Document [original]

Influence of Different Silica Nanoparticles on

Drop Size Distributions in Agitated Liquid-Liquid

Systems

Susanne Ro¨ hl*, Lena Hohl, Maresa Kempin, Frauke Enders, Nico Jurtz, and Matthias Kraume

DOI: 10.1002/cite.201900049

This is an open access article under the terms of the Creative Commons Attribution License, which permits use,

distribution and reproduction in any medium, provided the original work is properly cited.

Dedicated to Prof. Dr. techn. Hans-Jo¨ rg Bart on the occasion of his 65th birthday

The impact of different silica nanoparticles on rheology, interfacial tension and drop size distributions in liquid-liquid sys-

tems is determined experimentally. The particles vary in wettability and specific surface area. In contrast to commonly

used high-energy devices for Pickering emulsion preparation, low energy input by stirring allows to quantify drop break-

age and coalescence in steady state and dynamic conditions. The experiments can provide essential information for drop

size model development in nanoparticle-stabilized emulsions.

Keywords: Coalescence, Dispersion, Drop size distribution, Endoscope, Pickering emulsion, Stirred tank

Received: February 27, 2019; accepted: August 23, 2019

1 Introduction

Nanoparticles can be applied as emulsifying agents to stabi-

lize liquid-liquid systems towards coalescence (Pickering

emulsions) [1, 2]. Due to the adsorption of nanoparticles at

the liquid-liquid interface, coalescence is hindered or

arrested, and smaller drop size distributions and a higher in-

terfacial area can be achieved [3–5]. The higher interfacial

area promotes mass transfer so that nanoparticles can be

used as innovative additives for liquid-liquid reactions [6, 7].

However, the particles can also lead to an additional mass

transfer resistance if they are densely packed at the liquid-liq-

uid interface. It is crucial to understand the impact of particle

characteristics such as shape, size and surface modification

on their spatial arrangement at the interface, the drop size

distributions and the resulting mass transfer [8]. To achieve a

long-term stabilization of Pickering emulsions against coa-

lescence, small droplet sizes are needed [9]. These are often

realized by using high-energy dispersion units for emulsion

preparation, such as ultrasonication or rotor-stator homoge-

nizers. The formulation parameters and the corresponding

final emulsion properties have been investigated by various

authors [6, 7, 9–12]. However, for large-scale industrial appli-

cations with Pickering emulsions as innovative reaction sys-

tems, high energy consumption during emulsion preparation

should be avoided in order to achieve an economically viable

process. Furthermore, there still is a gap of knowledge con-

cerning the detailed emulsification mechanisms [13].

The aim of this work is to determine the influence of dif-

ferent silica nanoparticles on the dynamic and steady-state

drop size distributions at comparatively low energy dissipa-

tion rates induced by stirring. Therefore, an in situ endo-

scope measurement technique and image analysis is

applied. The silica nanoparticles vary in specific particle

surface area, determined via the Brunauer-Emmett-Teller

(BET) method [14], and in residual silanol content, which

affects the particle wettability, contact angles and adsorption

energies at the liquid-liquid interface [15]. To achieve a

thorough understanding of the emulsification process, the

impact of the nanoparticles on rheology and interfacial ten-

sion is investigated since these are crucial parameters for

dispersion and coalescence. Furthermore, drop size distri-

bution characteristics are analyzed as a function of agitation

speed, particle type and particle mass fraction in w/o and o/

w emulsions. In future studies, these results can be used to

adapt existing drop size distribution models for liquid-

liquid systems to the case of nanoparticle-stabilized disper-

sions.

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–

Susanne Ro¨hl, Dr.-Ing. Lena Hohl, Maresa Kempin, Frauke Enders,

Nico Jurtz, Prof. Dr.-Ing. Matthias Kraume

[email protected]

Technische Universita¨t Berlin, Chair of Chemical and Process

Engineering, Ackerstraße 76, 13355 Berlin, Germany.

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2 State of the Art

In this section, the current state of the art concerning rheol-

ogy of nanoparticle suspensions, interfacial phenomena and

drop size distributions is summarized.

2.1 Rheological Properties of Silica Nanoparticle

Suspensions

Dispersion, coalescence and the resulting drop size distribu-

tion depend on parameters such as density, interfacial ten-

sion and the viscosity of the dispersed and continuous

phase. The presence of nanoparticles in a liquid phase can

lead to complex rheological behavior, especially if the nano-

particles possess an irregular shape. Nanoparticle suspen-

sions are often shear thinning with viscoelastic properties

[16–18]. The flow curves and the viscoelastic response

depend on the chemical and morphological structure of the

nanoparticles and their interaction with the liquid phase.

Different types of interactions (particle-particle or particle-

liquid) are dominant and can provoke agglomeration pro-

cesses [19]. The viscosity of the oil-nanoparticle suspen-

sions depends considerably on the nanoparticles silanol

content [20]. Strong hydrogen bonds exist between the sila-

nol groups of particles, whereas the interaction of silanol

groups with weakly hydrogen-bonding liquids is less pro-

nounced [21]. Hence, particle-particle interactions are dom-

inant in comparison to particle-liquid interactions, espe-

cially in case of particles with high silanol content dispersed

in a nonpolar phase.

Viscoelastic fluids exhibit elastic and viscous characteris-

tics. Gel-like viscoelastic behavior with a loss factor of

tan d=G†/G¢< 1 often occurs in Pickering emulsions (stor-

age modulus G¢> loss modulus G†). Particles with a lower re-

sidual silanol content (25 % SiOH) develop less or smaller ag-

glomerates, which seem to be distributed more evenly in the

organic phase in comparison to more hydrophilic particles

(50 % SiOH) [20]. Furthermore, nanopar-

ticle suspensions often show a yield stress,

which is defined as the stress that must be

applied to the sample before it begins to

flow. Below this critical value, the sample

deforms elastically, and Hooke’s law is

valid. The elastic flow is a reversible pro-

cess and governed by the interaction of

the dispersed phase and the particles. The

reasons for the appearance of a yield

stress are intermolecular physical interac-

tions with bond energies below 20 kJ mol

–

[22]. Knowledge of the shear thinning

behavior, viscoelastic properties and yield

stress of the systems is crucial since it af-

fects the fluid dynamics in different parts

of the intended process, such as pumping,

emulsification and separation [12, 23].

2.2 Adsorption of Nanoparticles at the Liquid-

Liquid Interface

The stabilizing effect of nanoparticles in dispersions is

caused by their high adsorption energy at the liquid-liquid

interface, as compiled by Bresme and Oettel [24]. Their sur-

vey includes the adsorption of nanoparticles in terms of sta-

bility, self-assembly and mutual interactions of nanoparti-

cles at the liquid-liquid interface [24]. For a single spherical

particle, which is small enough that a deformation of the

interface due to gravity can be neglected, an equation to cal-

culate the energy of particle detachment from the interface

can be derived. Therefore, the free energy of the system in

two different states needs to be taken into account (see

Fig. 1): a) the equilibrium position of a particle at the inter-

face and b) the state when the particle is completely

immersed in either the aqueous or the organic phase.

The adsorption energy for spherical particles depends on

the particle radius R, the contact angle qmeasured in the aque-

ous phase and the liquid-liquid interfacial tension s

o,w

[9]:

Eads ¼pR2so;w1–cosqðÞ

2(1)

The term within the brackets becomes negative if the par-

ticle is moved from the interface into the aqueous phase

and positive if it is moved into the organic phase [9].

Hydrophilic silica particles lead to low contact angles

(q<90) and promote the formation of o/w emulsions,

whereas hydrophobic particles lead to high contact angles

(q>90) and promote the formation of w/o emulsions

[15, 25]. Usually the particles are dispersed in the liquid

with higher wettability and this liquid becomes the continu-

ous phase, which is in accordance with the Bancroft rule

[26]. Most stable emulsions are formed using partially

hydrophobic silica particles that have contact angles close

to 90and can stabilize both o/w and w/o emulsions [5, 27].

For nonspherical particles with irregular shape, the deter-

mination of a contact angle at the liquid-liquid interface is

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Figure 1. Spherical solid particle a) attached to the oil-water interface with immersion

depth h

and contact angle qand b) completely detached into the organic phase (ac-

cording to [9]).

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difficult due to the different possible particle orientations.

Therefore, the description of their adsorption behavior and

the determination of the adsorption energy is challenging.

The influence of particle geometry on the adsorption was

investigated amongst others by Faraudo and Bresme [28]

who investigated prolate and oblate particles with parallel

or perpendicular orientation with respect to the interface

plane. They found that nonspherical particles do not adsorb

at the interface if their aspect ratio bis larger than a critical

aspect ratio b

. Line tension and particle orientation also

play a major role in terms of stability of nonspherical par-

ticles at the interface. The adsorption process and the ener-

gy needed to remove the particles from the liquid-liquid

interface depend on particle wettability and directly influ-

ence the coalescence behavior and the drop size distribu-

tions of the systems. The particle size is another parameter

influencing the drop size distribution. Tsabet et al. [13]

investigated the impact of spherical glass beads with differ-

ent size but identical contact angle on the drop size distri-

bution in an agitated liquid-liquid system. With increasing

particle size higher Sauter mean diameter occurred. A larger

particle size influences the particle-drop collision force and

the film drainage process. Additionally, the degree of inter-

face coverage decreases, the wetted depth of the particle at

the interface rises and higher adsorption times occur [13].

2.3 Drop Size Distribution in Agitated Liquid-Liquid

Systems

The breakage and coalescence phenomena in stirred liquid-

liquid systems and the resulting drop size distribution are

defined by parameters such as tank and stirrer geometry,

agitation speed (energy dissipation rate) and the physical

properties such as viscosity, density and interfacial tension.

For common liquid-liquid systems, various approaches to

predict mean drop diameters or the whole drop size distri-

butions can be found in literature. Semi empirical equations

with the dimensionless Weber number can estimate the

Sauter mean diameter in breakage-dominated systems and

are often based on the correlation by Hinze [29] with d

~We

–0.6

. Coulaloglou and Tavlarides [30] published a modi-

fied empirical correlation for the Sauter mean diameter cal-

culation in Newtonian fluids which also takes the volume

fraction of the dispersed phase into account. Calabrese et al.

[31] modified the Weber correlation by the viscosity vessel

number, which also considers the viscosity of the dispersed

phase for Newtonian fluids.

A more elaborate approach to predict drop size distribu-

tions are population balance equations (PBEs), which are

often coupled with computational fluid dynamics (CFD) to

account for the local fluid dynamics. They allow describing

systems where coalescence cannot be neglected and include

equations for the drop breakage rate, drop-drop collision

frequency and drop coalescence efficiency, the number of

daughter drops per breakage event and the daughter drop

size distribution [30, 32, 33]. However, most PBE models

assume deformable droplets with mobile interfaces, which

is often not the case in presence of additives and especially

in presence of solid nanoparticles [8]. So far, the accurate

description of drop size distributions in presence of addi-

tives still is a challenging task and various submodels have

been developed in order to describe, e.g., the effect of pH,

ions or surfactants [34–36]. In contrast to surfactants, no

appreciable reduction of the interfacial tension in presence

of nanoparticles occurs, although this also depends on the

nanoparticle type and modification [37–39]. Often the

changes in physical properties such as density, interfacial

tension and viscosity do not suffice to adequately predict

the system behavior, so that empirical parameters need to

be fitted to a given material system.

The stabilization of droplets by nanoparticles is described

with two different criteria in literature: A thermodynamic

approach considering that stability is achieved when the

system reaches its minimal free energy, or a mechanical

approach considering that stability is reached when the sum

of forces is zero [13]. During the emulsification process,

droplet breakage, particle/droplet approach, particle

adsorption and a particle network formation leading to

droplet stabilization has to occur [13]. Hence, the contact

angle respectively the hydrophobicity of the nanoparticles

[20] and the surface coverage respectively the nanoparticle

concentration [8] possess an influence on the drop size dis-

tributions. Due to the rheological properties particularly at

high nanoparticle mass fractions and the steric barrier

caused by the presence of nanoparticles at the interface

[8, 13], an impact on drop deformation, drainage time and

film rupture during coalescence occurs.

The effects of formulation on the final emulsion proper-

ties produced with a high energy input by ultrasonication

were already investigated by numerous authors [4, 10, 12,

20, 23, 27, 40, 40, 41]. These emulsions often are stable

towards coalescence over a long period due to droplet sizes

in the range of a few micrometers. A rising nanoparticle

content leads to smaller drop sizes until a constant value is

reached and the interface of all generated droplets can be

completely covered with particles.

The influence of the energy input is amongst others

investigated by Skale et al. [42] who compared the disper-

sion devices ultrasonication and ultraturrax. However, there

still is a lack of studies investigating the energy input. The

final drop size distribution is governed by two effects: If

enough particles are available to cover the complete interfa-

cial area, the final drop size distribution is determined by

the interface generation capacity of the dispersion device. If

the particle concentration does not suffice to cover the com-

plete interface, coalescence occurs until the interface is com-

pletely covered and the final drop size distribution is gov-

erned by the coverage capacity [13]. However, the

dispersion and coalescence mechanisms are barely under-

stood [13]. Previous studies that considered this often

focused on characteristic diameters rather than the com-

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plete drop size distribution. The work by Tsabet and

Fradette [13] is one of the few examples where energy input

induced by stirring was used in order to achieve a fundamen-

tal understanding of the emulsification mechanisms itself. A

comparison of o/w emulsions in an agitated tank stabilized

with regular and modified glass particles showed that droplet

stabilization is highly sensitive to the viscosity of the dis-

persed organic phase, particle size and particle wettability.

High oil/particle affinity led to emulsions with the smallest

drop sizes and a narrow drop size distribution [13].

The sedimentation of droplet swarms is extremely sensi-

tive to droplet size, dispersed phase fraction and rheology

[43]. Furthermore drop-drop and drop-interface coalescence

rates in concentrated emulsions are important parameters

for the long-term emulsion stability [36, 43, 44], which can

be analyzed by observing the sedimentation and the height of

the completely coalesced interface over time with an external

camera. If the sedimentation speed exceeds the coalescence, a

dense-packed zone is formed where droplets deform and

grow in size until they coalesce with the interface. In case of

very low coalescence rates, other effects such as Ostwald rip-

ening in the dense-packed zone can become relevant.

This work aims to analyze the dispersion and coalescence

mechanisms with a detailed drop size distribution analysis

in stirred tanks. The complex rheological behavior and the

impact of nanoparticles with different characteristics at the

interface are effects that need to be considered in future

modeling approaches. Thereby, the stirred systems possess a

significantly lower energy input compared to the systems

dispersed via ultrasonication, so that not only the final emul-

sion characteristics are quantified. The impact of silica par-

ticles with different BET values and hydrophobicity on physi-

cal properties, dispersion and coalescence was quantified.

The influence of nanoparticles on the coalescence behavior is

also investigated with batch settling experiments by optical

evaluation of the dynamic phase separation process [44].

3 Materials and Methods

The used substances were n-heptane (Merck, purity

‡99 %), ultrapure water (k= 0.055 S cm

–1

, Purelab flex 2,

Elga) and different silica particles. The composition of the

systems is described using the oil mass fraction a, the mass

fraction of particles w

in relation to the mass of dispersed

phase and the mass fraction of particles w

p,s

in a suspen-

sion:

a¼mnheptane

mnheptane þmwater

(2)

wp¼mparticles

mdispersed phase þmparticles

(3)

wp;s¼mparticles

mnheptan þmparticles

(4)

3.1 Properties of Silica Nanoparticle

Fumed silica particles with different hydrophobicity and a

fractal-like, irregular shape (Wacker Chemie AG) were

used, which were manufactured by flame pyrolysis and hy-

drophobized with dichlorodimethylsilane to two extents

(50 % SiOH and 25 % SiOH). The particles possess more-

over different specific surface areas (BET values) as summa-

rized in Tab. 1. They were used without additional chemical

modification. The fused aggregates of primary particles pos-

sess an average size of F

= 150 nm and F

= 50 nm [8]. The

irregular shape of the particles is clearly visible in scanning

electron microsopy (SEM) images, as depicted for example

in [12, 20].

The adsorption energies of the particles (Eq. (1)) were cal-

culated with the interfacial tension s

o,w

= 52.0 ± 0.3 mN m

–1

measured by pendant drop method at T= 293 K (cf. Sect. 3.4).

Due to their different residual silanol content H20 and H30

particles might have a lower contact angle closer to 90in

comparison to the more hydrophobic particles H18 with

contact angles greater 90. The impact of the size on the

adsorption energy is exemplary calculated for two different

radii and two contact angles, which represents the relevant

range in this work. For a constant particle size, the more

hydrophobic particles (H18) will not adhere to the interface

as strongly as H20 and H30 due to their higher contact angle

that reduces the adsorption energy (cf. Tab. 2). The calcula-

tion is a rough estimation, since the specific particle surface

area and different possible particle orientations at the inter-

face due to the particle polydispersity were disregarded.

A variation in specific surface area can influence the size

and spatial complexity of the particles. Hence, the BET

value might influence the attachment and interlocking of

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Table 1. Properties of the silicia nanoparticles according to

manufacturer specifications.

Name SiOH content

[%]

specific particle surface (BET)

–1

]

HDK H20 50 200 ± 30

HDK H18 25 200 ± 30

HDK H30 50 250 ± 30

Table 2. Calculated adsorption energy for particles at the water/

n-heptane interface at T= 293 K for s

o,w

= 52.0 ± 0.3 mN m

–1

with

variation of contact angle and size.

Particles radius r

[nm]

Contact angle q

[]

Adsorption energy E

ads

[kT]

50 90 1986

100 90 3972

100 120 993

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particles at the interface, which can result in different con-

tact angles and adsorption energies. Consequently, the drop

sizes in emulsions may differ for varying BET values.

3.2 Density of Pure Components and Suspensions

The density of the pure components according to manu-

facturer specifications and literature are r(n–heptane) =

683 kg m

–3

,r(water) = 998.20 kg m

–3

and r(particles) =

2200 kg m

–3

at T= 293 K. The densities of the n-heptane/

nanoparticle suspensions are summarized in Tab. 3 as a

function of particle mass fraction. They were calculated

using the respective particle mass fractions while neglect-

ing possible excess volume. Since the different silica parti-

cle types possess the same density, no differences between

HDK H18, H20 and H30 suspensions occur.

For rheological and interfacial tension measurements the

particles were dispersed in n-heptane with an ultrasonica-

tion homogenizer (Bandelin Sonopulus HD70, P=70W,

f= 20 kHz, 75 % amplitude) for 5 min. The sample volume

was V= 0.05 L per batch. The second liquid phase for the

interfacial tension and drop size measurements was ultra-

pure water. For the drop size measurements in agitated sys-

tems, nanoparticles were added to the tank without pre-

vious suspension to avoid the use of additional dispersion

devices. No remarkable change in drop size distribution was

observed while comparing the addition of nanoparticles

with or without previous suspension.

3.3 Suspension Rheology

Rheological measurements were conducted using a tem-

pered cone and plate geometry (Anton Paar MCR 302,

Measurement system CP60-1: cone diameter 59.978 mm,

angle 1.008, gap size 0.117 mm). All measurements were

performed at T= 293 ± 0.1 K. The independence of the

results from the measurement time per data point was

checked in order to exclude an influence on the flow curves

and oscillatory measurements. Shear rate, shear stress, de-

formation and angular frequency were increased in loga-

rithmic scale. Before each experiment, the samples were

freshly produced by ultrasonication and rested on the plate

until a normal force of F

= 0 N was achieved. The yield

stress was determined experimentally in this work to avoid

approximation errors due to the choice of regression mod-

els, analysis area and shape of the curve.

3.4 Interfacial Tension

The liquid-liquid interfacial tensions were measured via

pendant drop method (Dataphysics OCA15). To verify the

purity of all device components, the interfacial tension of

pure n-heptane against water (s

o,w

= 52.0 ± 0.3 mN m

–1

T= 293 K) was checked against literature values

o,w

= 51.24 mN m

–1

[45]) before each measurement. A

droplet of n-heptane/ nanoparticle suspensions was created

at the tip of a bent nozzle pending in water. The drop vol-

ume was maintained as high as possible (> 15 mL) to mini-

mize errors during the optical evaluation method. The mea-

surements were carried out in a tempered measuring cell at

T= 293 ± 0.1 K. Steady-state values were taken after the

interfacial tension reached a constant value and at least

three replicate measurements were carried out.

3.5 Agitated Tank

Drop size measurements were performed in a temperature-

controlled agitated tank at T= 293 ± 0.1 K (cf. Fig. 2a). The

total volume was kept constant at V= 700 mL. The tank

dimensions were D= 0.1 m, H/D= 1.6, h

/D= 1.7,

/D= 0.45, and h

/D= 0.45. A Rushton turbine

= 0.045 m, d

= 0.045 m, blade height h

= 0.006 m,

width w

= 0.01 m, thickness s

= 0.001 m) and four rect-

angular baffles (height h

= 0.12 m, width w

= 0.07 m,

thickness s

= 0.001 m) were used. Stirrer speeds of n= 700,

800 and 900 rpm were investigated, which correspond to

energy dissipation rates determined by using torque mea-

surements in the range of e»0.9–2.1 W kg

–1

. Drop sizes

were measured in situ with an endoscope technique (Sopat

GmbH) connected to a camera (GX 2750, Allied Visions

Technology). Two different endoscopes with transflexion

principle were used with a measurement range of particle

diameters between 8–600 mm and 25–1000 mm. The endo-

scope was positioned at stirrer height in a horizontal dis-

tance of 0.01 m to the stirrer. To improve image quality, a

mirror was attached to the tip of the endoscope with a gap

size of 0.006 m. Image analysis was carried out with an algo-

rithm for automated drop detection (Sopat GmbH).

The shear rate distribution inside the tank was estimated

with computational fluid dynamics using the commercial

software StarCCM+. The simulations were performed

under steady-state conditions using a moving reference

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Table 3. Calculated densities of the n-heptane/silica nanoparti-

cle suspensions (T= 293 K).

p,s

[wt %] Density r[kg m

–3

]

0.05 683.24

0.15 683.71

0.25 684.18

0.5 685.36

0.75 685.55

1 687.74

2 692.55

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frame with the realizable k-eturbulence model. A polyhe-

dral mesh was used, and the emulsion was approximated as

a homogeneous mixture with a specified mixture density

and a shear rate dependent viscosity, by fitting experimental

flow curves with the Carreau model. The magnitude of the

symmetric velocity gradient tensor was used as a measure

for the shear rate, as proposed by Wollny [47]. The repre-

sentative shear rate near the stirrer was evaluated in a cylin-

drical element with the dimensions h

crit

= 0.023 m and

crit

= 0.025 m around the stirrer. The shear rates in the bulk

phase were evaluated in the circulating zones of the tank

outside the specified stirrer range.

Batch settling experiments were carried out in the same

vessel to achieve additional information on the coalescence

behavior by determination of sedimentation velocity and

separation time (Fig. 2a). Pictures were taken in defined

time steps after agitation stop with an external single lens

reflex camera (Canon EOS 700 D). The coalescence curve

signifies the height of the completely coalesced interface, as

shown schematically in Fig. 2b). The slope of the sedimenta-

tion curve can be used to estimate the sedimentation veloci-

ty v

=dh

/dtof the droplet swarm assuming that no coales-

cence occurs during free sedimentation [44]. The

sedimentation velocity can also be calculated with a swarm

sedimentation model based on the drop size measurements

and vice versa [44, 46].

4 Results and Discussion

The results concerning suspension rheology, interfacial ten-

sion and drop size distribution characteristics are provided

in the following.

4.1 Suspension Rheology

Pure n-heptane and water possess Newtonian rheological

behavior. The three investigated nanoparticle types are

partly hydrophobic and can only be suspended in the

organic phase. For the following rheological analysis, three

replicate measurements of the suspensions were performed.

To improve graph clarity, the results are shown as arithme-

tic mean values without error bars. The maximal relative

error of the dynamic viscosity calculated by the standard

deviation of three replicate measurements was ±15 % for

low shear rates (_

g= 1–10 s

–1

) and 9 % for higher shear rates

g= 10 – 1000 s

–1

). The deformation at given shear stress

within the elastic region had a maximal relative error of

±22 %.

All investigated nanoparticle suspensions show shear

thinning flow behavior. With increasing particle mass frac-

tion, the flow curves are shifted towards higher viscosities,

as is exemplary shown for HDK H20 particles in Fig. 3a.

The suspended particles formed particle-particle agglom-

erate network structures due to their fractal and irregular

shape, which break up with increasing shear rate [20].

Agglomerates could also be formed due to hydrogen bond-

ing between particles and n-heptane. In comparison to a

more hydrophobic solvent (e.g., 1-dodecene) [20], the flow

curves with n-heptane were shifted towards higher viscosi-

ties, caused by a higher hydrogen bonding ability of n-hep-

tane in comparison to 1-dodecene. For w

p,s

= 0.5–2 wt %

the systems exhibited a region with dilatant flow that led to

a local maximum of dynamic viscosity. It became more pro-

nounced with increasing particle mass fractions. This could

be caused by a reorientation and accumulation of the par-

ticles at shear rates between _

g= 20–50 s

–1

. In stirred tanks, a

broad range of shear rates can occur due to local fluid

dynamics and internals (e.g., distance to the stirrer) so that

the dependency of dynamic viscosity on shear rate and its

effect on drop breakage and coalescence phenomena should

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Figure 2. a) Experimental setup with endoscope technique and external camera, b) scheme of batch settling experiments (according to

[44]).

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be evaluated with care. Calabrese et al. [31] investigated the

impact of the dispersed phase viscosity on drop size distribu-

tions in stirred tanks with different silicone oils of Newtonian

rheology while keeping the interfacial tension and densities

approximately constant. They determined an increase of

Sauter mean diameter by a factor of approximately 2.3 if the

dispersed phase viscosity increased from 0.1 to 0.5 Pa s. For

these viscosities, the drop sizes were normally distributed,

whereas they became lognormal for higher viscosities around

5 Pa s. Due to small dispersed phase fractions, the assump-

tion of a breakage-dominated system without coalescence

and spatial independence of the steady-state drop size distri-

bution was applied. Tsabet and Fradette [13] compared

different oils, which mainly varied in dynamic viscosity

(h= 0.00953–4.88 Pa s) and density (r= 935–975 kg m

–3

The oils were dispersed in glass particle-water suspensions.

For constant particle concentration, mixing time and stirrer

speed they observed constant distribution widths (based on

v,10

v,90

and d

) and nearly constant diameters for oils

with h< 0.4855 Pa s. In this range, the droplet size was deter-

mined by the coverage potential or the particle concentra-

tion. At higher viscosities, the entire emulsification process

was influenced by the interface generation capacity (power

input) and the distribution width increased.

In Fig. 3b the impact of rising

particle mass fraction on the

deformation over shear stress is il-

lustrated for HDK H20 particles

in n-heptane. The slope of the

deformation changes between the

linear-elastic and viscous defor-

mation regime mostly with a

sharp bend [22]. The change in

slope determines the yield stress

that needs to be applied before the

samples begins to flow. The first

change of slope in the systems

presented here is shifted towards

higher values with increasing

particle mass fraction and an

increase over two decades from

= 0.01 Pa (w

p,s

= 0.05 wt %) to t

= 5 Pa (w

p,s

= 2 wt %)

arises. Hence, the shear modulus G=t/grose in the elastic

region with increasing particle concentration. This trend is

in accordance with literature [16, 48]. A yield transition

range instead of a sharp yield point occurred for suspen-

sions with low particle mass fractions (w

p,s

= 0.05 wt % and

p,s

= 0.25 wt %). It has to be considered that the deter-

mined yield stresses depend on the measurement condi-

tions, like the rotation speed resolution of the rheometer.

The effect of nanoparticle types with different silanol con-

tent (i.e., hydrophobicity) and different specific surface

areas are illustrated in Fig. 4a using the relative viscosity. It

is defined by the quotient of the dynamic suspension viscos-

ity at a shear rate of _

g= 100 s

–1

and the dynamic viscosity of

pure n-heptane:

hr¼h_

g¼100 1=s

hnheptane

(5)

With rising particle mass fraction, the increase of relative

viscosity became more pronounced for H20 in comparison

to H30 and H18 particles. The relative viscosity rose by a

factor of 22 between w

p,s

= 0 wt % and w

p,s

= 1 wt % for

H20, but only by a factor of 2.6 for H30 and H18.

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Figure 3. Suspension rheol-

ogy of HDK H20 particles in

n-heptane with different

HDK H20 particle mass frac-

tions. a) Dynamic viscosity

as a function of shear rate,

b) deformation as a func-

tion of shear stress.

Figure 4. a) Relative dynamic viscosity as a function of particle mass fraction for HDK H20, H30

and H18 suspended in n-heptane, b) frequency sweep measurements of HDK H20/n-heptan sus-

pensions for w

p,s

= 0.25 and 1 wt % values are illustrated for g= 0.4 %, T= 293 K.

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With CFD simulations, the volumetric mean value of the

representative shear rate was calculated as described in Sect.

3.5 around the stirrer (V

stirrer

) and in the bulk phase (V

bulk

)

of the reactor. The calculations are summarized in Tab. 4

and were performed for pure water and for o/w emulsions

(a= 0.15) with n-heptane stabilized by HDK H20 particles

with w

= 0.5 wt % and w

= 1 wt %. Agitation speeds of

n= 700 rpm and n= 900 rpm were examined in steady

state.

The impact of higher agitation speeds on the shear rates

is clearly visible for all material systems, especially in the

volume around the stirrer. For rising nanoparticle content

and increased shear-thinning behavior, the shear rates in

the stirrer region are barely affected. Larger differences

occur in the bulk volume while comparing 0.5 wt % and

1 wt % of particles. Due to the shear-thinning rheology of

the dispersed phase in the systems presented here, an esti-

mation of the impact of the dynamic viscosities on the drop

size distributions is not trivial. The drop breakage should

mainly occur in regions with large shear rates (V

stirrer

where differences between particle concentrations and par-

ticle types are less pronounced and the viscosity is compara-

tively low (cf. Fig. 4a and Tab. 4). However, the shear rates

and corresponding viscosities vary significantly between the

bulk phase and the region in vicinity to the stirrer. In con-

trast to the aforementioned work

by Calabrese et al. [31] coales-

cence cannot be neglected in this

work due to the higher dispersed

phase fractions and the depend-

ency of coalescence on the nano-

particle mass fraction. Coales-

cence will mainly occur in the

bulk phase, where lower shear

rates or higher viscosities exist in

comparison to the volume near

the stirrer (cf. Tab. 4 and Fig. 3a).

Higher viscosities usually hinder

the coalescence probability since

it influences the flow during film

drainage, the drag coefficient, the

relative velocity of the droplets

and the velocity boundary condi-

tion of the drainage flow [36].

The nanoparticle suspensions

also showed viscoelastic flow

properties, which were character-

ized using oscillatory measure-

ments. The linear viscoelastic

(LVE) area and an appropriate

deformation (g= 0.4 %) were

determined with an amplitude

sweep. Frequency sweeps for two

H20 particle concentrations are

shown in Fig. 4b. Viscoelastic

flow behavior with G¢>G†

occurred, which corresponds to gel character of the suspen-

sions. With higher nanoparticle content the moduli were

shifted towards higher values. For low frequencies, nearly

constant storage and loss moduli were observed, indicating

stability of the suspensions towards sedimentation.

The rheological properties of the investigated nanoparti-

cle suspensions are complex, which has an impact on the

flow field in the tank and can have a significant influence

on the drop breakage, the number of daughter droplets, the

deformation and film drainage during coalescence, and the

resulting droplet size distribution. In the following, the

impact of nanoparticles on the interfacial tension will be

discussed before the drop size distributions themselves are

quantified.

4.2 Interfacial Tension

The liquid-liquid interfacial tension was measured for dif-

ferent nanoparticle mass fractions and all three nanoparticle

types. Fig. 5a shows the equilibrium interfacial tensions for

HDK H20 particles as an example. The error bars indicate

an experimental error of 2 %, which was the maximum per-

centage deviation in three replicate measurements. The

nanoparticles barely influenced the interfacial tension, since

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Table 4. Volumetric mean values of calculated representative shear rates _

g[s

–1

] with CFD in the

volume around the stirrer (V

stirrer

) and in the bulk phase (V

bulk

Composition Shear rate _

g[s

–1

]

n= 700 rpm, V

stirrer

n= 900 rpm, V

stirrer

n= 700 rpm, V

bulk

n= 900 rpm, V

bulk

Water 163 210 39 50

a= 0.15,

= 0.5 wt %

168 219 34 58

a= 0.15,

= 1 wt %

159 215 16 32

Figure 5. Liquid-liquid interfacial tension of HDK H20 suspended in n-heptane against water,

T= 293 K a) for different particle concentrations in steady state, b) dynamic interfacial tension

for w

= 0.05 wt %.

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the values fluctuate in the range of the error bars. The same

result was achieved with HDK H18 and HDK H30 particles

(see Tab. 5). The transient curve for a particle mass fraction

of w

= 0.05 wt % depicted in Fig. 5b shows that the mea-

surement time was long enough to achieve a constant equi-

librium interfacial tension value.

The impact of nanoparticles on the interfacial and surface

tension is discussed controversially in literature. Nanoparti-

cles adsorb at the liquid-liquid interface, but it is not clearly

pointed out if a reduction of interfacial tension should occur.

Constant surface and interfacial tensions were observed for

example for silica particles at different pH values and particle

concentrations, for hydrophobized silica nanoparticles with

rising particle mass fractions up to 1 wt % at constant pH

[38], or for aqueous suspensions of spherical silica nanoparti-

cles with particle diameters in the range of 6–45 nm and par-

ticle volume fractions between 0.1–10 % [49].

Dugyala et al. [50] investigated aqueous suspensions with

1 wt % silica nanoparticle against decane and reported only

a slight decrease of the interfacial tension by 0.5 mN m

–1

Similar results were also found in water/1-dodecene/HDK

H20 systems under the condition that the oil phase does

not contain any surface-active impurities [8]. These results

are in agreement with the interfacial tension values shown

in Fig. 5. It should be noted that different behavior can be

observed for other nanoparticle types and with different

particle surface modifications [51–53]. A review concerning

the impact of nanoparticles on interfacial tension is pro-

vided by Fan and Striolo [39].

An alternative to interfacial tension measurements via

pendant drop method is to determine the surface pressure

with a Langmuir trough. The surface pressure pduring

compression of a particle monolayer per definition

describes the difference between the surface tension of the

pure liquid and the surface tension of the liquid phase with

particles [54]. Horozov et al. [55] reported different

increases in surface pressure while comparing HDK H20

(p=45mNm

–1

) and H18 (p= 30mNm

–1

) particles. This

impact on surface pressure and the corresponding change

in interfacial tension are not in agreement with the pendant

drop results. The main reason for this behavior could be

different degrees of interface coverage during pendant drop

and surface pressure measurements.

4.3 Drop Size Distributions

The drop size distributions were investigated as a function

of particle mass fraction in o/w and w/o emulsions with dif-

ferent particle types. Furthermore, an analysis of distribu-

tion self-similarity is performed, and the coalescence behav-

ior is determined after abrupt changes in agitation speed.

4.3.1 Influence of Particle Concentration in o/w and

w/o Emulsions

With a variation of the dispersed phase fraction induced by

a different oil/water ratio a, the systems with HDK H20

particles could be forced to develop o/w emulsions

(a= 0.15) or w/o emulsions (a= 0.85). This inversion

affected the drop breakage and coalescence phenomena and

the drop size distribution of the systems. Steady-state values

for o/w and w/o emulsions using different HDK H20

particle mass fractions at a constant stirrer speed of

900 rpm are depicted in Fig. 6a. The error for all endoscope

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Table 5. Steady state interfacial tension sof n-heptane/silica

nanoparticle suspensions of HDK H18, HDK H30 and HDK H20

particles for different particle mass fractions w

against water.

The average value of three replicate measurements is in each

case given with a maximum standard deviation for all measure-

ments of ±0.6 mN m

–1

[wt %] s

H18

[mN m

–1

H30

[mN m

–1

H20

[mN m

–1

]

0.25 52.03 50.60 51.20

0.5 51.79 52.17 51.38

1 49.6 51.87 51.69

Figure 6. Steady-state values for agitated o/w and w/o emulsions with HDK H20 particles, n= 900 rpm, T= 293 K. a) Sauter

mean diameter over particle mass fraction, b) drop size distributions for a constant particle mass fraction of w

= 1 wt %.

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measurements is assumed to be ±20 mm while also consider-

ing the error due to the automated drop detection [56].

With increasing particle mass fraction, the Sauter mean

diameters of both emulsion types decreased, which is in ac-

cordance with literature [4, 10, 13]. The higher number of

particles led to rising interface coverage so that coalescence

was more effectively hindered and smaller droplets oc-

curred.

The general shape of the curves is in accordance with the

ones described by Chevalier [41]. Larger Sauter mean diam-

eters occurred in w/o emulsions for low particle mass frac-

tions. This difference reduced with rising particle content

until nearly the same Sauter mean diameters existed at a

particle mass fraction of w

= 1 %. The corresponding cu-

mulative distributions of number Q

for w

= 1 % are shown

in Fig. 6b and characteristic diameters are summarized in

Tab. 6. A comparison of the minimum and maximum di-

ameters d

min

and d

max

and the number- and volume-based

spans (span

,span

) clearly indicates differences in the dis-

tribution widths. The drop size distribution of the w/o

emulsion (a= 0.85) in Fig. 6b had a smaller minimum and

larger maximum diameter and the complete distribution

spanned a wider droplet size range in comparison to a=

0.15. Hence, the similar Sauter mean diameters were mainly

a coincidence and do not allow drawing detailed conclu-

sions for the actual drop size distributions in o/w and w/o

emulsions.

In both systems, nonspherical droplets were observed (cf.

Fig. 6, right). At high particle concentrations, the surface

coverage of the particles is so high that the nanoparticles in-

terlock and arrested coalescence occurs. Due to the resulting

stiffness of the liquid-liquid interface, the deformed droplets

are not able to return into their energetically preferred

spherical shape and remain trapped in an intermediate

stage of coalescence [3, 57]. The combined surface area of

the deformed droplets is higher than the interfacial area of

spherical droplets. With the applied drop detection algo-

rithm, only spherical droplets could be determined. To

quantify how the arrested coalescence affected the auto-

mated drop detection results and the drop size distribu-

tions, a manual drop detection of nonspherical droplets was

performed using the software ImageJ. To reduce the expen-

diture of time, only the experiment with the highest amount

of nonspherical droplets (a= 0.85, HDK H20, w

=1%,n=

900 rpm, 300 images) was analyzed. In the investigated im-

age series, 2.87 % of all droplets possessed a nonspherical

shape. The circular equivalent diameter d

A,i

is used to deter-

mine the Sauter mean diameter d

Including the nonspherical droplets into the image analy-

sis increased the Sauter mean diameter by 10 mm, i.e., by

6 %. Although the image analysis clearly is flawed when it

comes to nonspherical droplets, these errors were still in the

range of expected deviations and not the reason for the ob-

served distribution shapes shown in Fig. 6b.

4.3.2 Self-Similarity

The comparison between o/w and w/o distributions in Fig. 6

b showed an immense impact of the dispersion type on the

distribution shape. Therefore, the self-similarity was investi-

gated also for other process parameters. The number-based

standard deviations s

normalized with the Sauter mean di-

ameter d

are shown in Fig. 7 for different agitation speeds,

particle mass fractions and both o/w and w/o emulsions.

Kraume et al. [58] showed that normalized standard devia-

tions in stirred tanks with water/oil systems often lead to

constant values of s

»0.32 ± 10 %. A change of coales-

cence behavior, induced for example by ions or a change of

pH, can reduce this value [58]. In w/o systems with amphi-

philic molecules a value of s

»0.35 was found while

varying agitation speed, temperature and tank geometry

[59]. In case of the nanoparticle-stabilized dispersions pre-

sented here, the values deviate around an arithmetic mean

of s

»0.32. Thereby, the values of o/w emulsions

(filled symbols) show fewer fluctuations than the values of

the w/o emulsions (blank symbols). No clear impact of the

increasing nanoparticle concentration and corresponding

reduced coalescence behavior on the s

values was ob-

served in these systems.

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Table 6. Comparison of characteristic diameters and normal-

ized drop size distribution widths of w/o and o/w emulsions sta-

bilized with HDK H20 particles w

=1 wt %.

Parameter a

0.15 (o/w) 0.85 (w/o)

[mm] 156 153

min

[mm] 69 16

max

[mm] 282 404

span

n,90

–d

n,10

n,50

[–] 0.74 2.23

span

v,90

–d

v,10

v,50

[–] 0.92 1.17

Figure 7. Normalized number-based standard deviation s

of HDK H20 emulsions in steady state for different agitation

speeds and particle mass fractions (filled symbols a= 0.15, blank

symbols a= 0.85) at T= 293 K.

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Fig. 8 shows number-based

distributions Q

and volume-

based distributions Q

for all pro-

cess conditions with the excep-

tion of the already discussed o/w

and w/o comparison. The drop

size don the abscissa was nor-

malized either with the Sauter

mean diameter or with the arith-

metic mean diameter. All distri-

butions nearly collapse onto each

other, which indicates self-simi-

larity despite variations of stirrer

speed and nanoparticle concen-

tration for a constant a= 0.15.

4.3.3 Influence of Nano-

particle Type

In Figs. 9a and 9b the Sauter

mean diameter and cumulative

distributions of number of o/w

emulsions with HDK H20 par-

ticles are compared to HDK H30

particles. The steady-state Sauter

mean diameters indicate that the

higher specific surface area of the

HDK H30 particles led to larger

Sauter mean diameters for all

particle concentrations. The same

holds true for the drop size distri-

butions, since the HDK H30 par-

ticles led to larger droplets espe-

cially above the 80 % percentile

(see Fig. 9b). Though the wetta-

bility of the particles is equal, the

coalescence was stronger inhib-

ited by particles with a lower spe-

cific surface area. If with increas-

ing BET value the fractal

structure of the particles rises,

one particle can cover a larger in-

terfacial area. However, this is

not in accordance with the lower

drop sizes at lower BET values

observed here. The higher specif-

ic surface area might influence

the contact angle and, therefore,

the attachment and collision of

the particles at the interface.

Highly irregular shaped and

larger particles might also have a positive effect on the film

drainage during coalescence. At the highest particle mass

fraction, the Sauter mean diameters still decline but already

nonspherical droplets occurred for HDK H30 and HDK

H20 at w

= 1 wt %. This leads to the conclusion that the

interface was already completely occupied with nanoparti-

cles at w

= 1 wt % and no further decline of droplet size

with rising particle mass fraction would occur.

The higher silanol content of 50 % of HDK H20 particles

led to smaller Sauter mean diameters in comparison to

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Figure 8. Cumulative drop size distribution of HDK H20 emulsions with a= 0.15 in steady state

of a) volume Q

and b) number Q

over the dimensionless drop diameter d/d

or d/d

, respec-

tively. Particle mass fraction and stirrer speed were varied, T= 293 K.

Figure 9. a) Steady-state Sauter mean diameter with different particle concentrations for HDK

H20 and HDK H30, a= 0.15, n= 900 rpm, b) cumulative drop size distribution of number for

= 0.75 wt % for HDK H20 and HDK H30 emulsions, a= 0.15, n= 900 rpm, c) steady-state

Sauter mean diameter with different particle concentrations for HDK H20 and HDK H18,

a= 0.85, n= 900 rpm, d) cumulative drop size distribution of number for w

= 0.75 % for HDK

H20 and HDK H18 emulsions, a= 0.85, n= 900 rpm and T= 293 K. A comparison of particles with

different silanol content is performed in Fig. 9c and 9d.

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HDK H18 with 25 % silanol content. The corresponding

H20 distribution of number Q

shown in Fig. 9d is shifted

towards smaller droplet sizes. The SiOH content led to dif-

ferent contact angles (cf. Tab. 2) and the result is in agree-

ment with the estimated lower adsorption energy for the

more hydrophobic particles HDK H18 in comparison to

HDK H20. The intermediate hydrophobicity of HDK H20

induced a higher interface coverage rate of nanoparticles

and a better coalescence hindrance of the droplets at all

mass fractions. The appearance of nonspherical droplets in

HDK H20 emulsions at w

= 0.75 % and w

= 1 % supports

this argument. No nonspherical droplets and, hence, no

arrested coalescence was observed for HDK H18 emulsions.

Consequently, not all particles of HDK H18 adsorbed at the

interface.

Binks and Lumsdon [60] analyzed water-toluene w/o

emulsions with spherical silica particles and toluene volume

fractions of 0.5 prepared by ultrasonication. In agreement

with our results, the volume distribution for particles with

50 % SiOH content was shifted to lower drop diameters in

comparison to particles with 20 % SiOH [60]. Furthermore,

the emulsions with 50 % SiOH exhibited a bimodal distribu-

tion of volume, which was not the case for 20 % SiOH. In

contrast to Binks and Lumsdon no bimodal drop size distri-

bution occurred for particles with 50 % SiOH content

(cf. Fig. 9d) in this work, which could be caused by the dif-

ferent power inputs, particle geometries or dispersed phase

volume fractions.

4.3.4 Impact of Nanoparticles on Coalescence

Behavior

The impact of nanoparticles on the coalescence behavior

was analyzed by abruptly changing the energy input in the

agitated system from n= 900 to 700 rpm after reaching

steady-state conditions. The response in terms of droplet

sizes is depicted in Fig. 10a for different particle concentra-

tions. The coalescence was severely hindered so that the

steady-state drop diameters reduced with rising particle

concentration. After reaching a critical surface coverage

around w

= 1 %, the oil-water interface was nearly fully

coated with particles so that coalescence was inhibited, and

a reduction of energy input did not lead to an increase of

the Sauter mean diameter within the considered time

frame.

Fig. 10b shows the response for different number-based

mean diameters for a particle concentration of w

= 0.25 %.

It is known that the coalescence efficiency is a function of

drop size, although various partly contradictory descrip-

tions of this relation can be found in literature [32]. For

example, a rising coalescence efficiency, a curve with a max-

imum or a declining coalescence efficiency with rising drop-

let sizes were reported [32]. The mechanisms are often

divided into different cases such as coalescence of a) nonde-

formable rigid droplets, b) deformable droplets with immo-

bile interfaces or c) deformable droplets with (partly)

mobile interfaces [32]. In nanoparticle-stabilized emulsions,

the droplet ability to deform and the interface mobility

depend on the interface coverage with nanoparticles. The

value of d

n,10

indicates that 10 % of all droplets possessed

diameters £100 mm. The change in energy input did not

affect this value, leading to the conclusion that the smallest

fraction of droplets is stabilized against coalescence because

their surface area was nearly fully covered by nanoparticles.

For comparison, a clear impact of the agitation speed on

the 90 % percentile value d

n,90

was observed in Fig. 10 since

an increase of Dd

n,90

=50mm occurred after the step-wise

reduction of agitation rate. Consequently, the larger droplets

exhibited a different coalescence behavior, caused by their

size and their lower degree of interface coverage. Hence, the

choice of a coalescence model in partly nanoparticle-stabi-

lized emulsions is not a trivial task.

The coalescence behavior was also analyzed for HDK H20

stabilized o/w emulsions using phase separation experi-

ments, where the agitation speed

was abruptly changed to 0 rpm

and the dynamic separation be-

havior was determined with an

external camera. The lack of

droplet movement relative to the

endoscope after agitation stop

prevented a representative drop

size quantification. Fig. 11a shows

the dynamic phase separation

process over time. The lower

curves represent the sedimenta-

tion of the organic droplets to-

wards the top of the vessel (sedi-

mentation curve). The upper

curves represent the height of the

completely coalesced interface

(coalescence curve). The overall

separation time where both

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Figure 10. Dynamic behavior of the systems (HDK H20, a= 0.15, T= 293 K) for a step-wise reduc-

tion of agitation speed from 900 to 700 rpm at t= 1200 s. a) Sauter mean diameter for different

particle mass fractions w

, b) number-based diameters at w

= 0.25 %.

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curves meet was 53 s for w

= 0.05 wt % and 117 s for the

higher particle concentration of w

= 0.15 wt %. The coales-

cence curves are similar and especially coalescence of the

largest droplets took place within the first seconds of the

separation experiments. The emulsions were only partly

stabilized since the droplets were not fully coated with

particles so that the phase separation was completed within

several minutes or less. For particle mass fractions of

= 0.75 wt % and higher, the stability against coalescence

rose and the phase separation took longer than 48 h. The

swarm sedimentation severely decreased with rising particle

mass fractions and lower droplet sizes. Fig. 11b shows the

overall sedimentation speed calculated from the slope of the

sedimentation curves over particle mass fraction. The shape

of the curve is similar to the graph of the steady-state Sauter

mean diameters over particle mass fraction in the agitated

system (cf. Fig. 6a and Fig. 11b).

The swarm sedimentation speed can also be used to cal-

culate the corresponding Sauter mean diameter of the drop-

let swarm and vice versa. The approach by Pilhofer and

Mewes [46] assumes a mono-disperse droplet swarm and

that no drop-drop coalescence occurs during sedimenta-

tion. The model is valid for Archimedes numbers of Ar >1

and dispersed phase volume fractions of 0.06 < j

< 0.55.

The Reynolds number during sedimentation Re

(Eq. (6))

Res¼3qjd

cwx1jd

ðÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1þAr cwx1jd

ðÞ

54 q2j2

s1

¼rcvsd32

(6)

is described using the Archimedes number Ar, the Hada-

mard-Rybczynski factor K

, the friction coefficient c

and

two coefficients xand q(definitions see Appendix).

The governing equations are described in detail in

[44, 46] and lead to calculated Sauter mean diameters of

32,wp = 0.015wt %

= 297 mmtod

32,wp = 1.00wt %

= 127 mm. This

represents the lower size range of the drop size distributions

in the agitated system measured in steady state. It should be

noted that the same dispersed phase fraction as in steady

state is used, since the actual values during sedimentation

are unknown. For the o/w emulsions investigated in this

case, the influence of the suspension viscosity was negli-

gible. Using viscosity values at shear rates of 10 s

–1

and

1000 s

–1

only changes the Sauter mean diameter value in the

first digit after the decimal point. For emulsions with high

particle mass fractions in the continuous phase, the com-

plex rheology should be taken into account since the swarm

sedimentation model is very sensitive towards the continu-

ous phase viscosity [46, 59]. However, this case was not in-

vestigated in this work.

5 Conclusions and Outlook

The impact of silica nanoparticles, which differ in residual

silanol content or specific surface area, on drop size distri-

butions in an agitated tank was analyzed. Physical proper-

ties that influence drop breakup and coalescence behavior

were determined. All three investigated nanoparticle sus-

pensions exhibited shear thinning flow behavior. Their yield

stress increased with rising nanoparticle mass fraction and

viscoelastic rheological behavior with gel character oc-

curred. In comparison to HDK H18 and HDK H30 par-

ticles, the increase in dynamic viscosity with rising particle

mass fraction is more pronounced for HDK H20 particles.

The specific surface area and silanol content especially for

higher particle mass fractions (w

= 0.5–1 %) has a major

impact on the liquid-particle and particle-particle interac-

tions. No remarkable change in interfacial tension occurred

for n-heptane suspensions with HDK H18, HDK H20 and

HDK H30 against water.

The steady-state Sauter mean diameters as a function of

particle mass fraction showed an impact of the hydropho-

bicity of the particles and their specific surface area. The

decrease of the droplet size with increasing particle mass

fraction was higher for HDK H20 par-

ticles in comparison to more hydropho-

bic particles (HDK H18) or particles with

a higher specific surface area (HDK

H30). The influence of the specific sur-

face area on the drop sizes is smaller in

comparison to the silanol content or the

hydrophobicity of the particles. Distribu-

tion self-similarity existed for the investi-

gated particles for one emulsion type. A

comparison of the distributions of HDK

H20 stabilized o/w- and w/o emulsions

showed similar Sauter mean diameters,

but no self-similarity of the drop size dis-

tributions. Future efforts to predict drop

sizes of (partly) nanoparticle-stabilized

emulsions need to include the complex

rheology of the systems. Furthermore, an

www.cit-journal.com ª2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Chem. Ing. Tech. 2019,91, No. 11, 1640–1655

Figure 11. Batch settling results for HDK H20 stabilized emulsions after stirrer stop from

900 rpm (a= 0.15, T= 293 K). a) Coalescence and sedimentation curves over time for

two nanoparticle mass fractions, b) sedimentation velocity over particle mass fraction,

calculated using the slope of the sedimentation curve.

1652 Research Article

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Technik

additional characterization of the system properties such as

interface rigidity, particle adsorption behavior and (local)

particle coverage might be needed for a comprehensive de-

scription of the systems.

We would like to thank Caroline Faller and Nina Fessler

for their supportive experimental work. This work is part

of the Collaborative Research Centre ‘‘Integrated Chemi-

cal Processes in Liquid Multiphase Systems’’ coordinated

by the Technische Universitat Berlin. Financial support

by the Deutsche Forschungsgemeinschaft is gratefully

acknowledged (TRR 63).

Appendix

Used Equations

Circular equivalent diameter d

A,i

(m)

dA;i¼ﬃﬃﬃﬃﬃﬃﬃﬃ

4Ai

r(A1)

Sauter mean diameter d

(m)

d32 ¼Pn

i¼1d3

i¼1d2

(A2)

Hadamard-Rybczynski factor K

KHR ¼3hcþhd

ðÞ

2hcþ3hd

(A3)

Coefficient q

q¼1jd

2jdþKHR

exp 2:5jd

10:61jd

 (A4)

Coefficient x

x¼5K3=2

1jd



0:45

(A5)

Friction coefficient c

cw¼Ar

6Res23

KHRRes

(A6)

Symbols used

A[m

] area

Ar [–] Archimedes number, rcDrgd3

[–] friction factor

d[m] drop diameter

A,i

[m] circular equivalent diameter

[m] arithmetic mean diameter

min

[m] minimum drop diameter

max

[m] maximum drop diameter

n,10

[m] 10 % percentile value of number

n,50

[m] 50 % percentile value of number

n,90

[m] 90 % percentile value of number

n,95

[m] 95 % percentile value of number

v,10

[m] 10 % percentile value of volume

v,50

[m] 50 % percentile value of volume

v,90

[m] 90 % percentile value of volume

[m] stirrer diameter

[m] Sauter mean diameter

D[m] tank diameter

ads

[kT] adsorption energy

f[Hz] frequency

[m] height of particles

[N] normal force

[m] length of particles

g[m s

–2

] acceleration due to gravity

G[Pa] shear modulus

G¢[Pa] loss modulus

G¢¢ [Pa] storage modulus

h[m] height

[m] baffle height

[m] height of coalescence curve

crit

[m] critical height of cylindrical element

[m] height of sedimentation curve

[m] stirrer blade height

[m] stirrer bottom clearance

total

[m] total dispersion height

H[m] height of fluid level

[–] Hadamard-Rybczynski factor

m[kg] mass

n[rpm] agitation speed

P[W] power

q[–] coefficient

[–] cumulative distribution of number

[–] cumulative distribution of volume

R[m] particle radius

crit

[m] critical radius of cylindrical element

[–] Reynolds number during

sedimentation, rcvsd32

[m] stirrer blade thickness

[m] baffle thickness

t¢[s] separation time

T[K] temperature

V[m

] volume

[m s

–1

] swarm sedimentation velocity

Vi [–] viscosity vessel number,

hcnd



0:5

[m] baffle width

Chem. Ing. Tech. 2019,91, No. 11, 1640–1655 ª2019 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.cit-journal.com

Research Article 1653

Chemie

Ingenieur

Technik

[wt %] particle mass fraction in dispersed

phase

p,s

[wt %] particle mass fraction in suspension

[m] stirrer blade width

We [–] Weber number, rcn2d3

Greek letters

a[–] mass fraction of oil

b[–] aspect ratio

[–] critical aspect ratio

g[%] deformation

g[s

–1

] shear rate

h[Pa s] dynamic viscosity

[–] relative dynamic viscosity

p[N m

–1

] surface pressure

e[W kg

–1

] energy dissipation rate

d[–] loss factor

[–] dispersed phase volume fraction

q[] contact angle

s[N m

–1

] interfacial tension

[m] standard deviation of number

r[kg m

–3

] density

[kg m

–3

] density of continuous phase

[kg m

–3

] density of dispersed phase

k[S cm

–1

] electrical conductivity

t[Pa] shear stress

[Pa] yield stress

w[rad s

–1

] angular frequency

x[–] coefficient

Abbreviations

BET Brunauer-Emmet-Teller method to determine the

specific surface area

CFD computational fluid dynamics

PBE population balance equation

SEM scanning electron microscopy

SiOH residual silanol group

o/w oil-in-water emulsion

w/o water-in-oil emulsion

o,w oil/water interface

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