the understanding of the mechanisms involved in the relaxation of particle-laden interfaces after a mechanical deformation is a problem with a marked multidisciplinary character [240–242]. In this framework, interfacial rheology explores the deformation and flow that occur at interfaces when mechanical perturbations are applied to them. The interfacial response of particle-laden fluid interfaces is characterized by the surface pressure, which is opposed to the surface tension and contributes to the in-plane deformations of the interfacial plane, dilations that cause changes in the material area, and shear stresses that induce changes in shape, generated by the coupling between the flows occurring at the interface and those of the bulk. On the other hand, under specific stress conditions, complex fluid interfaces exhibit out-ofplane deformations that push the monolayers or parts of the monolayers out of the interfacial plane (splaying or bending), inducing phenomena such as buckling of the monolayer, expulsion of material into the bulk or the formation of multilayers. Fig. 11 displays an idealized image of the different types of deformation that a particle-laden interface can undergo as result of the application of a mechanical stress. The study of the rheological response of a particle-loaded interface requires consideration of the role of thermodynamic and hydrodynamic interactions between the particles and the surrounding fluids. The solution to this complex problem is only straightforward when the mechanical response of the bulk fluids is decoupled from that of the interface, i.e., when the mechanical response of the fluid phases is negligible with respect to that corresponding to the interfacial layer [235,243]. If the above condition is fulfilled, the deformation of a particle-loaded fluid interface can be considered the result of two concurrent processes that govern the mechanical properties of the interface: (i) the change of the size and/or shape of the fluid interfaces, and (ii) the deformation of the interfacial layer. Hence, the energy input required for the interfacial deformation can be expressed as σ ij =γδij +Τij (57) where δ ij is the Kronecker delta and σ ij the interfacial stress tensor, that is comprised by two contributions: (i) the interfacial energy, which is related to the energetic cost of the existence of a fluid interface with a fixed area. This contribution also includes any adsorption/desorption phenomena, that modify the interfacial tension, and (ii) the Marangoni stresses resulting from the existence of spatial surface tension gradients. The second contribution, the so-called anisotropic tensor (Τ ij ), includes the energetic cost associated with the deformation of the particle layer [2,244]. 5.1.1.2.1. Interfacial dilational rheology. The trapping of particles at fluid interfaces does not influence only to the interfacial tension, but also leads to an increase of the resistance to compression that is characterized by the interfacial dilational viscoelastic modulus ε [27]. This magnitude provides information on changes in surface tension as a result of the modification of the area available for the distribution of the particles, which can be determined from the temporal evolution of the surface pressure δΠ(t) as result of the change of the interfacial area δA(t) upon the application of an uniaxial stress [245] δΠ(t) = Π(t)− Π0= ∂ Π ∂ AδA = − ε (t)u(t)(58) Here, u(t) and ε (t) are the temporal evolution of the compressional strain and dilational viscoelastic modulus, respectively, and Π(t) and Π 0 the temporal evolution of the surface pressure and the initial surface pressure, respectively. The time dependence of the viscoelastic dilational modulus is given by ε (t) = − A0( ∂ Π ∂ A)T (59) and that of the compression strain by u(t) = δA A0(60) Fig. 11. Idealized representation of the different types of deformation that can appear at particle-laden interfaces as result of the application of a mechanical stress. (a) Equilibrium particle-laden interface characterized by its values of surface tension γ and surface pressure Π. (b) Particle-laden interface subjected to dilational (left panel) and shear (right panel) deformations, characterized by surface dilational elasticity ε ’ and viscosity κ, and shear elasticity G’ and viscosity η S , respectively. (c) Particle-laden interfaces subjected to out-ofplane deformations (from top to bottom): buckling (characterized by the bending elasticity κ b ), expulsion of material to the bulk, and multilayer formation. Adapted from Garbin [26], Copyright (2019), with permission from Elsevier. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 19 Considering a fluid layer under equilibrium condition, the limit value of the dynamic modulus at zero frequency can be defined as the static modulus in terms of the Gibbs elasticity ε 0 as ε (t)→ ε 0=Γ( ∂ Π ∂ Γ)eq (61) where Γ=1/A is the interfacial concentration. For an oscillatory deformation of small-amplitude and characteristic frequency ω , the complex dilational viscoelastic modulus is defined as ε ( ω ) = ε ´ ( ω )+i ω κ( ω )(62) where the real part ε ’( ω ) is the storage modulus or interfacial dilational elasticity and the imaginary part ε ”( ω ) = ω κ( ω ) the loss modulus. Here, κ represents the surface dilational viscosity. The above definition of the viscoelastic interfacial dilational modulus considers that the stress associated with the interfacial deformation can change both the adsorption state of the particles and the interfacial structure. Under these conditions, the modification of the interfacial area can promote other different relaxation processes, with different characteristic timescales [36,229,246,247]. One of the first attempts to shed light on the response of particleladen fluid interfaces to dilational deformations was made by Miller et al. [247]. They provided a theoretical description for the relaxation mechanisms emerging in particle-laden interfaces upon the application of a dilational stress following a similar approach to that was previously reported for the description of the dilational rheology of proteins and proteins–surfactant systems [65,248]. This allows describing the dilational response of particle-laden interfaces in terms of the information provided by the adsorption isotherms. Despite the interest in obtaining models that combine equilibrium information with dynamic one, the above model was not further extended, mainly because of the difficulties associated with determining a true equilibrium isotherm. The particle wettability is probably the most important parameter for defining the trapping of particles at fluid interface, and hence the contact angle of the particles may modify decisively the performance of particle-laden interface against dilational stresses as was demonstrated by Safouane et al. [249]. They studied the rheological response against dilation of monolayers of fumed silica nanoparticles at the water/vapor interface using measurements of the damping of capillary waves in the frequency range 200–1000 Hz), and found the existence of important correlations between the interfacial morphology and the interfacial rheological response. The elastic component of the dilational viscoelastic modulus was found to increase with the particle hydrophobicity and the interfacial coverage, whereas the loss modulus remained almost. This leads to a situation in which the compressibility modulus of hydrophilic particles trapped at the water/vapor interface emerges close to 0, increasing its value up to values close to 200 mN/m with the increase of the hydrophobicity of the particles. This rigidification mediated for the particle hydrophobicity may be understood considering a densification of the interfacial layer coupled to the strengthening of interactions between the particles at the interface [250]. Kirby et al. [251] showed that the inter-particle interactions play a very important role on the control of the interfacial mechanical response. They found that the screening of the electrostatic repulsion between particles leads to a strong hysteresis on the dilational response of the particle-laden interface, which may be explained considering the formation of rigid incompressible films at the interface mediated for the aggregation of the particles. Safouane et al. [249] also found that the storage modulus appears always higher than the loss one, irrespectively of the particle hydrophobicity and the interfacial coverage. Zang et al. [252] enlarged the frequency range explored by Safouane et al. [249], including data corresponding to the low frequency range. This study provides information on the relaxation processes emerging at the interface as result of the application of the dilational stress. Thus, it was found that the reorganization of the particles at the interface leads to a relaxation process with a characteristic time of about 1000 s. The importance of this relaxation process was found to increase as the particle hydrophobicity decreases, which may be understood considering the reduction of the interfacial coverage, and hence the reduction of the steric hindrance associated with the reorganization of the particles at the interface which favors the motion of particles at the interface. The response against dilation of particle-laden interface formed by polymer particles presents some differences with the above discussed for silica nanoparticles as it was reported by Kobayashi and Kawaguchi [253]. These differences may be ascribed to the partial deformability of the polymer particles. Kobayashi and Kawaguchi [253] showed that the dilational response of latex particles at the water/vapor interface presented a mostly viscoelastic character, independently of the strain rate. Furthermore, the elastic and viscous dilational moduli undergo an increase with the interfacial coverage up to reach a critical value at a surface pressure of about 15 mN/m, and then both start to decrease steeply. This may be explained considering the emergence of out-ofplane deformations (buckling) of the monolayer upon the application of the dilational stress, which leads to a distortion of the quasi-2D organization of the particle-laden interface. Analyzing the frequency dependences of the viscoelastic moduli, it was possible to observe the emergence of a transition from a fluid-like behavior to a solid-one as the interfacial packing density increases, which agrees with the structural picture extracted from the studies by Bonales et al. [222]. Therefore, the dilational rheological response may be considered strongly dependent on the specific region of the phase diagram analyzed [222,253,254]. It is worth to stress that the rigidity of spread layers appears in most of the cases higher than that obtained for particle-laden interfaces with the same interfacial density obtained upon compression of the area. This may be the results of the emergence of non-equilibrium arrested states which add some additional relaxation process to the response of the particle-laden interface against dilational stresses [252]. The understanding of the interfacial organization-rheological response correlations in particle-laden interfaces were further explored by del Rio et al. [255], confirming the importance of the nature of the monolayer, i.e., its phase, on the control of the dilational viscoelastic modulus of particle-laden interface. Furthermore, their results confirmed the finding by Safouane et al. [249] in relation to the mainly elastic character of the monolayers, i.e., the storage modulus appears higher than the loss one. The storage modulus was found to increase with the interfacial coverage within the region of low surface pressure of the isotherm, whereas the loss modulus appears similar to that expected for the pristine water/vapor interface. This results from the contribution of the electrostatic repulsion between the particles trapped at the fluid interface. Furthermore, when the interfacial coverage is pushed beyond a threshold value, the storage modulus undergoes a sharp increase up to a value close to 350 mN/m, which can be explained considering the formation of a close-packed particle film at the interface, as was evidenced by using Brewster Angle Microscopy (BAM). It is worth mentioning that the screening of the electrostatic interaction, i.e., in presence of weak repulsive electrostatic interactions, the storage modulus can reach values close to 600 mN/m, which is the results of the minimization of the number of defects remaining in the close-packed monolayer [256]. It should be noted that emergence of out-of-plane deformations at the highest values of the surface pressure makes dropping both the storage and loss moduli in agreement with the results previously reported by Kobayashi and Kawaguchi [253]. On the other, the rheological response against dilation of latex monolayers can be considered qualitatively similar for particles adsorbed at both water/ vapor and water/oil interfaces [254,256]. The size of the particles is a very important parameter to be considered when the rheological response against dilational stresses of particle-laden interfaces is analyzed. Vella et al. [257] reported that the Young’s modulus of monolayers monodisperse particles with the same E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 20 chemical nature at fluid interfaces is inversely proportional to the size of the particles. It should be noted that the interfacial dilational flows induced in common laboratory experiments are smaller than those what are expected in industrial processes. This was demonstrated by Hilles et al. [258], who explored the dilational response of latex particles at the water/octane interface against oscillatory deformations with different deformation amplitudes and found that particle-laden interfaces present a very narrow region of low strain in which the interfacial response appears as linear. 5.1.1.2.2. Interfacial shear rheology. The existence of bulk flow can induce the emergence of interfacial shear deformations at particle-laden interface involving mass and momentum transport [216]. For shear deformations, the amplitude and time evolution are not coupled to any of the other interfacial modes [259]. This leads to a situation in which is possible to provide a definition of the shear elasticity corresponding to an in-plane shear deformation as a constant that defines the proportionality between the applied strain (u xy ) and the stress ( σ xy ). In a solid like-film, considering a Hookean-like behavior, the shear elasticity is given by σ xy =Gu xy . On the other side, the behavior of fluid-like layers is dominated by the viscous character of the layer, and the shear stress can be expressed as σ xy = η Sduxy dt (63) where du xy /dt and η S are the strain rate and the interfacial shear viscosity, respectively. In most of the systems the viscoelastic parameters (G, η S ) are higher when the system presents strong interactions between the particles, which can be explained by considering the flow induced in the surface elements as result of the energy required to overcome interfacial interactions [27]. For an oscillatory deformation, the complex shear modulus G * is defined as G*( ω ) = G ´ ( ω )+iG ´ ´ ( ω ) ≡ G'+i ωη S(64) with G’ and G” being the storage or shear elastic, and loss moduli, respectively. For experiments in which the amplitude of the oscillatory deformations at fixed frequency ω remains small, it is possible to define the shear viscosity as G”= ωη S . The study of the response of particle-laden fluid interfaces to shear has gained importance in recent years, especially because of the implication of the shear process in different aspects related to the stability of emulsions and foams [28,36,247]. This has stimulated significant research work attempting to unravel the correlations that arise between the interfacial micro-structure and the shear response of particle-laden fluid interfaces, with inter-particle interactions playing a key role in modulating these correlations [260]. It should be noted that the differences between the inter-particle interactions that arise when the particles are dispersed in bulk and at fluid interfaces give rise to important differences in the shearing behavior of 3D particles suspensions and their interfacial counterparts [261]. The seminal work on the characterization of particle-laden interfaces against shear stresses was done by Cicuta et al. [262]. They compared the behaviour of polystyrene latex particles (3 μ m of diameter) at the water/decane interface with that of β-lactoglobulin layers. While the interfacial rheological response of the particle monolayers presented a mainly viscous character (G′′ >G′), the β-lactoglobulin laden interface turned out to be mainly elastic. The difference can be attributed to the possibility that the protein undergoes deformation and compression processes when shear deformations are applied. At low coverage, the response against shear was found to be dominated by the viscous contribution, which can be considered reminiscent of what is expected for liquid-like films. On the other hand, it was found that the viscoelasticity of particle-laden interface undergoes a sharp increase for surface coverage above 75-80% as a result of particle jamming. This agrees qualitatively with the findings by Yu et al. [263] for monolayers of silica particles. In the limiting conditions, at higher coverages, the response is dominated by the elastic contribution, and the monolayers can be considered as solid-like films. It should be noted that the transition from viscous-like to solid-like behaviour can be modulated by changing the ionic strength, i.e., by modifying the inter-particle interactions. The increase of the ionic strength does not significantly modify the dependence of the viscoelastic moduli on the interfacial coverage. However, the transition from viscous to elastic-like behaviour occurs at lower values of the interfacial coverage as the ionic strength increases, which can be understood considering that the screening of the electrostatic repulsions between particles favours interfacial aggregation [263]. The role of interfacial coverage in the response of particle-laden fluid interfaces to shear stresses was also analysed by Imperiali et al. [264]. They showed that the reorganization ability of the particles plays a central role in controlling the interface response against shear, which qualitative agrees with the results of Barman and Christopher [265] for polystyrene latex at water/vapor interface. They used a double-walled interfacial shear rheometer that allowed characterization of the interfacial microstructure, and found a transition from shear thinning behaviour, characterized by the breakup of particle clusters, to one of yielding with increasing interfacial coverage. The origin of this transition was attributed to differences in the mechanism of viscous stress dissipation. The occurrence of yielding at interfacial coverages well below that corresponding to interfacial jamming, suggested that the solid-like behaviour can occur prior to reaching close-packing or jamming conditions. In addition, the authors found that monolayers with high interfacial coverage can undergo a shear-induced ordering phenomenon. Barman and Christopher [265] found that increasing interfacial coverage reduces the range in which the rheological response is linear, with the coverage dependence of the viscoelastic shear modulus being described in terms of a power law. The above studies were extended, leading to the conclusion that the viscoelastic response of particle-laden interface is governed by constrains on particle motion. These constrains were associated with the inter-particle capillarity attraction and the caging-effects emerging from the local micro-structure. Furthermore, Barman and Christopher [266] reported the important role of mesostructural organization in determining the elasticity and yield. They found that the formation of aligned domains of hexagonally packed particles gives rise to elastic-like particle films, and that decreasing domain size leads to interfacial flows and viscous-like behaviour. The study of the effect of the interfacial packing on the response of particle-laden interfaces against shear stresses was extended by Reynaert et al. [267]. They provided further evidence of the influence of inter-particle interactions in modulating the interfacial rheological response, showing that particle aggregation leads to an interfacial shear response reminiscent of that found in bulk counterparts. This agrees qualitatively with the results obtained by Wijmans and Dickinson [268] using Brownian dynamics simulations. The role of the inter-particle interactions in the response of particle-laden interfaces to shear stresses was also studied by Beltramo et al. [247]. They found that the existence of strong lateral interactions between the particles promotes the emergence of interfacial yield stress, and that the elastic modulus and the yield stress increase tenfold when the interfacial coverage increases from 0.47 to 0.88. For interfacial coverages below 0.64 the viscoelastic modulus was almost negligible, while above that threshold the viscoelastic modulus of the particle films increase. For interfacial coverages in the range 0-75-0.80 the viscoelastic modulus reached a plateau, which was attributed to the emergence of interfacial jamming. Muntz and Thijssen [269] have recently delved into the correlations between the structure of particle-laden interfaces and their rheological behaviour. For this purpose, they studied poly(methyl metacrylate) particles at water/dodecane interfaces using a shear rheometer coupled to a confocal microscope. The results obtained showed that, at low surface coverage, the particle-laden interface behaves as a twoE. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 21 dimensional Newtonian fluid, which undergoes aggregation when a shear stress above a threshold value is applied. The increase in interfacial coverage leads to an interfacial behaviour dominated by the elastic contribution, and above the yield stress, the interface undergoes plastic deformation. As was mentioned above, particle roughness plays a very critical role in the entrapment of particles at fluid interfaces and thus in their interfacial organization. Hence, it is necessary to consider its impact on the response of particle-laden interface upon the application of shear stresses. The role of the particle roughness in the shear response of the particle-laden interfaces is closely correlated to the interfacial coverage [270], which can be explained in terms of inter-particle friction [271]. At low interfacial coverage, the interfacial shear viscosity of the particleladen interfaces decreases as the surface roughness increases, while the response is the opposite as jamming approaches [272]. This behaviour can be understood considering the trapping of the particles at metastable positions as result of the contact line pinning [273]. The emergence of contact line pinning may lead to a situation in which particles behave very differently to that what was expected considering their wettability, i.e., hydrophilic particles may behave upon trapping at fluid interfaces as hydrophobic ones, and the latter as hydrophilic ones. This offers the possibility for stabilizing both water-inoil and oil-in-water by using a single type of particles, without needing any change of its wettability. Therefore, it is clear that the shear response of particle-laden interfaces appears strongly influenced by the hydrophilic-lipophilic balance of the particles. Safoune et al. [249] confirmed such picture. They studied monolayers of fumed silica particles having different hydrophobicity degrees, and found that the increase of the hydophobicity of particles for a similar value of the interfacial coverage leads to monolayers with higher values of the shear elastic and viscous moduli. The particle monolayers were found to present a behavior governed mainly by the elastic contribution for particles with a low hydrophobicity degree, becoming purely viscous when the hydrophobicity degree is high. Thus, a cross-over between elastic and viscous films was found, i.e., a gel point (G’ =G”), for particles with an intermediate wettability which are trapped at the fluid interface with a contact angle around 90◦. The above studies were extended by Zang et al. [90,252,274], who explored the effect of the particle hydrophobicity on the response against shear stresses. They studied monolayers of fumed silica particles at the water/vapor interface, and did not find any dependence of the elastic modulus on the strain amplitude when the latter was small. Furthermore, an elastic modulus with values ten times higher than the viscous one was found. On the other side, Zang et al. [90,252,274] reported the possible appearance of a melting transition for particle monolayers when the strain amplitude overcomes a threshold value (yield stress). Under such conditions, the loss modulus reaches its maximum value, whereas the storage modulus drops. The response of the particle-laden fluid interface to the application of small deformations of low frequency evidences a viscous character, whereas for deformations of high frequency the behavior becomes mainly elastic. Furthermore, a quasi-linear dependence of the relaxation time on the shear rate was found. This may be considered analogous to that what is found in 3D softs solids, and may be explained considering the reduction of the characteristic time of the structural relaxation that occurs because of the increase of the strainrate amplitude [275], in agreement with the results reported by Vandebril et al. [276]. A further important aspect to be considered, for the response of particle-laden fluid interfaces to the application of shear stresses is related to the analysis of its time evolution. For elucidating this aspect, Krishnaswamy et al. [277] studied, by using shear rheology, the adsorption kinetics of silver nanoparticles (in the range 10-50 nm) at toluene/water interfaces by using shear rheology, and found an increase of both the storage and loss moduli with time. This is due to the densification of the monolayer during the adsorption process. Furthermore, upon interfacial equilibration it was found that the particle-laden interface has a behavior that presents some reminiscence to that what may be expected for a 2D glassy material, with the shear response depending strongly on the stain amplitude. On the other side, the use of strain sweep measurements evidenced a shear thickening behavior of G” upon deformations with a large strain amplitude, whereas no dependences of G’ on the strain amplitude were reported up to the shear thickening point. Furthermore, it was found that the shear thickening may be described using a power-law in which the exponents for describing the storage and loss moduli assumed values of 2 and 1, respectively. The behavior found for silver nanoparticles may be considered very different to that for gold nanoparticles at the water/ vapor interface [278]. The latter shows a behavior reminiscent of a gellike systems undergoing strain induced softening. Furthermore, for gold nanoparticles the rheological response does not present any dependence on the applied stain for values below a threshold corresponding to 0.1%, and then the storage modulus drops. On the other side, the viscoelastic moduli can be described as a function of the interfacial coverage using a power law with an exponent around 0.65. This seems a reminiscence from that what is found in percolating systems [246]. 5.1.1.2.3. Out-of-plane deformation. The deformation of particleladen fluid interfaces upon the application of large compressional stresses may induce the emergence of elastic instabilities in the monolayer, which leads to out-of-plane deformations of the quasi-2D particle layer [11,26]. This may be explained considering the emergence of different types of phenomena in particle-laden interfaces upon compression. An initial compression of the particle-laden fluid interface leads to the formation of close-packed films, which can undergo in and out-of-plane deformation upon further compression. This results in monolayer buckling, expulsion of material from the interface or multilayer multilayer formation [279]. The buckling in particle-laden interfaces occurs when the surface pressure is high enough to cause a dropping of the effective interfacial tension down to a quasi-null value. However, under specific conditions the expulsion of particles from the interfacial layer may be favored with respect to the buckling. This may be rationalized considering the differences existing between the trapping energy ΔE p , and the mechanical work required for compressing the interface dW=ΠdA. This allows one to consider that the expulsion of particles from the interface is only possible when the work associated with the compression exceeds to the trapping energy. Therefore, it is possible to define a boundary condition which defines the expulsion of particles as W=ΔE p . This provides a definition for the force balance associated with the particle expulsion as [280] Π=γ12(1±cosθ)2(65) It should be stressed that the above expression does not include the role of the interfacial interactions, which may modify the deformation profile. Thus, the presence of attractive inter-particle interactions may induce the formation of elastic solid-like films, in which the emergence of particle expulsion upon compression is not possible [93]. Leahy et al. [281] found that the compression of monolayers formed for gold nanoparticles beyond the close packing leads to the folding of the monolayer followed by the formation of multilayers. The wavelength of the wrinkles allows obtaining information related to the bending modulus of the particle monolayers and multilayers by applying the elasticity theory. The emergence of wrinkles on particle-laden interfaces was ascribed by Vella et al. [257] to the formation of particle clusters at the fluid interface, which allows considering that the compression of particle-laden interfaces beyond the collapse leads to an elastic behavior characterized by a buckling length defined as λ= π [4 3(1−ϑ)(1−vP)]1/4  2Rlc √(66) where ν P represents the Poisson ratio, which provides information about the deformation of the interface following the direction perpendicular to E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 22 the direction of application of the stress. In this particular case, the Poisson ratio evaluates the ability of the interface for undergoing out-ofplane deformations. It should be noted that the above model provides a good description of the interfacial behavior for particles with diameters in the micrometer range (above 1 μ m). However, for smaller particles, it provides an underestimation of the buckling wavelength, which may be the result of a high bending elasticity, κ b [282]. In the case of monolayers of anisotropic particles, the compressive stress can be released by their interfacial rearrangements, which may induce a flipping transition upon compression. Further compression of bucked particle-laden interfaces may result in the expulsion of some particles to one of the adjacent fluid phases [283]. Most of the phenomena occurring at particle-laden interfaces when the monolayer is compressed beyond the collapse may be modulated by changing the particle contact angle [284]. This may be understood considering the important contribution of the inter-particle interaction on the control of the interfacial microstructure and rheological response. Thus, hydrophilic particles lead to the formation of fluid-like particleladen interfaces which may undergo an irreversible collapse with a noticeable expulsion of particles from the interface to the bulk. On the other side, solid-like films formed by hydrophobic particles present a high compressional elasticity due to the strength of the cohesive interactions between particles. This commonly leads to the emergence of a reversible collapse through the formation of wrinkles and folds. This can be understood considering the arrest of the mechanisms guiding the expulsion of particles from the monolayer to the bulk fluids as result of inter-particle interactions with attractive origin. 5.1.2. Anisotropic particles at fluid interfaces The above discussion has been focused on the analysis of the behavior of spherical or nearly spherical particles trapped at fluid interfaces. However, the adsorption of particles may be modulated by the chemical and geometrical characteristics of the particles [285,286], which has stimulated the interest for studying the interfacial behavior of particles with anisotropy in their shape or in their chemistry [287,288]. 5.1.2.1. Chemically homogeneous non-spherical particles. The shape anisotropy of particles presents a key role in the attachment of particles to the fluid interface. This is clear considering that, whereas for spherical particles the position in relation to the interfacial plane can be defined exclusively by the contact angle, the analysis of the trapping of nonspherical particles, including ellipsoids, dumbbells or cylinders, need to consider both the shape and wettability of the particles [289,290]. Particles with a relatively high degree of anisotropy, i.e., particles with a large aspect ratio, adsorb commonly at fluid interfaces orienting their major axes parallel to the fluid interface. Fig. 12 is a sketch showing the orientation of particles with different aspect ratios (S I ) trapped at fluid interface. It should be noted that the aspect ratio provides a relationship between the two main radiuses of the anisotropic particles. The existence of different possible configurations for the trapping of a specific type of particles at a fluid interface influences the balance of interfacial inter-particle interactions, which in turn modifies the assembly of particles at the interface, and consequently the properties of the particle layers. On the other side, the ability of particles with anisotropic shape to remain trapped at the fluid interface is strongly dependent on their geometries. A critical aspect ratio exists beyond which the adsorption of anisotropic particles becomes unstable. The emergence of adsorption instabilities results from the high values of the line tension [10]. The correlations between the line tension and the aspect ratio have driven important research efforts trying to optimize the adsorption of different anisotropic particles, e.g., carbon nanotubes, at fluid interfaces. Thus, for particles with similar volume, the trapping energy changes according to the following order disks>rods>spheres. On other side, the maximum differences of the trapping energy in relation to that what are found for spherical particles can be found at the extreme wetting conditions, i.e., close to 0 and 180 degrees [291]. For cases in which the wetting conditions are fulfilled, ensuring the attachment of chemically homogeneous but geometrically anisotropic particles to the fluid interface, it is possible to find a deformation of the fluid interface in the vicinity of the particles, that leads to attractive capillary interactions that overcome the repulsive electrostatic contributions [188]. Furthermore, the short-range interactions, e.g., van der Waals or steric, are also strongly modified as result of the shape anisotropy of particles [10]. The impact of the shape anisotropy on the assembly was evidenced from the work by Loudet et al. [187]. They explored the assembly of micron-sized particles with ellipsoidal shape at a fluid interface, and found that the asymmetric distribution of the interactions within the interface leads to the association of the particles in open branched aggregates of particles which tends to be oriented forming particle chains as a result of the directionality of the interactions [287]. This behaviour is very different to that what is found for spherical colloids trapped at fluid interfaces which form well-defined close-packed film structures [222]. The differences on the interfacial assembly of particles resulting from the specific particle shape should be ascribed to the capillary interactions. Thus, non-spherical particles interact through long-range capillary interactions with quadrupolar origin, which exceed by several times the thermal energy (k B T), leading to a complex interfacial assembly [10,187,287,288]. In particular for ellipsoidal particles trapped at the water/vapour interface, the quadrupolar interface deformation characterized by depression and ascension of the interface around the tip and side regions, respectively lead to the assembly of side-to-side or tip-to-tip structures as was reported by Loudet et al. [309]. The quadrupolar deformation of the interface was also reported for the adsorption of cylindrical particles at both water/vapour and water/oil interfaces [188,292]. Thus, for cylinder-like particles trapped at fluid interfaces, the interface deflects upward on the planar end surface and downward around the sides. The prominent interfacial deformation on the end surfaces leads to the formation of linear chain-like structures. The above differences on the organization of anisotropic particles at fluid interfaces depending on their shape are due to the very different energetic landscapes [292]. Thus, the side-to-side chains obtained from the assembly of ellipsoidal particles present a certain degree of flexibility, whereas the end-to-end configurations obtained from the assembly of cylindrical particles present a high rigidity. This confirms the important directional character of the capillary interactions in monolayers of anisotropic particles at fluid interfaces. The ability for selforganizing of anisotropic particles can lead to a rich interfacial phase behaviour, including the formation of isotropic, 2D nematic, 2D smectic and 3D nematic phases, as was evidenced by Kim et al. [293] for BaCrO 4 nanorods and by Hern´ andez-L´ opez et al. [294] for carbon nanotubes. The differences in the assembly induced by the anisotropic shape also affects the interfacial response against mechanical stresses. Madivala et al. [289] explored the interfacial behavior of ellipsoidal particles Fig. 12. Sketch representing the adsorption of different chemically homogenous particles with different degree of shape anisotropy trapped at fluid interfaces. Reprinted from Park and Lee [285], Copyright (2014), with permission from Springer-Nature. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 23 made of polystyrene at water/decane and water/vapor interfaces, and found that the assembly of the particles at the fluid interfaces may be tuned by changing the electrostatic interactions within the systems. This leads to the formation of arrangements of individual particles coexisting with linear aggregates at water/decane interfaces, and flower-like aggregates at water/vapor one. The different organization of the particles depending on the nature of the interface leads to very different responses upon the application of shear stresses. This agrees with the general picture that correlates the interfacial packing and the mechanical response of the particle-laden fluid interfaces. In particular, ellipsoidal particles at the water/decane interface behave as an elastic system, with its viscoelastic modulus increasing with the interfacial coverage. Such increase was found to be governed by a strong increase of the elastic component of the shear modulus. It should be noted that the importance of the elastic component on the behavior of ellipsoidal particles is just the opposite situation that what reported by Cicuta et al. [262] for spherical particles, which may be due to the existence of very different relaxation mechanisms [283]. Furthermore, on the contrary to that what was found for spherical particles, ellipsoidal particles trapped at a fluid interface can undergo buckling processes when the interfacial coverage is relatively high. Therefore, it is possible to assume that the differences on the rheological response due to the shape anisotropy of particles may be understood considering the broad range of interfacial packings that can appear for non-spherical particles. This is strongly correlated to the specific degree of anisotropy of the considered particles, which modifies the balance of interfacial interactions, and hence changes the aggregation pattern and interfacial rheology of the particle-laden interface. The effect of the morphology of the particles on the response of the interface upon the application of shear stresses was extended by Brown et al. [271]. They studied particles with different aspects ratios, and found a shear thickening phenomenon independent of the anisotropy degree of the particles. However, the anisotropy becomes a critical parameter for controlling the jamming of the particles at the fluid interface. Thus, the increase of the degree of the anisotropy of the particles reduces the threshold value of the coverage for the onset of the jamming region. On the other side, it has been reported that the asymmetry of the particles may induce the formation of kinetically trapped films, which modifies the shear flows at the interface [295,296]. 5.1.2.2. Chemically anisotropic particles. The interest in exploiting chemically anisotropic particles for stabilizing interfaces was originated from the Nobel Lecture of Pierre-Gilles de Gennes, in which the use of colloidal particles with two separated regions with different chemical nature, the so-called Janus particles, was proposed for replacing molecular surfactants [297]. However, the advances in the synthetic routes used for the fabrication of colloidal particles has allowed to introduce other types of chemical anisotropic particles, e.g., dumbbells, patchy colloids or shape anisotropic Janus particles [118]. The adsorption of spherical Janus particles tries to ensure the energy minimization condition. This leads to a situation in which particles with two symmetric domains of different wettability adsorb to the fluid interface in such a way that each domain is paired with its preferred fluid phase, i.e., the phase of higher affinity, and their trapping occurs with the Janus boundary pinned at the interface. This means that particles having a non-polar domain and a polar one will adsorb to water/ oil interfaces with the non-polar and polar regions placed in contact with the oil and the aqueous phases, respectively. This conformation leads to the largest decrease of the interfacial energy [298]. Furthermore, the adsorption of Janus colloids in which the domains of different wettability are not symmetric, i.e., present different size also adopts the configuration at the fluid interface that allows minimizing the interfacial energy, which may not correspond to the pinning of the Janus boundary at the interface [299]. It should be stressed that the trapping energies for Janus colloids at fluid interface can be several times higher (up to 3-fold higher) than that corresponding to homogeneous particles [300]. According to the above discussion, the equilibrium position of Janus particles at fluid interfaces may be predicted using similar approach to that used above for defining the contact angle (see Section 2.4) [301]. However, the dual chemistry of Janus particles makes necessary to define two contact angles, the first one in relation to the polar phase θ P and the second one in relation to the non-polar phase θ A [299]. This allows defining a degree of amphiphilicity for a Janus particle as Δθ = (θ A −θ P )/2. Thus, it is possible to define the Janus boundary using the angle α , which is placed at 0 and 180 degrees for polar and non-polar particles, respectively, whereas for particles with two patches of the same size assumes a value of 90◦[302]. Therefore, it is possible to modify the amphiphilicity of Janus particles by changing the wettability of each patch, i.e., modifying θ P and θ A , or the value of the Janus boundary α . Thus, assuming the absence of rotation of Janus particles at the interface, the equilibrium contact angle may lead to up to three different equilibrium positions defined for their equilibrium contact angle θ E . Fig. 13a-c reports different situations for the equilibrium positions of different Janus particles in relation to their chemically homogeneous counterparts [301,302]. The above discussion clarifies the orientation of spherical Janus particles upon the adsorption to fluid interfaces. However, the situation is less clear when Janus particles with anisotropic shapes (ellipsoids, dumbbells or cylinders) are considered in which the anisotropy provides extra degrees of freedom for modifying the orientation of the particles upon the adsorption at the fluid interface, which influences significantly the interaction between particles at the interface [303]. It has been reported that Janus particles with large aspect ratios adsorb preferentially in a tilted configuration, i.e., with the Janus boundary parallel to the interface. However, the increase of the wettability differences between the two domains of the Janus particle may induce the adsorption in an upright orientation to maximize the contact between each region and its preferred fluid phase. On the other hand, for particles with domains of similar wettability, it is possible to find the coexistence of upright and tilted orientations, which may be considered as a metastable orientation at a secondary energy minimum [303]. Therefore, the rotational freedom of Janus particles emerges as an essential aspect governing their stability at fluid interface [286,298,302]. This was confirmed by Bon and Cheung [304] using Monte Carlo simulation. They reported that neglecting the rotational freedom of Janus particles at the interface underestimates the trapping energy. Furthermore, different studies demonstrated the role of the amphiphilicity of the Janus particles on their orientation at fluid interfaces [190,298]. The adsorption of dumbbells is more straightforward because the narrow neck hinders the secondary energy minimum, which limits the possibility to absorb in the tilted configuration [303]. The existence of this preferred direction for the adsorption was evidenced by the contact angle measurements by Isa et al. [305]. The situation for the adsorption of patchy colloids is analogous to that what appears for dumbbells, with their adsorption occurring in a preferential orientation defined for the opening angle of the patches [199,306]. Fig. 13d shows an example of the different orientations that can emerges for Janus particles for which a combination of shape and chemical anisotropies exists. The above discussion has evidenced the importance of anisotropies on determining the equilibrium position of particles at fluid interfaces. However, a more detailed analysis allows evidencing that the equilibrium position of Janus particles is defined for the balance between shearand capillarity induced torques. The former emerges from the shear forces occurring at the particle surface, wherear the latter are a result of the preferential wetting of the particles for one of the fluid, and the equilibrium orientation of Janus particles is given for the point in which the net torque assumes a null value [118]. 5.1.2.2.1. Inter-particle interactions. The contact angle pinning of Janus particles trapped at fluid interfaces leads to irregular deformations of the interface which induce attractive interactions between particles [298]. This is because inter-particle interactions are governed by the minimization of the interfacial energy, which requires a reduction E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 24 of the contact area between the two fluids. Thus, the reduction of the inter-particle distance between particles placed at the interface with different orientations leads to the overlapping of the interfacial distortions, which leads to strong capillary interactions. On the other side, for particles having similar orientation angles, the interfacial deformations do not overlap and hence the interfacial energy increases as particles are closer. This leads to strong repulsions between particles, which contrast with the situation for particles with opposite orientation angles. As a consequence, the approaching of particles with opposite orientation angles trongly decreases the interfacial energy, thus inducing the formation of capillary bridges as result of the strong attractive interactions between particles [290]. The above picture may be also applied for the description of the inter-particle interactions of patchy particles trapped at fluid interfaces [306]. Thus, for hydrophilic particles containing hydrophobic patches, a capillary attraction may be expected upon approaching. However, the situation changes when the patches of the approaching particles present different amphiphilicity. In this case, the menisci of the particles appear deflected in opposite direction which is translated in inter-particle repulsion. 5.1.2.2.2. Interfacial rheology 5.1.2.2.2.1. Dilational rheology The response against dilational stresses of Janus particles trapped at fluid interface has been explored for different types of Janus colloids, and many times the results have been put in comparison with those what were found for chemically homogeneous particles. Kadam et al. [307] studied the response of different biofunctionalized silica Janus nanoparticles at the water/vapor interface, and found that the elasticity increases in relation to monolayers of bare silica, with the elastic modulus appearing for monolayers of some specific Janus particles up to six-fold higher than that what was found for bare silica. The increase of the elastic contribution of monolayers of Janus particles in relation to monolayers of non-Janus counterparts was confirmed by Fern´ andezRodríguez et al. [308] for monolayers of polymeric Janus particles. They studied the compressional elasticity of such particles at both water/ vapour and water/decane interfaces, and found that Janus particles leads to monolayers with higher compressional elasticity than those of homogeneous particles, which may be ascribed to the ability of Janus particles to form particle networks at the interface. Furthermore, an increase of the dilational storage and loss moduli with the increase of the interfacial coverage was reported. Razavi et al. [302] expanded the above studies in relation to the interfacial dilational response using Janus particles of different degree of amphiphilicity. They found that the increase of the amphiphilicity of the Janus particles leads to an increase of their ability for remaining trapped at the water/vapour interface, and enhances the elasticity of the particle-laden interface. Furthermore, it was found that monolayers of highly amphiphilic Janus particles undergo a reversible collapse through interfacial bucking with a reduced number of particles expelled to the subphase after successive compression/expansion cycles. On the other side particles with low amphiphilicity undergo an irreversible collapse upon compression. This difference on the rheological response may be ascribed to the differences on the orientation of particles at the fluid interface. Thus, particles with low amphiphilicity appear trapped at the fluid interface with a random orientation, whereas those with high amphiphilicity are placed at the interface in such a way that they have paired their different regions with the more favourable fluid. 5.1.2.2.2.2. Shear rheology The study of the response of Janus particles against shear stresses is currently a very active research field [29]. Yin et al. [309] explored the rheological response of silica-based Janus nanosheets at water/oil interfaces by means of frequency sweep experiments performed at small strain amplitude (around 1%), and found a strong increase of the interfacial viscosity up to 1000 mN∙s∙m -1 . Furthermore, the increase of the shear rate up to 2.5 rad/s results in a reduction of the interfacial viscosity followed by a plateau region, which may be rationalized in terms of a disruption of the interfacial network. Rezvantalab et al. [310] explored the response of interfacial layers of Janus particles at fluid interfaces against shearing by calculations using a multicomponent Lattice-Boltzmann method, which allows the study of Fig. 13. Equilibrium position of Janus particles at fluid interfaces. (a) Equilibrium contact angle defined for the contact angle of the non-polar phase. (b) Equilibrium contact angle defined for the Janus boundary. (c) Equilibrium contact angle defined for the contact angle of the polar phase. (d) Impact of shape and chemical anisotropies. Reprinted from Correia et al. [29], with permission from MDPI under Attribution License Creative Common 4.0 (2021). E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 25 the interfacial ordering induced upon shearing for monolayers of different sizes and intermediate interfacial coverage (in the range 3265% of the total interfacial area). They found that the capillary induced interactions emerging from the overlapping of the interfacial deformations induced by the shear flow induced the formation of particle chains aligned in the direction normal to the shear deformation, independently of the characteristic of the particle-laden interface, i.e., the type of particles and the interfacial coverage. The chain-like structures remain intact upon the removal of the flow field, with the only modification being associated with the rotation of the particle for adopting an upright orientation. Rezvantalab et al. [311] extended their studies for understanding the combined role of chemical and shape anisotropies in the behaviour of Janus particles at fluid interfaces against shear stresses. They found the existence of two rotational dynamics (smooth tilt and tumbling), which depends on the particle shape, degree of amphiphilicity and shear rate. Despite the existence of two type of dynamics, all the particles reach a steady-state orientation at the interface which depends on an intricate balance between torques induced by shear and capillarity. Therefore, it is possible modulate the orientation of Janus particles at fluid interface by controlling the shear rate and the surface chemistry of the particles. Further studies on the shear induced assembly of Janus particles at fluid interfaces were performed by Paiva et al. [312]. They found that anisotropic Janus particles exhibit tumbling behaviour upon the application of shear stresses that allows overcoming the capillary torques. This leads to the formation of a Janus antiparallel configuration or stacked aggregate sheets. Wang et al. [313] studied the correlation between the interfacial morphology and the shear response of Janus particles of poly(vinylidene fluoride)/poly(L-lactide) at fluid interface, and found that the obtained films present a high elasticity (several times that corresponding to homogeneous particles) and low interfacial tension. This solid-like behaviour was ascribed to the formation of ordered arrays of Janus particles at the fluid interface. 5.2. Soft particles A paradigm of soft colloidal particles are those made up by microgels (i.e., chemically cross-linked polymers forming networks of colloidal size) that can undergo swelling in liquid environments. The degree of swelling depends on the density of cross-linking and the solvent quality [314]. Microgel particles have properties that can be considered intermediate between those corresponding to colloidal particles, and those that are expected for polymer chains [35,314]. The most common microgel particles are those obtained from poly (N-isopropyl acrylamide) (PNIPAM), a thermosensitive polymer that undergo a reversible swelling/shrinking transition at a temperature around to the physiological temperature of the human body [315,316]. In some cases, it is possible to add some co-monomers that change their ionization state by pH changes, e.g., acrylic or methacrylic acid, which allows obtaining pH responsive microgels [317]. The dual character of the microgels plays a very important role in their trapping at fluid interface. On one side, they are particles and hence they remain trapped at the fluid interface very strongly. On the other side, they present a polymer character which favors their attachment from dispersion to the fluid interfaces [35]. Therefore, the softness is not a limitation to the adsorption of particles at fluid interface. However, it introduces a competition between the bulk elasticity and surface tension, which leads to the particle stretching at the fluid interface. This leads to a change of the energetic landscape associated with the trapping of the particles at the interface, which is characterized by an increase of the trapping energy [75,182,318]. Furthermore, the deformability of the particles enhances the contribution of the capillary interactions and reduces that corresponding to the direct interactions [319]. This results in the formation of interfacial mesostructures, which can be exploited for the stabilization of dispersed systems, mainly emulsions [320–323]. The enhancement of the contribution of the capillary interactions to the global balance of the interface may be understood considering that the capillary interactions are related to the deformation of the interface upon particle adsorption. Therefore, the modification of the wetting properties of soft particles as result of the change of their conformation may induce very different contribution of the capillary forces in such a way that depends on the specific size of the particles [324]. This leads to a degree of propagation of the particle in each phase depending on the quality as solvent of the specific fluid, resulting in very different deformation profiles of the fluid interface. In fact, for small particles the role of the capillary forces can be considered almost negligible, and the interfacial behavior is reminiscent from that expected for monolayers of polydisperse soft disks, whereas monolayers of big particles undergo strong attractive capillary forces, appearing clustering between the particles from the lowest values of the interfacial coverage. 5.2.1. Trapping of soft particles at fluid interfaces The trapping of soft particles at fluid interfaces, both water/vapor and water/oil, is aimed to reduce the interfacial energy between the two fluids, similarly to that what happens for hard particles [325]. However, the softness of microgels allows its deformation upon adsorption at interfaces, which determines two main aspects of the interfacial organization of the microgels at the interface: (i) the surface activity of most microgels induce that in contact with the interface, microgels can appear stretched out at the interface to maximize the interfacial coverage, and (ii) microgels protrudes into the two fluid phases according to their respective affinities. The latter results in an asymmetric distribution of the microgels between the two phases. It should be noted that the extension of the in-plane deformation and the asymmetry across the interface depends on the specific structure of the microgel and the nature of the fluid phases [326]. Different studies have evidenced that microgels at interfaces between a polar fluid and a non-polar one adopt “fried-egg” morphologies. These result from the lower cross-linking of the external region of the microgel (corona) in relation to the inner one (core), which determines a higher deformability [143,318,323,327]. It should be stressed that the bulk elasticity of the microgels emerges as a restriction to their deformation upon adsorption at the fluid interface. This may be understood considering the balance between two contributions: (i) reduction of the interfacial energy between two immiscible fluids, and (ii) the elastrocapillary length L EC =γ S /E defined as the ratio between the surface tension of the solid γ S and its Young’s modulus E [318]. Thus, particles with radius larger than the elastocapillary length can be considered effectively as non-deformable particles, and only slight deformations close to the contact line may be expected. On the other side, for particles with radius smaller than the elastocapillary length, particles behave almost as a liquid. It may be expected that the deformation of soft particles upon adsorption at a fluid interface can appear strongly dependent on the interfacial coverage. At low coverage, the adsorption of the particles occurs with the particles adopting a stretched-out conformation at the interface. This may be understood considering that such conformation ensures the maximization of the fraction of interfacial area occupied by the particles. This introduces a favorable entropic contribution, allowing overcoming the energy penalty associated with the elastic deformation of the particle. Under the above conditions, the major portion of the particles remains immersed in the polar phase, and only a very small fraction appears protruding to the non-polar phase [328]. On the other side, the increase of the interfacial coverage leads to a situation in which the particles at the interface start to touch each other. This drives the collapse of particles at the interface, reducing the contribution of the elastic energy [35]. The above picture can be interpreted considering that at low coverage, microgels can appear forming either monolayers resembling a liquid-like state or clusters mediated through capillary interactions [327,329]. On the other side, the increase of the coverage induces a crystallization of the microgels forming a hexagonal array E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 32 crystallites [383]. In all these processes, the applied field plays the role of an effective inverse temperature. If the applied field is oriented parallel to the interface, the induced magnetic moments are nearly coplanar with the confining surface and the particles form trapped structures aligned along the imposed direction, with complexity depending on the applied field strength and monolayer concentration [385]. At intermediate particle density and field amplitude, the equilibrium state consists of linear aggregates of one particle thickness. The emerging interactions between the induced linear aggregates depend on the distance between them, but also on the chain lengths and the relative displacement along the chain direction. However, in most possible configurations, the magnetostatic potential between two parallel chains presents a minimum attraction along the lateral direction at short range, when the two chains are almost in contact, followed by an energy barrier and a repulsion region at long range. The energetic barrier is located at a characteristic length, the escape distance, which increases with chain length [386]. As the area fraction increases, the chains are closer together, so some of them are forced together by a zipper mechanism and form ordered hexagonal bundles of zippered chains, in which the particles of adjacent chains are arranged out of register by a distance of radius [385]. Tilting the applied field with respect to the confining surface can transform the hexagonal order of the floating crystals into metastable structures with other planar crystal symmetries, such as oblique, centered-rectangular, rectangular and square lattices [383], and promote the unzipping of chains laterally aggregated [211]. The unzipping propagation is consistent with an Arrhenius process, in which one of the constituting particles jumps over an energy barrier, before entraining adjacent particles in the chain. Throughout this process, the chains maintain their integrity as they continue separating along the perpendicular direction. The subsequent increase in the slope of the applied field results in the partial fragmentation of the chains, the gradual separation of the monomers, and finally the abrupt colloidal explosion. In this system, the different dismantling mechanisms are reversible and are mainly governed by the tilt angle, but are also strongly influenced by thermal energy, particle contact angle and local magnetization [387]. When the number of adsorbed particles is small, then the particles form finite aggregates, that can be used in the study of border and confinement effects [209,218]. Due to the super-paramagnetic character of the components, all the described structures are stable only under the presence of the external field, while immediately disintegrate due to thermal fluctuations once the applied field is switched off. 7.1.1.3.2. Dynamic self-assembly of adsorbed magnetic particles. Floating magnetic particles have been widely used in the bottom-up fabrication of novel and disparate dynamic self-assemblies, strongly determined by the size and magnetic character of the particles, the geometry and dynamics of the applied field, and the rheological properties of the comprising fluids. In pioneering work, Grzybowski et al. used millimeter-sized magnetic disks adsorbed on a liquid-air interface, and rotating synchronously with the applied field, to study the formation of various dynamic structures [214]. The latter, resulting from the equilibrium between hydrodynamic repulsion and averaged magnetic attraction, were strongly determined by the geometry and chirality of the spinners [388]. In a different work, rotating ferromagnetic microdiscs with cosinusoidal edge-height profiles, confined by an externally applied magnetic potential and subjected to a rapidly rotating field, were assembled and disassembled in different configurations dictated by the directionality of capillary interactions, which were ultimately determined by the profile of the particles and the rotational speed of the applied field [389]. Snezhko et al. reported snake-like structures formed by antiferromagnetically aligned segments, themselves composed of ferromagnetic microfloaters. These objects self-assemble dynamically, upon application of an oscillating field perpendicular to the air/water interface, through coupling between surface waves generated at the fluid interface and magnetic interactions [365]. At the liquid-liquid interface, the oscillating chains generated a hydrodynamic flow in both media that promoted the formation of aster-like structures, organized in 2D periodic arrays at sufficiently high surface concentrations. When energized with an in-plane alternating field, the particles formed monolayers of equal-sized spinners, single-particle-thick linear aggregates, and pulsed clusters [390]. Under low frequency planar rotating fields Melle et al. showed using a microscopic model that paramagnetic microparticles on a plane formed rotating chains of given length and shape as a balance of magnetic dipolar interactions and hydrodynamic drag [391,392]. Abdi et al. extended the analysis to high frequency fields, where —they showed— the chains break and can form clusters, using computer simulations of a microscopic model in the overdamped regime with hydrodynamics treated in the far-field approximation [393]. In these high frequency conditions, the application of in-plane rotating fields at the confining interface induces an attractive interaction between adsorbed magnetic particles, which ultimately promotes dynamic self-assembly into finite hexagonal lattices. Under external magnetic fields rotating on the plane of a fluid-fluid or solid-fluid interface at high frequencies, paramagnetic colloids were shown to form 2D structures with different morphology depending on the polarization of the external actuation, as rationalized in terms of effective averaged particle-particle interactions. Circularly polarized fields were shown to form isotropic clusters —carpets— and crystals of rotating particles [394], whereas elliptically polarized fields can generate both chains and carpets depending on the ellipticity of the actuation [394]. The inclusion of a component perpendicular to the confining boundary induces the transition from planar carpets to separate chains, capable of transporting passive charges through the flow generated by the rotating constituents [211]. 7.1.1.3.3. Magnetic interfacial swimmers. Some of the dynamic selfassemblies, formed from the equilibrium of viscous, inertial, capillary, and magnetic forces, can be used as models of numerous intriguing issues, such as the organization in biological structures or the transport of matter in the low Reynolds number regime [395]. In bulk, the main strategies are based on local generation of flow fields through forced rotation of non-perfectly symmetric objects, helical shapes in most designs that mimic some existing natural systems, the roto-translation coupling strategy described above, and the controlled actuation of flexible filaments. On the other hand, controlled transport of microparticles along fluid interfaces has traditionally been induced through strategies that make use of auto-phoresis, capillarity phenomena, or spatial symmetry breaking. For example, the interfacial snake and aster structures described above spontaneously break spatial symmetry at relatively high field frequency, inducing unbalanced surface flows that lead to propulsion and can be used to transport passive charges. At low frequency, it is the presence of a nearby non-magnetic object that introduces the imbalance of the generated fluxes necessary for propulsion [396]. In asters, the latter can be generated by applying an in-plane magnetic field, which promotes the formation of asymmetric extended objects [365]. Using a different strategy, Lumay et al. exploit the balance between field-induced dipole repulsion and capillary attractions to generate propulsion [209]. In the proposed design, three magnetic millimeter spheres adsorbed on a planar water-air interface were energized by both a vertical field and an in-plane oscillating field, so the three spheres form a sequence of triangular configurations that satisfy the time reversibility breakdown required in the low Reynolds regime. At moderate values of the Reynolds number, the energized arrays formed by particles of different sizes follow a non-reciprocal deformation sequence, as the one described by the Najafi-Golestanian microswimmer [397]. Larger magnetocapillary arrays showed metachronal waves at the periphery when subjected to a precessing magnetic field [398]. Recently, Fei et al. applied static or time-varying fields to force magnetic Janus particles adsorbed on curved fluid interfaces to move to the zones where the magnetic moments align parallel to the field [399]. Other alternative propulsion strategies do not rely on the use of hydrodynamic interactions. In these, adsorbed or non-adsorbed colloids E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 33 are transported by the action of a moving magnetic potentials generated by a variety of self-assembled structures of magnetic particles. The adsorbed magnetic colloids can be collectively transported across modulated energy landscapes generated by dynamic self-assembled monolayers of differently sized particles, located at different positions with respect to the interface [9]. On the other hand, the subtle balance between magnetic and viscous torques allows the transport of the submerged colloids under straight tracks of adsorbed particles, which function as if they were microassembly lines or Tyrolean traverses [400]. 7.1.2. Dielectric colloidal particles adsorbed at a fluid-fluid interface under the action of an external electric field The response of adsorbed colloidal particles at a fluid interface to an electric field depends on the strength and frequency of the field, as well as on the dielectric properties, electrical conductivity and geometry of both the particles and the surrounding media [401]. The use of an electric field to manipulate colloids and induce self-assembly has some advantages, compared to magnetic field, since the strength and frequency of the former are more tunable, both spanning on several orders of magnitude. However, electric fields, especially DC fields, can cause Faradaic reactions and electrical breakdown that can degrade the sample [402]. Moreover, the implied results are more difficult to interpret, as the electric field interacts with particles, the surrounding media and mobile and immobile charges [403] -consider, for example, the controversial discussion around the long-range interaction described by Nikolaides et al. [404] and Aveyard et al. [189]. To avoid, at least partially, these impediments, high-frequency AC electric fields are often preferred [405]. In the presence of a uniform electric field, charged particles surrounded by an electrolyte are pushed by the field towards the oppositely charged electrode, in a process called electrophoresis [406]. If the applied field is not uniform, which can be promoted or stressed by the proximity of the fluid interface, and the dielectric constant of the particle is different from that of the surrounding media, then the particle experiences a dielectrophoretic force resulting from the electric stress acting on the particle surface [407]. In addition, particles exhibit dipoledipole interactions that promote the formation of field-induced chains, bundles and 2D lattices at fluid interfaces, while anisotropic particles undergo field-induced alignment [405]. At low frequency, the interaction between the applied field and the polarization of the ionic double layers surrounding the particles can also give rise to nonlinear electroosmotic flows [408]. All emerging phenomena have been widely used to generate controllable Janus droplets [406], to separate particles on the surface of droplets [406], in the destabilization of Pickering emulsions, or to desorb particles from fluid interfaces [409]. On the other hand, the applied field can induce free charge accumulation at interfaces and local electrical stresses, coupled to interface deformation and flow generation of either fluid [410]. These electrohydrodynamic flows have also been used extensively in the collection and transport of adsorbed particles at fluid interfaces [402,405]. When charged particles adsorbed at a fluid interface are upon the influence of an external electric field, the interface deforms via the electro-dipping force that emerges from the interaction between the surface charge of the particles and the two media. The vertical component of this force, positive or negative depending on the dielectric constant and particle contact angle, is balanced by interfacial tension [411], while the lateral interaction between two adsorbed particles is always repulsive [412]. To our knowledge, all studies concerning adsorbed dielectric particles subjected to the action of external electric fields have been performed on Pickering droplets, but none of them have been carried out on planar charged interfaces. Only in the electrocapillary wave technique is an external AC electric field applied locally through a knife-edge electrode placed just above the interface. However, the field is not used here to arrange or transport adsorbed colloidal particles, but to excite the fluid interface in a Langmuir trough, and measure the rheological properties of the laden particle interfaces [30]. In a similar experimental setup, recently designed by Jia et al., the application of the external field triggers charge injection, allowing modulation of the charge-induced repulsive force, along with the corresponding reversible induction of the repulsion-dominated colloid assembly or dispersion of aggregated particles [413]. 7.1.3. Active particles Active systems, those that can convert convert chemical [414], thermal [415], or electromagnetic [416] energy into mechanical propulsion, are present at a wide range of scales, in assemblies of living organisms such as bacterial colonies and bird flocks or in collectivities of artificial components. In the last decade, the manipulation of active colloids has generated significant experimental and theoretical attention, because the study of self-propelled microparticle suspensions opens the door to the understanding of systems far from equilibrium and to the development of disruptive technologies. The self-propulsion capability of synthetic chemical powered active colloids is supported by different mechanisms, from induced-charge electrophoresis [408], or bubble propulsion [417], to catalytic local reactions and self-phoresis [380]. In autophoresis, a chemical reaction is catalyzed at the particle surface, leading to the generation of asymmetric gradients (thermal, surface tension, ionic and/or chemical) around the particles. The occurrence of these gradients, which may be coupled to each other and/or induced by an external field, such as a light source, ultimately leads to the movement of the particle relative to the solution, due to the action of phoretic forces and the triggering of hydrodynamic flows [418]. These induced flows can also be used to generate long-range hydrodynamic attractions that trigger the assembly of microscale particles [372]. In these experiments, the inherent asymmetry of Janus microbeads, spheres consisting of two different (chemically or thermally) active and passive material faces, is often used to promote a preferred direction of motion. Active particles have potential applications in the engineering of smart lab-on-a-chips, in the transport of drugs [419], cells [420], pollutants [421] or cargoes [422], in the detection of chemicals as well as in the study of active crystals and glasses [423]. In these systems, individual particle active motion is coupled to Brownian rotational diffusion, similar to what is observed in run-and-tumble systems, while the collective behavior exhibits a variety of complex phenomena, such as local clustering [424], melting of clusters [425], swarming [416], active self-assembly [426] as well as segregation of active and passive species [427], mimicking on many occasions the collective behaviors exhibited by many biological systems. All these phenomena can be to some extent controlled using magnetic [361] and optical fields [428] or by modifying the swimmer geometry. Ensembles of active particles dispersed in a fluid, near fixed obstacles [429] or a solid-liquid interface [430], where particles exhibit alignment interaction [431] and circular trajectories [432], have been widely studied in the last years, and numerous reviews of the subject can be found in the literature [380]. 7.1.3.1. Active particles adsorbed at fluid interfaces. Fluid-fluid interfaces are often ignored in most fundamental research, even though they are present in many real systems. However, the dynamics of phoretic colloids is particularly sensitive to the proximity of solid and liquid interfaces [8,38]. Proximity of a fluid interface induces orientation of the active particles laterally and propulsion parallel to the interface, allowing for a robust guidance mechanism along the fluid interface [433], while restricting rotation out of the swimming plane [434]. The hydrodynamic interaction with the fluid-fluid boundary favors the appearance of circular trajectories, like those observed for solid interfaces, but in the reverse direction [362]. When trapped at a fluid interface, active Janus particles exhibit strongly enhanced persistence length and velocity, compared to those observed in the bulk [418], due to the implicit constraints of particle reorientation, slowed down due to local pinning of the three-phase E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 34 contact line [185,430]. The above constrictions lead, in some cases, to circular trajectories that deviate significantly from random rectilinear motion by Brownian rotational motion [435]. Since the rotation of the particles about the axes tangent to the interface is strongly hindered by local pinning of the three-phase contact line and the capillary forces, the motion of active Janus particles is strongly determined by the fastened orientation of the particle with respect to the fluid interface, resulting in heterogeneous populations of non-moving and moving particles [430]. The activity of adsorbed particles often induces local surface tension gradients, which give rise to Marangoni stresses. Marangoni surfers use external energy inputs or chemical reactions to create local gradients of temperature and surfactant concentration, propelling themselves at high velocity toward regions of higher surface tension, along directions partially determined by the symmetry of surfers [418]. In principle, Marangoni navigation requires asymmetries in the surface tension gradient of the interface around the particles. However, even symmetric particles exhibit rapid translational and rotational motions when placed at a water-air interface, generated by a convective instability that provokes the spontaneous rupture of the initial axial symmetry. In the above systems, the propulsion mechanism is strongly dictated by the degree of exposition of the catalytic surface to aqueous phase [418]. The interplay between motility, capillary interactions and induced Marangoni flows promotes in some systems instability and rupture of thin films [436], while in others it favors the existence of self-assembled dynamic and stationary states [437,438]. In another type of experiments, where micro-sized floating objects are illuminated with light, the applied radiation is adsorbed by the Janus particles and converted into mechanical work thanks to the coupling between the temperature and surface tension gradients. The micro-machines powered through this mechanism have the advantage of being long-lived and easily switchable, while the linear and angular velocities are easily controlled by the laser power and the surfactant concentration at the interface [418]. 7.2. Theory and simulation of dynamic self-assembly The self-assembly of colloidal particles at liquid-liquid interfaces can occur as a result of a wide range of processes and interactions, both in equilibrium and out of equilibrium. From a theoretical standpoint, systems in thermodynamic equilibrium have been thoroughly studied over many years and are understood using classical concepts of thermodynamics and statistical physics, requiring the minimization of the appropriate thermodynamic potential of the system. At least in principle, the knowledge of interparticle interactions allows us to program the most stable structures that will be spontaneously formed by selfassembly. Here we focus our attention on the theoretical description of aggregation processes at interfaces that occur out of thermodynamic equilibrium, be it by actuation with external fields or due to collective processes stemming from individual consumption of energy from the environment. A common general theoretical framework which dictates the emergence of such self-assembled structures and their properties is still missing. In search for a deeper understanding of such phenomena, on the one hand microscopic models have been developed to analyze and characterize non-equilibrium structures. On the other hand, numerous investigations have been devoted to find a thermodynamic principle to characterize the emergence of steady structures out of equilibrium. 7.2.1. Self-assembly under time-dependent external fields In the previously noted work of Grzybowski and co-workers [214], the dynamic structures formed by rotating ferromagnetic disks at a fluid interface were explained as a process governed by the equilibrium between magnetic particle attraction and hydrodynamic repulsion with inertial effects [439]. These systems were also investigated using magneto-hydrodynamic models defined through boundary value problems [440]. The method uses the Navier-Stokes equation, which includes multi-body interactions exerted on the fluid due to the rotations of magnetic particles. The numerical solution of the model permitted the calculation of the energy dissipation rates of the self-assembled steady states of rotating particles. In Ref. [441], the sole effect of hydrodynamics on the collective behavior of spinning discs was studied with the help of simulations of fluid particle dynamics, a technique that allows to properly account for hydrodynamic interactions between particles. The authors concluded that hydrodynamics alone can generate a rich phase behavior of spinners, including a fluid state, clustering, hexatic ordering and glassy states [441]. The formation of clusters of spinning magnetic particles at liquid-liquid interfaces was also investigated using Lattice Boltzmann simulations, which properly accounts for the hydrodynamics (of an incompressible flow) generated by the rotating particles [442]. Using this technique, they demonstrated that hydrodynamics can cause the separation into a particle-rich region and a particle-poor region [442]. G¨ otze and Gompper analyzed the effects of confinement on the assembly and dynamics of magnetic discs driven by a rotating field using multiparticle collision dynamics simulations, which naturally includes both hydrodynamics and thermal effects [443,444]. As mentioned previously, Snezhko et al. [365,396,445] also demonstrated that the coupling between the collective response of ferromagnetic colloidal particles under alternating magnetic fields and the surface waves generated at liquid-air interfaces is responsible for the formation of dynamical self-assembled dynamical patterns. The structure and dynamics of such structures was theoretically described through both a continuum phenomenological approach and also a microscopic model which couple the dynamics of surface waves with the Navier-Stokes equations for the flow [445]. It was shown later on that such structures could be used as self-propelling agents [396]. The transport on self-assembled dynamical structures was also studied in the work by Martínez-Pedrero et al. [446], where Brownian dynamics simulations were used to investigate the dynamics of two types of superparamagnetic particles of different size in a fluid-fluid interface under precessing fields. The authors demonstrated that under such actuation, self-assembled lattices formed by one type of particle could be created and, simultaneously, transport of the other type could be established from node to node of the lattice. 7.2.2. Clustering and phase separation of active particles So far, the theoretical modelling of active particle systems used to study their collective emergerging effects, e.g., self-assembly, has been mostly done considering highly simplified models. In these models, hydrodynamic interactions are often neglected or considered in an effective manner, and in most cases the systems considered are restricted to move on a plane. However, some of the conclusions drawn from these studies should be general, in the sense that they should be applicable to processes where such restrictions are not imposed, and have been used to predict and interpret experimental behavior of active particles at liquid interfaces. The sole capacity of particles to self-propel was shown to induce the formation of dynamic clusters (living crystals), even if their mutual interactions are repulsive and no alignment interactions are included [447–450]. This is reflected in long-lived density fluctuations and anomalous clustering. While a system of N passive particles in a volume V exhibits number fluctuations of ΔN ~ √ N, the number fluctuations in active particle systems scales as ΔN ~ N α , where α can become of order 1 in two dimensional systems [451,452]. The principle of such cluster formation can be explained qualitatively. Active particles follow a diffusive dynamics with long persistence length in absence of other particles. When they collide with other particles their velocity is reduced due to excluded volume interaction, since it impedes motion induced by the active force. If the characteristic time to reorient and escape from the collision is larger than the characteristic time to encounter another particle clustering will occur. In fact, self-mobility alone was shown to induce the separation of particles into a dense and dilute fluid phases (Motility Induced Phase E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 35 Separation, MIPS). This athermal transition was suggested by Tailleur and Cates [447] using theoretical arguments on a one-dimensional system and later on it was shown using computer simulations of discs moving in a 2D plane [448–450]. Experimental evidence of clustering and phase separation of such active systems was given later on [453,454]. The nature of the transition to the mobility induced phase separated state has been widely investigated from a theoretical persepective [447,455–461]. In case of active brownian particles with no alignment interactions, the pressure exerted by the system was demonstrated to be a state function independent of the interaction with the walls [455–457], and pressure-volume non-equilibrium phase diagrams were obtained. The MIPS transition was found to satisfy the characteristic properties of an equilibrium first-order liquid-gas phase transition [461]. The origin of phase separation was attributed to mechanical [455,456] and diffusive instabilities [447,459,460]. To control the size of the dynamic clusters, systems of active brownian particles moving on a plane and interacting through a short range attraction and a long-range soft repulsion have been studied using computer simulations [462]. In practice, most active and actuated particles used in experiment develop aligning interactions both with other particles and the container walls. These can be originated, for example, from hydrodynamic interactions [463], steric interactions for geometrically anisotropic particles [464], or electrostateic interactions [416]. Such interactions can lead to the emergence of swarming collective motions of particles, as demonstrated by analysis of the Vicsek model [465] and generalized versions of it. In these models, the direction of an active particle is determined by the average direction of the neighboring particles and a phase transition is obtained at high enough concentrations from a fluid of isotropically directed particles to a state where all particles move in the same direction in the form of bands [466,467]. Solon and co-workers demonstrated that systems of active particles with aligning interactions cannot be described by an equation of state, since the pressure that they exert depends on the specific nature of the interaction with the wall, which is not a function of state [457,458]. This result evidences the difficulty of building a general theory to describe the macroscopic outof-equilibrium behavior of active particle systems. 7.2.3. Seeking a principle for non-equilibrium self-assembly In equilibrium, the self-assembly of a subset of particles of the system occurs as a process to minimize the overall free energy. For self-assembly processes out of equilibrium there is a constant energy dissipation and entropy production and in general there is not a thermodynamical potential which becomes a minimum at steady states. In this context, the quest for a general thermodynamic criterion to predict the evolution of non-equilibrium systems and identify steady states —in particular selfassembled states— has motivated a great number of investigations over the years. In analogy to the second law of thermodynamics, Onsager proposed the principle of least dissipation to understand the evolution of nonequilibrium systems [468]. Built upon the seminal work of Rayleigh, Onsager formulates his variational principle in terms of a dissipation function which contains the rate of change of entropy and the hydrodynamic dissipation. Onsager’s principle has been very influential over the years, with recent applications being discussed [469]. Based on Onsager’s work, Prigogine introduced the minimal entropy production theorem to understand steady states out of thermal equilibrium. This theorem asserts that in systems out of equilibrium the rate of production of entropy is a minimum [470]. In dynamical selfassembled states of particles, this theorem would constraint the possible structures in the steady state to those which dissipate the least amount of energy and consequently minimize the rate of entropy production. The theorem is derived in the linear regime where Onsager’s reciprocal relations hold, and under the assumption of local thermodynamic equilibrium [470]. However, most of non-equilibrium steady structures, including those of particles at interfaces under timedependent actuations, occur far from thermal equilibrium and the theorem cannot be applied. In particular, Grzybowski and co-workers studied experimentally how dissipation dictates the selection of given non-equilibrium structures of rotating magnets at an interface, and concluded that the system does not always evolve into the least dissipative structure, minimizing the entropy production as the minimum entropy production claims. Rather, they observed the existence of alternative more dissipative structures although with a probability which decays exponentially with the dissipation rate [471]. To understand steady states far from equilibrium where local thermodynamic equilibrium cannot be applied, Evans and Baranyai proposed an alternative approach in terms of an alternative variational principle [472], although it was found to be only approximately valid [473] Other approaches have attempted to describe non-equilibrium stationary states using extensions of the concept of entropy. Dewar investigated the emergence of non-equilibrium self organization processes using Jaynes’ formalism of statistical mechanics [474,475], based on the path information entropy S I = − ∑ Г p Г log p Г . Here, Г represent the microscopic phase-space paths, with probability p Г , and the sum extends to all possible paths [474,475]. Attard formulated a theory to describe non-equilibrium stationary states introducing a second entropy or transition entropy, defined in terms of the number of molecular configurations associated with a transition between macrostates at a given time [476]. The author then argues that the nonequilibrium steady states of systems under fixed thermodynamic gradients are defined by the maximization of this entropy, providing the optimum rate of change or flux in a given system. Recently, Arango-Restrepo et al. [477,478] investigated the formation of self-assembled structures under non-equilibrium conditions. They show that the architecture of the formed structures is determined by the entropy production in the process of formation. Furthermore, they demonstrate that such structures are characterized by being extreme values of the entropy production as a function of a structural parameter, and test their findings against experimental results of gelation processes and of Liesgang ring formation [477]. The same authors proposed a criterion to identify the formation of self-assembled structures under nonequilibrium conditions [478]. They propose an effective potential function which takes into account the energy required to change the configuration of the system and its stationary probability. Using a phenomenological approach, they determine that the effective potential becomes a minimum at the stationary structures formed by self-assembly in nonequilibrium conditions. The criterium is successfully tested against experiments of Liesgang rings formation and also against experiments of self-assembly of colloidal particles at interfaces under time-dependent field actuations. In particular, they show that the minimization of the effective potential can predict the most stable structure given an external actuation [478]. 8. Potential applications of particle-laden fluid interfaces Colloidal particles confined at fluid interfaces offer many opportunities on the design of materials. From a practical perspective, the stabilization of interfaces by using particles allows obtaining emulsions and foams with enhanced stability in relation to those stabilized by molecular and polymer surfactants. The combination of quasi-2D confinement of particles adsorbed at fluid interfaces with the advances in the synthesis of new colloids, makes possible to take advantage of the microscopic complexity of colloidal interface-dominated materials for the design of new functional materials with tunable macroscopic properties, which can open new avenues in different technological applications [44]. The controlled and guided exploitation of particle-laden fluid interfaces requires addressing the relationship existing between different correlated aspects, such as the characteristics of the particles, the degree of adsorption, the structure of the emerging assemblies and their magnetic, electrical or rheological properties. Some examples of the E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 36 potential applications of particle-laden interfaces are given in this section, while more specific details can be found in the literature [1,2,41,285]. 8.1. Particles at fluid interfaces for the stabilization of emulsions and foams The correlation between the interfacial properties of particle-laden fluid interfaces, and their ability to stabilize emulsions and foams emerges as a very important issue in different technological and industrial fields, ranging from the design and manufacture of new food and cosmetics products to wastewater or oil recovery treatments [19,20,100,237]. The use of particle-laden fluid interfaces for the stabilization of dispersed systems is widespread because they provide novel rheological properties to the fluid interface. As a consequence, they improve long-term stability in foams and emulsions because of the reduction of the interfacial area upon the quasi-irreversible trapping of particles, and the mechanical stability provided by the formation of a rigid protective shell overlaying the external surface of droplets or bubbles, which contribute to hinder, at least partially, the different destabilization processes occurring in dispersed systems, e.g., creaming (or sedimentation), flocculation, coalescence, and Ostwald ripening [14,479]. Therefore, it is possible to assume that the stability and properties of emulsions and foams are closely correlated to the interfacial and mechanical properties of single particulate interfaces, and that the layers of adsorbed particles help to dampen the external mechanical perturbations and thus contribute to minimize destabilization and rupture events of dispersed systems [100,280]. Currently it has become obvious that the increase of the surface density of particles adsorbed at fluid interfaces is critical for the enhancement of the stability of emulsions and foams [295,480]. Processes such as jamming and clogging of colloidal monolayers may induce an arrest of the interfacial dynamics, which in turn minimizes the coarsening processes due to the reduction of the interfacial tension, and enhances the interfacial stability. The stability of emulsions and foams is also associated with the rheological properties of the layers [58,59,236,237,481]. Thus, at high interfacial coverages, strong interparticle interactions tend to promote the formation of particle-laden interfaces with a mainly elastic behavior, controlling the film thinning phenomena [482]. According to the Gibbs criteria, which define the stability of dispersed systems in terms of the ratio between the interfacial tension and elasticity, emulsions and foams are stable only when ε ’ >γ/2. However, this criterion only applies to emulsions and foams formed by spherical droplets or bubbles [236]. The close correlation between stability and surface rheology was confirmed by Sullivan and Kilpatrick [483], who found that the formation of rigid, stagnant particle films via the formation of particle bridges, especially when the interfacial coverage is relatively low, results in dispersed systems with increased stability. Besides, the formation of particle zips between close interfaces helps droplets or bubbles to aggregate forming stable flocs, avoiding, at least partially, the coalescence phenomena [238,480]. The increase of both the shear viscosity and the dilational moduli also plays an important role in the control of the drainage phenomena, which are especially relevant for the stability of foams [296]. The impact of the latter is clearly shown in the studies by Cervantes-Martínez et al. [481]. They found that the resistance against compressive stresses presented by particle-laden fluid interfaces minimizes shrinkage of small bubbles and improves foam stability. Despite the extensive research efforts on seeking correlations between the dilatational rheological properties of particle-laden interfaces and their ability for dispersed system stabilization, the current understanding is far from clear, as evidenced by the studies by Santini et al. [4,60,61,107]. They found no correlation between the stability of dispersed systems and the rheological response of the single interfaces. A similar conclusion was reached at when fluid interfaces are stabilized with layers of silica nanoparticles decorated with palmitic acid [61,106]. The above mixture leads to the formation of very rigid interfaces, with very high values of dilational viscoelastic modulus (>100 mN/m). However, this is not enough to ensure the stabilization of the foams [61]. A different study showed no correlation between the stability of emulsions stabilized by the above mentioned mixtures and the properties of the single water/oil interface [106]. The potential role of the dilatational modulus in controlling the stability of foams and emulsions is inferred from the above discussion, at least under some experimental conditions. However, the shear modulus also plays a very important role on the stability of dispersed systems, mainly due to its correlation to the interfacial structure and packing [276,289]. Brugger et al. [320] found that emulsions stabilized using poly(N-isopropylacrylamide) particles were stable only when the particle-laden interface exhibited an elastic character, whereas viscous interfaces, with high G” values, were easily destabilized. This coincides with the rapid destabilization shown by asphaltene-stabilized emulsions [484]. Apparently, the increase of the interfacial shear viscosity enhances the coalescence rate (on the order of seconds) between droplets in close contact, whereas the coalescence is hindered when the droplets are coated by a layer with a microstructure dominated for the elastic properties of the single interfaces. The differences in the coalescence rate observed as a function of the viscoelastic properties of single interfaces are commonly related to the existence of a high shear yield stress (~10 4 Pa), which in turn is closely correlated to the film shear yield point and the film thickness. The increase of the elastic stiffness prevents the mobility and rupture of the particle layer, and hence the formation of a solid-like film may introduce an energetic barrier against coalescence. The morphology and size distribution of the droplets and bubbles can be modulated by changing the size or contact angle of the adsorbed particles. These parameters also play a very important role on the control of the stability of emulsions and foams. It should be stressed that the stabilization of emulsions and foams requires partial wetting of the particles for both fluid phases. This leads to the formation of oil/water dispersions in the case of hydrophilic particles (θ <90◦), whereas water/ oil dispersions are formed when the interface is stabilized by hydrophobic particles (θ >90◦). The change of the particle wettability by the addition of surfactant can be used in the modulation of the stability of emulsions and foams [243] as demonstrated Binks et al. [111]. They found that mixtures of silica nanoparticles and a bicatenary cationic surfactant can stabilize different types of emulsions, with the surfactant concentration being the control parameter dictating the transition between the different emulsion types. In these mixtures, the degree of hydrophobicity of the particles, and consequently their contact angle at the fluid interface, varies as result of their association with the surfactant molecules, with the inversion point appearing in dispersions stabilized with particles of similar affinity for both interfaces, i.e., for θ = 90◦[100]. The addition of a low surfactant concentrations is not enough to modify significantly particle hydrophobicity, which remains mainly hydrophilic with a contact angle lower than 90◦. Hence, the stabilization of oil in water (o/w) emulsions should be expected, while the increase of the surfactant concentration enhances the particle hydrophobicity, resulting in a trapping of the particles at the interface with θ >90◦, and hence the formation of water in oil (w/o) emulsions is found. Further increases in surfactant concentration lead to the re-hydrophilization of the particles, which leads again to the formation of o/w emulsions [485]. Similar transitions were found by using chemically modified particles [486]. The modification of the particle wettability has been also exploited for modulating foam stability [487,488]. However, to the best of our knowledge, the study of the transition from aqueous foams to free aqueous droplets surrounded by a particle shell, e.g., dry water or liquid marbles, has not been systematically done, e.g., by changing the hydrophobicity of the particles. However, there is strong evidence for the formation of dry water and liquid marbles by the use of hydrophobic particles [489,490]. Fig. 17 shows an idealized picture of the possible correlations E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 37 existing between the contact angle of particles trapped at fluid interface and the interfacial curvature in relation to the stabilization of water/ vapor interfaces. It should be noted that the existence of a non-uniform wetting of the particles at the interface modifies the interfacial energetic landscape, which can change the ability of particles for stabilizing emulsions and foams [102,207,272]. Furthermore, the deformation of the contact line promoted by the weight of large adsorbates may introduce an additional contribution to the destabilization of the dispersed systems as result of the gravitational forces [186]. Particle-stabilized foams and Pickering emulsions have been widely used as templates for the manufacture of solid porous materials, the socalled solid foams. This type of systems can be obtained from the dispersed precursor systems following two different approaches: (i) sintering and drying the wet system, or (ii) direct solidification of the bulk liquid phase [487,491]. Gonzenbach et al. [488] exploited these strategies to obtain solid foams using precursor liquid foams stabilized by mixtures of particles and different short-length surfactant. A similar approach was followed by Zabiegaj et al. [3,4] for the fabrication of particle stabilized solid foams using carbon and alumina particles. Alumina-based aqueous foams were also used by Santos et al. [492] in the preparation of macroporous refractory ceramics by adding calcium aluminate cement as a binder. The addition of the binder allows reducing the time required for setting the solid structure, improving its mechanical strength. Similar results were found by Finhana et al. [493]. 8.2. Colloidosomes Colloidosomes are solid capsules formed by a shell of densely packed particles with their size ranging from the sub-micrometer scale to millimeter scale. They have as main properties their controllable permeability and mechanical strength [2,494]. The most common methodology for the fabrication of colloidosomes is based on the assembly of colloidal particles into emulsion droplets that are locked together by sintering or electrostatic binding of oppositely charged polyelectrolytes, avoiding the destruction of the shell by transferring them to a different fluid [2,40]. Dinsmore et al. [494] prepared colloidosomes by self-assembly of carboxylated polystyrene latex microparticles on the surface of oil-inwater and water-in-oil of emulsions droplets. After the assembly of the particles on the surface of the droplet, they were bound by heating the system just about the glass transition of polystyrene (around 105◦C). During this step, glycerol was added to the aqueous phase to prevent water evaporation. The high temperature required for sintering becomes a major drawback in the preparation of colloidosomes, which can be partially overcome by using particles with a lower glass transition [495]. The sintering process can also be performed locally by heating using laser irradiation, as demonstrated L´ opez-de-Luzuriaga et al. [496]. By self-assembly of spherical gold nanoparticles at the interface of oleic acid (OA) nanodroplets formed in n-hexane, followed by laser irradiation, they fabricated plasmonic gold colloidosomes with collective plasmonic absorptions tunable in surface, size and shape. The assembly of oppositely charged polyelectrolytes on particles has also been exploited to prepare colloidosomes and avoid the use of high temperatures. Gordon et al. [497] used this methodology for the assembly of latex particles in toluene/water systems by introducing poly (L-lysine) into the aqueous phase. During the assembly, the poly(Llysine) chains adsorb on the latex surface, which allows locking them in a superstructure. The formed colloidosomes were strong enough to withstand the osmotic stresses that occur during their transference to a different solvent. Another possibility to fix the particles in colloidosomes is the use of polyelectrolyte multilayers obtained by the Layer-by-Layer (LbL) method [498,499]. Colloidosomes can be also obtained using an internal phase containing a gelling agent. Gelation of the internal phase of water-in-oil colloidosomes generates a solid-like structure, which provides the colloidosomes enough stability and structural strength to prevent their collapse upon solvent exchange processes [500]. Cayre et al. [500] fabricated colloidosomes through the assembly of amine-functionalized polystyrene latex on water droplets containing agarose dispersed in sunflower oil at 70◦C. Afterwards, the gelation of the aqueous droplets took place by reducing the temperature from 70 to 20◦C. The gelling agent can be replaced by wax to obtain solid capsules. This requires preparing wax-in-water emulsions stabilized by colloidal particles, at high temperature, and then the obtained dispersions must be cooled down to crystallize the oil phase [299]. The stability of the colloidosomes can be improved by polymerization after their preparation, within or on the surface of the Pickering precursor emulsions, which favors the particle entrapment at the interface. This approach was followed by Chen et al. [501] on the preparation of paraffin in water emulsions stabilized by functionalized silica particles in such a way that atom transfer radical polymerization (ATRP) can be induced on their surface. Thus, after preparing the Pickering emulsions, a polymerization process was induced by the addition of 2-hydroxyethyl methacrylate in the medium, which allows obtaining colloidosomes cross-linked by a poly(hydroxyethyl methacrylate) network. An alternative approach is to perform the polymerization inside the droplets by including vinyl monomers. This strategy was used by Bon et al. [502], who stabilized droplets containing styrene and divinylbenzene, using poly(methyl methacrylate) particles as reactors for the copolymerization process. This procedure allowed the formation of colloidosomes with sizes in the range of 5-30 μ m reinforced by a polystyrene core. Precipitation of a preformed polymer in the inner core of the Pickering emulsion can be exploited as an alternative to polymerization, as was demonstrated by Cayre et al. [503]. They prepared oil-in-water emulsions stabilized with silica and gold particles. In this work, a linear poly(methyl methacrylate) was dissolved in the oil phase, a mixture of dichloromethane/n-hexadecane. After preparing the emulsions dichloromethane was evaporated, at 40◦C. As the polymer is less soluble in hexadecane than in the mixture, the evaporation induced its precipitation on the inner walls of the capsules, blocking the inorganic particles at the interface. The reduction of the amount of polymer leads to a degradation of the mechanical properties of the obtained colloidosomes [504]. In the literature, there are many other examples following similar methods to improve the stability of the colloidosomes obtained [505]. The methodologies discussed above, designed to improve the mechanical strength of colloidosomes, often involve heating steps that should be avoided in certain applications, e.g., encapsulation of biological compounds. This limitation may be overcome by choosing particles suitable for obtaining a covalently cross-linked structure at room Fig. 17. (a) Idealized representation of the particle position at the water/vapor interface as a function of the wettability. (b) Bending behavior of particle-laden fluid interfaces as function of the particle contact angle. Reprinted from Yu et al. [491], Copyright (2021), with permission from Elsevier. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 38 temperature [506]. There are many examples in the literature of colloidosomes reinforced by chemical cross-linking. This idea was used by Croll et al. [507] for the fabrication of colloidosomes upon the assembly of poly-(divinylbenzene-alt-maleic anhydride) microspheres at an oil/ water interface, followed by cross-linking via amide or ionic bonds. In the formation of microcapsules, the length of the cross-linker is critical, as low molecular weight species are often too small to span the gap between adjacent particles. Covalent cross-linking was also used in the reinforcement of colloidosomes formed by quantum dots [508]. Skaff et al. [509] obtained cross-linked CdSe/ZnS capsules by a ring-opening metathesis polymerization of norbornene attached to the quantum dots, which allows the quantum dots to be arrested in a superstructure at room temperature. Another strategy used to exploit ionic crosslinking was developed by Arumugan et al. [510] for the fabrication of magnetic colloidosomes stabilized with FePt particles. Here, complexation of terpyridine tethered to the particle surface with Fe(II) metal ion lead to nanoparticle networks at the liquid−liquid interface. Sharh et al. [511] prepared thermo-sensitive colloidosomes by crosslinking primary amine functionalized PNIPAM particles with glutaraldehyde. These colloidosomes undergo a strong reduction of the size with the increase of the temperature. The combination of covalent crosslinking and steric stabilization is also very popular, as evidenced the study by Walsh et al. [512]. They fabricated colloidosomes of polystyrene latex stabilized by the adsorption of poly(ethylene imine) quaternized with 4-vinylbenzyl chloride, which can be cross-linked by using different bis-epoxy polymeric cross-linkers. A similar approach was followed for the fabrication of colloidosomes by using different organoclays [513,514] and silica particles [515]. Yuan et al. [516] reported another design that combined covalent cross-linking with steric stabilization, by decorating polystyrene particles with a poly(2dimethylaminoethyl methacrylate)-poly(methyl methacrylate) diblock copolymer. The later can be cross-linked at the oil/water interface though a quaternization process, using 1,2-bis(2-iodoethyloxy)ethane. 8.3. Coffee ring suppression Particles homogeneously dispersed within liquid droplets may lead to the formation of ring-like deposits upon evaporation of the solvent, resulting in the so-called coffee-ring effect [113,234]. The formation of this type of deposits is often undesirable in application such as inkjet printing, and the fabrication of microand nanostructures, or coatings, where a more homogenous deposition of the material is required [517–524]. In the last years, the use of colloidal particles trapped at water/vapor interfaces has been very common for a complete suppression, or partial mitigation, of the formation of the coffee-rings when sessile droplets are droplets are evaporated [48,149]. This is the result of the competition between adsorption at the fluid/fluid interface and at the solid/fluid interface occurring during droplet evaporation. Therefore, by modulating the properties of the particles dispersed within the evaporating droplet it is possible to modify their adsorption to the interfaces involved, which in turn provides a large degree of control over the morphology of the deposits obtained. The latter is the result of an intricate balance between particle−particle, particle−fluid/fluid interface, and particle−substrate interactions [338]. There are several methodological approaches enabling the reduction of the coffee-ring effect in the deposition droplets containing colloidal particle suspensions. Bigioni et al. [525] controlled the order of the selfassembled particle array on the solid surface by pushing the particles towards the fluid/fluid interface. This was possible by a combination of a rapid evaporation of the solvent, faster than the diffusion of the particles in the bulk, which favors particle segregation towards the liquid/ vapor interface, and the appearance of attractive capillary interaction between particles once they reach to the fluid interface. This leads to the the formation of particle network with a high degree of long-range order, preventing partially the deposition of the coffe-ring on the solid surface. Selective segregation of the particles towards the fluid interface can be also stimulated by the use of a mixture solvent/co-solvent [526]. The combination of water with a co-solvent, with higher vapor pressure, leads to segregation of the co-solvent near to the liquid/vapor interfacial region, which favors the transport of hydrophobic particles to the liquid/vapor interface where they self-assemble into an ordered array. Surfactant-mediated interactions can be also be exploited to modulate the deposition patterns of particles on solid surfaces [338]. In this case, it was possible to adjust the electrostatic and hydrophobic particle−particle, particle−interface, and particle−substrate interactions to create deposits with very different morphologies, from rings to disks. The use of particles with high hydrophobicity (decorated with intermediate concentration of oppositely charged surfactants) leads to the formation of deposits with the highest homogeneity, which is associated with the formation of a skin of colloidal particles at the water/vapor interface during evaporation. On the other side, the deposition of particles decorated with very low and very high surfactant concentrations (highly hydrophilic particles) results in the formation of ring-like deposits. Another possibility for the suppression of the coffee-ring effects, proposed by Li et al. [527], is based on the capture and self-assembly of a rapidly descending liquid/vapor interface. This method requires the use of an environmental chamber, designed to allow control of the temperature and the relative humidity. High temperature evaporation hinders the deposition in the border of the three-phase contact line, promoting the formation of homogeneous deposits. This happens because at high temperature the rate of descent of the liquid/vapor interface is faster than the diffusion of the colloidal particle, which favors that a part of the particles can be retained by the fluid interface. Thus, the jamming of the particles at the fluid interface leads to an enhancement of the interfacial viscosity in relation to that of the bulk, which introduces an additional resistance to the capillary outflow and leads to the formation of uniform deposits. Particle shape anisotropy can be also exploited to modulate the morphology of the deposits obtained upon evaporation [528]. Spherical or slightly deformed colloidal particles are usually transported very efficiently to the three-phase contact line because of the evaporationdriven capillary flow, whereas ellipsoidal particles are deposited homogeneously during solvent evaporation. This difference is due to the fact that ellipsoidal particles can be entrained towards the edge of the evaporating droplets due to the outward capillary flow, until they are trapped by the descending liquid/vapor interface, where they undergo strong attractive inter-particle force. These phenomena are accompanied by a strong increase of the interfacial viscosity, associated with the adsorption of ellipsoidal particles that introduces an additional resistance to the outward capillary flow. In colloidal suspensions of spherical particles, the situation changes significantly, as the particles can be desorbed from the descending interface due to the weakness of the interparticle attraction. The above mechanism based on the balance between capillary and hydrodynamic forces, is quite general. Thus, in systems where the interfacial forces are greater than the hydrodynamic ones, the formation of stable particle networks at the interface is favored and, therefore, their migration towards the three-contact line is hindered. On the contrary, when the hydrodynamic forces overcome the capillary forces, the particles are easily transported to the contact line, where they form heterogeneous deposits [529]. Parthasarathy et al. [530] explored the evaporation of droplets of highly diluted suspensions containing particles of diameters from 3 to 10 microns to study the pattern formation on solid substrates. They stated that the process is governed by the combined effect of gravity and interfacial hydrodynamic forces, such that when the gravity driven deposition exceeds capillary driven transport, it is possible to suppress the coffee ring formation. They also found the existence of a transition in the morphology of the evaporative patterns, from monoto multilayers, with the increase of the particle diameter and the initial particle concentration of the suspension. Furthermore, they described an orderdisorder transition, which disappears at relatively high particle E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 39 concentrations. This transition was strongly determined by the organization of the particles at the edge of the deposits. A more recent approach for minimizing the coffee-ring effect involved the direct spreading of particles at the liquid/vapor interface of the evaporating droplet. This leads to a situation in which the particles can assemble at the interface during the evaporation enabling the formation of a uniform film. This occurs in three steps: (i) spreading of the particles at the surface of the evaporating droplet; (ii) assembly of the particles at the liquid/vapor interface, and (iii) settling of the particle film onto the substrate upon evaporation. This approach can be exploited for the fabrication of low interfacial tensions inks containing colloidal particles and a high interfacial tension liquid, e.g., water or ethanol/water mixtures [531,532]. Recently, Nath and Ray [533] demonstrated the power of the lattice Boltzmann method to predict the 3D-microstructures obtained after evaporation of droplets containing nanoparticles. For P´ eclet number above the unity, non-uniform coffee ring deposits are obtained in the vicinity of the pinning regions. Besides, the increase of the pattern dimensions and the difference between the pattern and substrate surface energies lead to the formation of deposits with stereoscopic morphologies. 8.4. Fluid interfaces laden with active/actuated particles Laden fluid interfaces of tunable colloids are promising candidates for designing new smart materials with remarkable properties. For example, Pickering emulsions stabilized with magnetic particles can be destabilized at will simply by approaching a magnet or applying a homogeneous magnetic field. [368,399], and magnetic needles can be used as probes for rheological characterization of fluid interfaces [184]. Guided motion of active and actuated adsorbed particles can be used in the transport of adsorbed matter at the microscale, in confined environments, in the enhancement of mass transport or in the modulation of interfacial properties. However, chaotic flows generated at low Reynolds numbers by dispersions of active colloids [534] can also be harnessed to promote mixing in the microscale or in water remediation. Although the uptake of these emerging applications in commercial technologies is still low, we anticipate that adsorbed active colloids will soon be regularly employed in microand nanofluidic devices and at the fluid interfaces inherent in all living organisms, and that out-ofequilibrium assemblies will be used as piloted carriers for precise and targeted interfacial drug transport at biological fluid interfaces, such as oral mucosa and saliva, tear films or those stabilised by lung surfactants [535]. 9. Concluding remarks The impact of particle-laden fluid interfaces in different problems with interest for academia and industry has stimulated to researchers with very different backgrounds to deepen on the understanding of the main forces driving the assembly of colloidal microand nano-particles at fluid interfaces as well as of the physico-chemical behavior of the obtained layers. This is essential for opening new avenues allowing the explotaition of the power of particle-laden fluid interfaces in applications, e.g., the fabrication of interface-dominated systems such as foams, emulsions and thin films. Also reconfigurable devices, or the modulation of processes with technological interest, e.g. ink-jet printing, where the broken symmetry of fluid interfaces becomes an ideal platform for the confining of materials to fabricate materials with reduced dimensionality will benefit from particle laden interfaces. Therefore, the analysis of different aspects allowing the modulation of the assembly of particles at the interface, mainly the particle wettability and the inter-particle interactions, and the understanding of the response of particle-laden interface upon the application of external stimuli (mechanical, thermal, magnetic or electric) become of paramount importance. The behavior of particle-laden fluid interfaces is governed by a complex interplay between the individual and collective behavior of the trapped colloids which confer novel mechanical (shear and dilational) and functional properties to the fluid interface. These properties emerge strongly dependent on the specific chemistry, moprhology, wettability and charge of the considered colloids as well as on the modification of their surface by addition of surfactants or covalent binding of other types of molecules. Nowadays, there is a reasonably good understanding on the behavior of single hard particles at fluid interfaces. However, the current knowledge on the behavior of soft particles as well as of particlemediated interactions and the collective behavior of particle-laden fluid interfaces remain relatively poor. Therefore, it is necessary to move the research on particle-laden interfaces to such topics. In fact, the interactions are responsible of the ability of particle for migrating, being dispersed or assembly at the interface, resulting in specific ordered structures which in turn define the mechanical behavior of the particleladen interface. This is very important because defines the high stability of Pickering emulsions and particle-stabilized foams. Furthermore, the dynamical behavior of particles trapped at fluid interfaces also requires further studies. In fact, colloid adsorbed at fluid interfaces show very different motion pathways than colloids in the bulk. The characterization of the dynamical aspects are not only important itself, and the potential application of particles as microrheological traces requires to understand the motion of individual particles. On the other side, the understanding of the dynamics of particle-laden interfaces becomes very important because they play a very important role on the behavior on active colloids trapped at fluid interfaces. These offers very interesting dynamic behavior and phase transitions which deserveds further attention. This review has tried to present a broad perspective to the study of particle-laden interface, which makes this review an excellent guide for researchers and technologist addressing for first time problems related to particle-laden interface as well as for experienced researcher trying to exploit the whole potential of particle-laden fluid interfaces for opening new avenues in nanoscience and nanotechnology. CRediT authorship contribution statement Eduardo Guzm´ an: Conceptualization, Methodology, Software, Data curation, Writing – original draft, Writing – review & editing, Investigation, Visualization, Funding acquisition. Fernando MartínezPedrero: Conceptualization, Methodology, Software, Data curation, Writing – original draft, Writing – review & editing, Investigation, Visualization, Funding acquisition. Carles Calero: Writing – original draft, Writing – review & editing, Investigation. Armando Maestro: Writing – original draft, Writing – review & editing, Investigation. Francisco Ortega: Supervision, Validation, Writing – review & editing, Resources, Investigation, Funding acquisition. Ram´ on G. Rubio: Supervision, Validation, Investigation, Writing – review & editing, Resources, Project administration, Funding acquisition. Declaration of Competing Interest The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. Acknowledgements This work was funded by MICINN under grants PID2019-105343GBI00 and PID2019-106557GB-C21, and by EU in the framework of the European Innovative Training Network-Marie Sklodowska-Curie Action NanoPaInt (grant agreement 955612). We thank Patricia GuisadoBarrado for her help in adapting Fig. 3. E. Guzm´ an et al. Advances in Colloid and Interface Science 302 (2022) 102620 40 References [1] Shi S, Russell TP. Nanoparticle assembly at liquid–liquid interfaces: from the nanoscale to mesoscale. Adv. Mater. 2018;30:1800714. [2] Forth J, Kim PY, Xie G, Liu X, Helms BA, Russell TP. Building reconfigurable devices using complex liquid–fluid interfaces. Adv. Mater. 2019;31:1806370. [3] Zabiegaj D, Santini E, Ferrari M, Liggieri L, Ravera F. 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