Modelling the non-linear interfacial shear rheology behaviour of chickpea protein-adsorbed complex oil/water layers

1 Modelling the non-linear interfacial shear rheology behaviour of chickpea 1 protein-adsorbed complex oil/water layers 2 Manuel Felix1, Alberto Romero2, Cecilio Carrera-Sanchez3, Antonio Guerrero1,* 3 1Departamento de Ingeniería Química, Escuela Politécnica Superior, Universidad de Sevilla, 41011 Sevilla, 4 Spain. 5 2Departamento de Ingeniería Química, Facultad de Física, Universidad de Sevilla, 41012 Sevilla, Spain. 6 3Departamento de Ingeniería Química, Facultad de Química, Universidad de Sevilla, 41012 Sevilla, Spain 7 ------------------- 8 *Antonio GUERRERO 9 Escuela Politécnica Superior, Universidad de Sevilla, 41011 Sevilla, Spain. 10 E-mail: [email protected] 11 Phone: +34 954557179; fax: +34 954556447. 2 Abstract 12 The objective of this work is the evaluation of chickpea protein adsorption at oil/water (O/W) 13 interface as a function of protein concentration and pH value (2.5, 5.0 and 7.5). To assess 14 molecular interpretation, interfacial tension is determined as a function of concentration with a 15 Wilhelmy plate, whereas interfacial small amplitude oscillatory shear (i-SAOS) properties are 16 determined using a double wall-ring (DWR) geometry controlled by a DHR3 rheometer (TA 17 Intruments) and a pendant drop tensiometer (IT Concept) is used to determine linear 18 viscoelastic dilatational measurements. This work provides a model which could predict both 19 the linear and non-linear viscoelastic behavior of complex fluid-fluid interfacial layers. To this 20 end, relaxation tests using the DWR device are carried out at the interface under the linear and 21 non-linear regimes. Steady state viscosity values are also obtained to check the ability of the 22 model to predict the interfacial flow behaviour. Results show that the Wagner-I model can 23 reproduce fairly well the steady state flow behaviour of chickpea protein-adsorbed interfaces. 24 This model is based on the use of a memory function calculated from the generalized Maxwell 25 (obtained from i-SAOS measurements) and a damping function obtained by the Laun model 26 from linear and non-linear relaxation tests. 27 Keywords: Damping function; Interfacial Rheology; Legume proteins; Non-Linear 28 viscoelasticity; Pendant Drop; Wagner Model 29 3 1. Introduction 30 The adsorption of protein layers at fluid-fluid interfaces is a widely studied phenomenon, 31 however its comprehensive understanding requires to overcome some complexities related to 32 the mechanisms which govern the protein adsorption, the denaturation process that takes place 33 once protein molecules reach the interface, the nature of protein interactions, the formation of 34 protein aggregates and the interactions with other biopolymers [1,2]. The complex behaviour 35 of protein aggregates, polymers, or colloidal particles at the fluid-fluid interface is usually 36 related to a complex microstructure, which is generally dominated by surface rheological 37 properties [3,4]. It is for this complexity of protein-based interfacial layers that most of the 38 studies use model proteins, either being carried out by means of interfacial small amplitude 39 oscillatory shear (i-SAOS) or by dilatational measurements [5–7]. Unfortunately, commercial 40 products based on emulsions or foams require the use of far more complex systems typically 41 containing a mixture of proteins. Therefore, a further effort has to be carried out in order to 42 characterize surface properties, particularly interfacial rheology, of complex fluid-fluid layers 43 at which these proteins are adsorbed. Among these proteins, those extracted from plants are 44 fairly attractive for food applications as they can replace those widely used proteins from animal 45 sources. In this sense, knowledge of the main factors which affect the techno-functional 46 properties of proteins at complex fluid-fluid interfaces would foster the development of new 47 food products with novel functionalities based on commercial proteins [8]. Among the different 48 options available in global markets, legume proteins (i.e. chickpea protein) has attracted 49 attention since these proteins are regarded to be fairly cost efficient and present high nutritional 50 and techno-functional properties [9,10]. Chickpea proteins have been called to be used in many 51 food products, substituting other proteins as functional constituents. Chickpea seeds are rich in 52 protein (20–25%) and starch. In this context, the development of a procedure which increases 53 the protein content can be interesting for its use in food products [11,12]. Protein concentrates 54 4 from chick peas have a globulin fraction with the albumins constituting approximately one-55 fourth of the former [13]. In this globulin fraction, legumin (11S):vicilin (7S) ratio is 6:1 [14]. 56 These protein fractions make chickpea protein concentrates suitable for the stabilization of 57 interfaces, being already demonstrate for other legume such as soy bean [15]. 58 Functional properties of proteins have been related to the response of these proteins to surface 59 shear and dilatational deformations at complex fluid-fluid interfaces is particularly relevant. 60 Some authors correlated the stability and bulk rheology of emulsions to the interfacial rheology 61 of complex fluid-fluid interfaces [5,16–20]. However, this correlation should be carefully 62 considering since cross-linking between protein films may lead to droplet aggregation, 63 decreasing the kinetic stability [21]. In fact, Karbaschi et al. [22] only correlated surface 64 dilatational visco-elasticity and the bulk viscoelasticity. However, there are other authors such 65 as Lucassen-Reynders et al. [23] who indicated that dilatational rheology can be correlated to 66 short-term stability, whereas i-SAOS measurements may provide information about the middle 67 or long-term stability. Nonetheless, obtaining significant interfacial rheological functions is 68 demanding: firstly, because of the deformation of an interface generally requires the application 69 of very small stresses. Secondly, and more fundamentally, because of this challenge is 70 associated to the effect that the shear viscosity of the bulk exerts on the response of the interface 71 to a deformation or flow. In fact, the influence of the adjoining sub-phases often hinders the 72 analysis of the fluid mechanics at fluid-fluid interfaces [24–26]. To overcome the first 73 requirement, it is necessary to use a highly sensitive equipment. However, to discard the second 74 limitation it is necessary to verify that interfacial shear rheological measurements are not 75 affected by the adjoining sub-phases. When a planar interface is deformed by shear, the 76 contribution of the subphase to the measured torque can be assessed through the Boussinesq 77 number (𝐵𝐵𝐵𝐵) which is proportional to the ratio between the interfacial and bulk viscosities (𝜂𝜂𝑠𝑠 78 and 𝜂𝜂𝑏𝑏): 79 5 𝐵𝐵𝐵𝐵= 𝜂𝜂𝑠𝑠 𝐺𝐺·𝜂𝜂𝑏𝑏 (1) 80 where 𝐺𝐺=𝑎𝑎·𝐿𝐿𝑆𝑆𝐿𝐿𝐵𝐵 ⁄ is a characteristic length that will be dependent on the dimensions of the 81 measurement geometry. This parameter involves three length scales: 𝑎𝑎, wchich is related to the 82 ratio of the contact area and the contact perimeter between the geometry and the interface; LS 83 and LB that are the interfacial and bulk momentum decay length scales. According to Fitzgibbon 84 et al. [27], these later characteristic lengths correspond to the distance required for the interfacial 85 and bulk momentum to be attenuated, respectively. In this study, it is assumed that the responses 86 of the measured torque to shear deformations are dominated by the interface, which gives rise 87 to large 𝐵𝐵𝐵𝐵 values (𝐵𝐵𝐵𝐵>10) and, hence, the contribution of the adjoining sub-phases can be 88 neglected. 89 Most of the research studies found on interfacial shear rheology are devoted to the linear 90 viscoelasticity regime, using i-SAOS measurements [20,24,28–30], or creep measurements 91 [31,32]. However, applications where interfacial shear rheology has been found to be relevant, 92 typically involve occurrence of non-linear interfacial shear deformations, far beyond the linear 93 viscoelastic limit. Thus, the manufacture of emulsions and foams typically requires the use of 94 high energy inputs, which give rise to fairly non-linear interfacial deformations. Basically, the 95 research studies found on the characterization of non-linear viscoelastic properties of complex 96 fluid-fluid interfaces has been carried out by means of large amplitude oscillatory shear 97 measurements [33–35]. An interesting review on the use of this technique for fluid-fluid 98 interfaces has been recently published by Sagis & Fischer [3]. In contrast, some studies on the 99 steady state shear flow measurements has been carried out for the interfacial shear rheological 100 characterization [6,32]. However, to our knowledge, other techniques such as stress relaxation 101 tests or creep tests have not been applied to complex interfaces in the non-linear regime. 102 In addition, modelling the viscoelastic behaviour of the planar oil/water (O/W) interface 103 (including the linear regime and particularly the non-linear viscoelasticity regime) is of 104 6 paramount importance to predict its behaviour when a shear field is applied to the complex 105 fluid-fluid interface. This modelling would bring substantial benefits for the understanding of 106 protein-adsorbed interfacial behaviour, as well as for the assessment of emulsion or foam 107 stability patterns and eventually for emulsion or foam-based product development [36]. 108 Unfortunately, this modelling issue has received much less attention at the interface than in the 109 bulk. To this end, modelling of the planar interface has been used in this study following an 110 analogue scheme to some of those used in the bulk by means of well-known constitutive 111 equations, in order to achieve a suitable description for both the surface linear and non-linear 112 viscoelasticity behaviour. 113 This study is conducted within the framework of a research project with the overall objective 114 of analysing the ability of legume proteins (i.e. from chickpea) to form biointerfaces which 115 would provide long-term stability to food emulsions. A comprehensive characterization of 116 linear viscoelastic properties, as well as transient and steady state flow properties of the 117 chickpea protein-based fluid-fluid interface is essential to gain a better understanding of its 118 behaviour under different conditions. The specific aim in this work is the analysis of the 119 interfacial behaviour of chickpea protein at three pH values (2.5, 5.0 and 8.0). The interfacial 120 assessment is carried out by: i) surface dilatational measurements (using a pendant drop 121 tensiometer) and ii) interfacial shear rheology (using a double-wall-ring geometry controlled 122 by a rheometer). 123 2. Material and methods 124 2.1. Protein powder 125 Herba Ingredients (Seville, Spain) supplied a chickpea (CP) flour used in the framework of this 126 research. This protein flour was obtained from direct milling of chickpeas. However, a protein 127 concentrate was obtained due to its low protein content (c.a. 19 wt.%) according to previous 128 studies [11]. This procedure consisted of two stages: (i) Alkalinisation of protein dispersion at 129 7 pH 8, to improve protein solubility and centrifugation to remove the non-soluble fraction 130 (depleted in protein); (ii) Neutralization an acidification of the aqueous phase (rich in protein) 131 up to the isoelectric point (IEP). At the IEP, protein aggregation is favoured by the lack of net 132 surface charges, which leads to the precipitation of most of the proteins present. In this case, 133 the aqueous phase (depleted in protein) was discarded and the pellet (rich in protein) was 134 freeze-dried. The protein content of the CP system was around 64 wt. %. Thus, according to 135 the Pearson classification this protein system cannot be considered as a protein concentrate. 136 Moreover, the CP protein system contained up to 16.4 wt. % of lipids. Regarding the ashes, the 137 ash content of the CP systems was 3.8 wt. %. These ashes are inorganic soluble salts, since the 138 non-soluble salts were removed during the protein-extraction procedure. In any case, 1 wt.% of 139 NaCl was added to all samples in order to cushion the effect of these inorganic salts on 140 interfacial measurements. The composition of the CP protein system was completed with 0.1 141 wt.% moisture (related to the previous stage in the freeze-dryer). All measurements were carried 142 out using this CP protein concentrate, avoiding any further processing. Moreover, all interfacial 143 measurements were carried out using Capicua high-oleic sunflower oil supplied by Coreysa 144 (Seville, Spain). Finally, appropriate buffers from Sigma-Aldrich were used to compare results 145 obtained under different conditions: at low pH, when protein surfaces are positively charged; 146 near the isoelectric point (IEP), at which the net charge is virtually zero; and at pH higher than 147 the IEP where a dominant negative charge is observed. 148 2.2. Interfacial characterization 149 2.2.1. Determination of interfacial tension at equilibrium 150 Interfacial tension was determined after 24h protein adsorption using a Wilhelmy plate fitted to 151 a Sigma tensiometer (KSV, Helsinki, Finland). These measurements were performed as a 152 function of bulk protein concentration (0.1, 0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0 and 5.0 wt.%) and 153 at three different pH values (2.5, 5.0 and 7.5). Oil phase was added after placing the Wilhelmy 154 8 plate in the interfase, continuous interfacial tension values were recorded until reaching 155 constant values over 5 min. 156 2.2.2. Pendant droplet measurements 157 Interfacial characterization of protein adsorbed at O/W interface was carried out by means of 158 pendant droplet (TRACKER, IT Concept, France), determining adsorption kinetics. 159 Water-droplet profiles were processed according to the Laplace equation as was described by 160 Castellani, Al-Assaf et al. [37]. Moreover, the viscoelastic moduli of protein adsorption layers 161 were determined at 5 % strain amplitude at 0.1 Hz before reaching the pseudo-equilibrium state, 162 as well as after reaching the pseudo-equilibrium state (10,800 s protein adsorption) as a function 163 of frequency (from 0.0075 to 0.1 Hz). 164 2.2.3. Interfacial shear rheological properties 165 Interfacial shear rheology analysis was carried out using a double-wall-ring geometry (DWR). 166 Details about the geometric features of the DWR were reported by Vandebril et al. [25]. The 167 protein solution was contained in a double wall cup and the ring was then positioned at the 168 air/water (A/W) interface. Subsequently, sunflower oil was carefully added to the interface. The 169 ring was controlled by a DHR-3 rheometer (TA Instruments, USA) [25]. 170 Mechanical spectra were obtained by means of frequency tests, which were carried out within 171 the linear viscoelastic range (assessed through stress sweep tests that were performed before 172 frequency sweep tests). The frequency tests were performed during the protein adsorption (from 173 0.314 to 6.14 rad/s) and after reaching the equilibrium (from 0.06 to 6.14 rad/s). In addition, a 174 time sweep test was carried out over the protein adsorption, over 10,800 s at 0.1 Hz. The stress 175 relaxation measurements were carried out after the protein adsorption, applying several torque 176 values at O/W interface. The deformation obtained was measured for 900 s. Finally, flow curves 177 were carried out from 0.5·10-4 to 50 s-1, monitoring the viscosity of the O/W interface. 178 9 Boussinesq number (𝐵𝐵𝐵𝐵) was used to analyse the flow field as a function of the interfacial 179 viscoelastic properties, evaluating the contributions of the subphases [25]. 180 2.3. Statistical analysis 181 At least three replicates of each measurement were carried out. Measurement uncertainty was 182 determined by means of standard deviation. 183 3. Results and discussion 184 3.1 Characterization of the O/W interface 185 3.1.1. Determination of interfacial tension at equilibrium 186 First of all, the protein system was adsorbed at O/W interface over 24h to reach an apparent 187 equilibrium state and subsequently the interfacial tension was measured with a Wilhelmy plate. 188 Then, interfacial pressure (𝛱𝛱) values are calculated from interfacial tensions of protein layers 189 at the apparent equilibrium (𝜎𝜎) at several CP concentrations (0.1, 0.25, 0.5, 0.75, 1.0, 2.0, 3.0, 190 4.0 and 5.0 wt.%) and pH values (2.5, 5.0 and 7.5) as follows: 191 𝛱𝛱=𝜎𝜎0−𝜎𝜎 (2) 192 Parameter 𝜎𝜎0 is the O/W interfacial tension in absence of any surface active agent. 193 Fig. 1 shows the values obtained for the interfacial pressure at the O/W interface, after reaching 194 the apparent equilibrium. It can be noticed that, although some effects can be masked by minor 195 components of the oil phase and protein system, the effect of pH should be mainly attributed to 196 changes in the protein surfaces. Thus, regardless of the pH used, an increase in interfacial 197 pressure between sunflower oil and water was observed with increasing protein content, 198 showing a tendency to reach a plateau value that corresponded to the saturation of the interface. 199 The interfacial tension value strongly depends on protein conformation, which in turn depends 200 on the pH value. In this sense, the pH value affect to the net charge of protein surfaces as it 201 departs from the IEP (being positive at pH below the IEP or negative above this point). Previous 202 results indicated that, for this protein system, pH 2.5 is below the IEP, pH 5.0 is close to the 203 16 It must be pointed out that for solid-like viscoelastic interfaces one of the relaxation times must 349 be infinite and its contribution should be represented by 𝐺𝐺𝑠𝑠,𝑒𝑒.In the present case, three Maxwell 350 elements and 𝐺𝐺𝑠𝑠,𝑒𝑒 are considered. Thus, the linear functions of the interface (i.e. 𝐺𝐺′𝑠𝑠(𝜔𝜔), 351 𝐺𝐺"𝑠𝑠(𝜔𝜔) or 𝐺𝐺𝑠𝑠(𝑡𝑡)) can be obtained from this model as follows [50,51]: 352 𝐺𝐺′𝑠𝑠(𝜔𝜔)=𝐺𝐺𝑠𝑠,𝑒𝑒+�𝐺𝐺𝑠𝑠,𝑘𝑘𝜔𝜔2𝜆𝜆𝑘𝑘 2 1 + 𝜔𝜔2𝜆𝜆𝑘𝑘 2 𝑛𝑛 𝑘𝑘=1 (9) 353 𝐺𝐺"𝑠𝑠(𝜔𝜔)=�𝐺𝐺𝑠𝑠,𝑘𝑘𝜔𝜔𝜆𝜆𝑘𝑘 1 + 𝜔𝜔2𝜆𝜆𝑘𝑘 2 𝑛𝑛 𝑘𝑘=1 (10) 354 𝐺𝐺𝑠𝑠(𝑡𝑡)=𝐺𝐺𝑠𝑠,𝑒𝑒+�𝐺𝐺𝑠𝑠,𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒�−𝑡𝑡−𝑡𝑡′ 𝜆𝜆𝑘𝑘� 𝑛𝑛 𝑘𝑘=1 (11) 355 According to these expressions, Eq. (9) and (10) can be used to calculate the discrete relaxation 356 spectrum by selecting a set of relaxation times 𝜆𝜆𝑘𝑘 (provided that 𝜆𝜆𝑚𝑚𝑚𝑚𝑚𝑚𝜔𝜔𝑚𝑚𝑚𝑚𝑛𝑛 > 1 and 357 𝜆𝜆𝑚𝑚𝑚𝑚𝑛𝑛𝜔𝜔𝑚𝑚𝑚𝑚𝑚𝑚 < 1) [51], calculating the values of 𝐺𝐺𝑠𝑠,𝑘𝑘 by simultaneously using the method of least 358 squares to both equations. The experimental values of 𝐺𝐺′𝑠𝑠(𝜔𝜔) and 𝐺𝐺"𝑠𝑠(𝜔𝜔) are successfully fitted 359 to the generalized Maxwell model (Eq. (9) and (10)). Moreover, the values obtained for 𝜆𝜆𝑘𝑘 and 360 𝐺𝐺𝑠𝑠,𝑘𝑘 can be used to calculate 𝐺𝐺𝑠𝑠(𝑡𝑡) (results shown later). 361 Fig. 5 shows the evolution of the interfacial shear mechanical spectra obtained during protein 362 adsorption at the O/W interface until the pseudo-equilibrium state was reached, as a function 363 of pH (2.5, 5.0 and 7.5). These results suggests that these globular legume proteins are able to 364 provide high values of interfacial shear viscoelastic properties, which suggests that the adsorbed 365 proteins are able to form a fairly cohesive interfacial layer [52]. 366 A marked evolution can be clearly distinguished as protein is continuously adsorbing at the 367 O/W interface particularly at pH 5.0. Thus, the first frequency sweep test, after 10 min of protein 368 adsorption, is dominated by the viscous component over the experimental frequency range. 369 Subsequently, the mechanical spectrum shows a crossover point between 𝐺𝐺′𝑠𝑠(𝜔𝜔) and 𝐺𝐺"𝑠𝑠(𝜔𝜔) 370 17 which shifts to higher frequencies along protein adsorption, eventually leading to the formation 371 of a gel-like behaviour at the O/W interface. This process taking place after protein adsorption 372 at the interface would involve protein unfolding and aggregation, leading to the development 373 of a 2D elastic gel network. The gelation process at the interface has been described previously 374 by several authors using other techniques different than interfacial shear rheology such as the 375 use of gelators or high intensity ultrasounds [53,54]. It is worth mentioning that the interfacial 376 shear rheology technique used in this study allows to monitoring the evolution of the 377 viscoelastic properties over the development of the protein-adsorbed interfacial layer. These 378 results indicate that the rheokinetics of the above-mentioned evolution is rather different 379 depending on the pH value. At pH 7.5, the evolution is similar to the one found at pH 5.0, 380 however the rheokinetics is faster, showing the crossover at higher frequencies and 381 disappearing from the experimental frequency window at shorter times. This effect must be 382 related to the presence of negative charges at the protein surfaces that would lead to electrostatic 383 repulsive interactions between protein segments [29,55]. 384 In contrast, at low pH, a gel-like protein-adsorbed interfacial layer is already formed after 10 385 min (Fig. 5A). This apparently faster evolution found at pH 2.5, may be related to the high 𝑘𝑘𝐷𝐷 ∗ 386 and kA, especially to kA since it is related to the protein unfolding and rearrangement, which 387 cause the gelation of the interface [56]. This effect may be probably related to some protein 388 denaturation occurring at this low pH value. The presence of electrostatic repulsive interactions 389 among positively charged protein surfaces has to be also taken into account, leading to the 390 development of higher viscoelastic moduli. 391 According to Narsimhan [52], the interfacial shear rheology is influenced by the ability of the 392 adsorbed proteins to exhibit cohesive interactions with neighbouring molecules, which in turn 393 depends on pH. Previous results obtained for other protein systems indicate that if the substrate 394 is close to the IEP, repulsions between protein molecules adsorbed at the interface are 395 18 minimized, promoting the formation of more cohesive adsorbed layers [57,58] and, as a result, 396 leading to a slower rheokinetics [59]. 397 It should be emphasized that the evolution found from interfacial dynamic shear measurements 398 (where a crossover point was observed) can be hardly measured by oscillatory dilatational tests. 399 This may be a consequence of the predominance of bending rigidity on the dilatational response 400 as it was previously indicated. In any case, note that after reaching the pseudo-equilibrium state 401 all interfacial O/W protein-adsorbed layers show an apparent gel-like response, regardless of 402 the pH value. 403 Dilatational vs. interfacial shear rheology 404 Table 2 summarizes the parameters obtained from both, dilatational rheology and interfacial 405 shear rheology obtained at 0.1 Hz. (tan 𝛿𝛿𝑠𝑠(0.1), 𝐸𝐸′𝑠𝑠(0.1) and 𝐺𝐺′𝑠𝑠(0.1)). In this sense, values 406 obtained from dilatational measurements evidence the predominant gel-like behaviour of the 407 interface since these values of tan 𝛿𝛿𝑠𝑠(0.1) are lower than 0.15 in all cases. This parameter also 408 reflects the strong pH dependence exerted by the CP protein system. A comparison with 409 previous studies reveals that similar or even much lower tan 𝛿𝛿𝑠𝑠(0.1) values are obtained in the 410 present study. Thus, tan 𝛿𝛿𝑠𝑠(0.1) values are around 0.1 for rice protein-stabilized O/W interfaces 411 at pH 2.0 and 8.0 [60], whereas potato protein-stabilized O/W interfaces led to values around 412 0.6 and 0.1 at pH 2.0 and 8.0, respectively [19]. O/W interfaces stabilized by crayfish protein 413 isolate showed tan 𝛿𝛿𝑠𝑠(0.1) values around 0.2 and 0.13 at pH 2.0 and 8.0, respectively [61]. 414 These low values for tan 𝛿𝛿𝑠𝑠(0.1) may indicate either the occurrence of strong interactions at the 415 interface [62] or the formation of a densely packed interface with denatured protein molecules 416 [28]. The interfacial shear parameter (tan 𝛿𝛿𝑠𝑠(0.1)) is always higher than the dilatational one, 417 which is a consequence of the smaller values obtained for the shear elastic modulus. As 418 discussed above, the elastic modulus obtained from dilatational measurements is dominated by 419 bending rigidity; while the moduli obtained from the interfacial shear rheology is related to 420 19 protein-protein interactions. In fact, it is worth analysing the difference between the elastic 421 parameters obtained from dilatational and interfacial shear measurements. As may be seen in 422 Table 2, the highest difference between 𝐸𝐸′𝑠𝑠(0.1) and 𝐺𝐺′𝑠𝑠(0.1) is obtained at pH 5.0, followed by 423 pH 2.5 and 7.5. 424 Non-linear viscoelastic interfacial shear measurements 425 When the strain applied to a material or to an interface exceeds a limiting value, a deviation 426 from LVE response takes place. This being the case, Eq. (7) no longer applies and the material 427 or the interface exhibits nonlinear viscoelasticity. To describe this behaviour a constitutive 428 equation for nonlinear viscoelasticity must be used. A class of constitutive equations that has 429 been widely used in bulk rheology is given by the Kaye-BKZ equation [49,63]: 430 𝝉𝝉𝒔𝒔(𝑡𝑡)=� �2𝜕𝜕𝑈𝑈𝑠𝑠 𝜕𝜕𝐼𝐼𝑠𝑠1 ·𝑪𝑪𝒔𝒔 −𝟏𝟏−2𝜕𝜕𝑈𝑈𝑠𝑠 𝜕𝜕𝐼𝐼𝑠𝑠2 ·𝑪𝑪𝒔𝒔�𝑑𝑑𝑡𝑡′ 𝑡𝑡 −∞ (12) 431 where 𝑪𝑪𝒔𝒔 is the interfacial Cauchy tensor, Is1 and Is2 are the first and second invariants of 𝑪𝑪𝒔𝒔 −𝟏𝟏 432 and 𝑈𝑈𝑠𝑠=𝑈𝑈𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2,𝑡𝑡−𝑡𝑡′) is the interfacial elastic potential function. The selection of a 433 variety of expressions for the interfacial potential function 𝑈𝑈𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2,𝑡𝑡−𝑡𝑡′) will allow to 434 define different constitutive equations for the description of different types of non-linear 435 viscoelasticity behaviour. A particularly interesting simplification consists in selecting a 436 potential function that can be separated in two terms, one depending on the interfacial strain 437 and the other being a function of time: 438 𝑈𝑈𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2,𝑡𝑡−𝑡𝑡′)=𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·𝑢𝑢𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2) (13) 439 where 𝑢𝑢𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2) is the scalar interfacial potential, which would be only dependent on the 440 invariants 𝐼𝐼𝑠𝑠1 and 𝐼𝐼𝑠𝑠2. Introducing the specific function given by Eq. (13) into Eq. (12), the well-441 known time-deformation factorable or separable expression of the Kay-BKZ constitutive 442 equation may be written in terms of 𝑚𝑚𝑠𝑠 and 𝑢𝑢𝑠𝑠: 443 20 𝝉𝝉𝒔𝒔(𝑡𝑡)=� 𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·�2𝜕𝜕𝑢𝑢𝑠𝑠 𝜕𝜕𝐼𝐼𝑠𝑠1 ·𝑪𝑪𝒔𝒔 −𝟏𝟏−2𝜕𝜕𝑢𝑢𝑠𝑠 𝜕𝜕𝐼𝐼𝑠𝑠2 ·𝑪𝑪𝒔𝒔�𝑑𝑑𝑡𝑡′ 𝑡𝑡 −∞ (14) 444 This equation can be rewritten in terms of two non-dimensional scalar functions for the 445 deformation of the interface ℎ𝑠𝑠1(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)= 2 𝜕𝜕𝑢𝑢𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2) 𝜕𝜕𝐼𝐼𝑠𝑠1 and ℎ𝑠𝑠2(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)= 2 𝜕𝜕𝑢𝑢𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2) 𝜕𝜕𝐼𝐼𝑠𝑠2 as 446 follows: 447 𝝉𝝉𝒔𝒔(𝑡𝑡)=� 𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·[ℎ𝑠𝑠1(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)·𝑪𝑪𝒔𝒔 −𝟏𝟏−ℎ𝑠𝑠2(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)·𝑪𝑪𝒔𝒔]𝑑𝑑𝑡𝑡′ 𝑡𝑡 −∞ (15) 448 A further simplification is obtained by assuming that the contribution of the surface Cauchy 449 tensor can be neglected. This may be achieved by assuming that ℎ𝑠𝑠2(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)= 0. In this way, 450 the Wagner-I equation, which also involves time–strain separability, is obtained [49,64]: 451 𝝉𝝉𝒔𝒔(𝑡𝑡)=� 𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·[ℎ𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)·𝑪𝑪𝒔𝒔 −𝟏𝟏]𝑑𝑑𝑡𝑡′ 𝑡𝑡 −∞ (16) 452 where ℎ𝑠𝑠(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2)=ℎ𝑠𝑠2(𝐼𝐼𝑠𝑠1,𝐼𝐼𝑠𝑠2) is the interfacial expression for the so-called damping 453 function. 454 Considering only the simple shear component of the interfacial stress tensor, the equation 455 results: 456 𝜏𝜏𝑠𝑠(𝑡𝑡)=� 𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·ℎ𝑠𝑠(𝛾𝛾𝑠𝑠)·𝛾𝛾𝑠𝑠(𝑡𝑡−𝑡𝑡′)𝑑𝑑𝑡𝑡′ 𝑡𝑡 −∞ (17) 457 where 𝛾𝛾𝑠𝑠(𝑡𝑡−𝑡𝑡′) is the interfacial simple shear strain component and ℎ𝑠𝑠(𝛾𝛾𝑠𝑠) is the damping 458 function for this component. This constitutive equation can be applied to reproduce the flow 459 behaviour of the O/W interface studied, provided that suitable expressions for the interfacial 460 memory and damping functions could be found. Such expressions should fit experimental 461 results with reasonable accuracy and, on the other hand, they should be simple enough to permit 462 21 prediction of the interfacial flow behaviour by solving Eq. (17). It should also be borne in mind 463 that the interfacial memory function must reflect the LVE behaviour, whereas the damping 464 function aims for the description of the non-linear behaviour of the interface at shear strains 465 larger than the critical value. 466 A classical procedure extensively used to obtain information about non-linear viscoelasticity at 467 the bulk has consisted in the application of non-linear relaxation tests. This kind of test may 468 also be applied to the interfacial layer to obtain the non-linear shear viscoelasticity response 469 under shear. Interfacial relaxation tests involve the sudden imposition of a shear strain at the 470 interfacial layer which is maintained over time, recording the stress response over the relaxation 471 of the O/W interface, from which the relaxation modulus can be obtained 𝐺𝐺𝑠𝑠(𝛾𝛾𝑠𝑠,𝑡𝑡). It is 472 important to distinguish between the application of either a small or large strain. Likewise, for 473 bulk relaxation tests, when a small strain is applied to the interfacial layer, the linear relaxation 474 modulus response is obtained, being independent of the applied strain. However, above a 475 critical strain the response corresponds to the interfacial relaxation modulus corresponding to 476 the non-linear viscoelastic regime. The experimental values of the relaxation moduli, 𝐺𝐺𝑠𝑠(𝛾𝛾𝑠𝑠,𝑡𝑡), 477 are provided in Fig. 6 at three different pH values: 2.5, 5.0 and 7.5 (A, B and C, respectively). 478 Their respective values for the linear relaxation modulus predicted by the GM model, 479 previously obtained from i-SAOS measurements, are also shown in Fig. 6. In this sense, when 480 the strain applied is small, the relaxation modulus tends to overlap onto the linear viscoelastic 481 modulus 𝐺𝐺𝑠𝑠(𝑡𝑡). Moreover, the magnitude of the overlapped relaxation modulus is the same as 482 the linear relaxation modulus obtained from the GM model (Eq. (11)), where the only deviation 483 was found at pH 5.0. 484 On the other hand, when the interfacial shear strain is increased, the non-linear relaxation 485 modulus decreases dramatically, being nearly parallel regardless of the strain applied. 486 Consequently, the interfacial film shows a relaxation behaviour that may be regarded as time-487 22 strain factorable at the three pH values studied. This being the case, the non-linear viscoelastic 488 interfacial shear relaxation modulus 𝐺𝐺𝑠𝑠(𝛾𝛾𝑠𝑠,𝑡𝑡) can be separated into a time-dependent function, 489 the interfacial linear relaxation modulus, 𝐺𝐺𝑠𝑠(𝑡𝑡), and the strain-dependent interfacial damping 490 function, ℎ𝑠𝑠(𝛾𝛾𝑠𝑠), as follows: 491 𝐺𝐺𝑠𝑠(𝛾𝛾𝑠𝑠,𝑡𝑡)=𝐺𝐺𝑠𝑠(𝑡𝑡)·ℎ𝑠𝑠(𝛾𝛾𝑠𝑠) (18) 492 This time-strain factorability has been widely used for the bulk rheology of entangled polymers 493 [65–67], or even emulsions [68–70] and other complex fluids [64]. However, the damping 494 function has not been previously calculated for the O/W interface. Rolón-Garrido and Wagner 495 [64] have reported an extensive review on the damping function in shear and elongational bulk 496 rheology. Some extensively used models, derived from the K-BKZ equation, have been chosen 497 to interpolate the experimental results [71–73]. Among the most used of them are the 498 exponential models that can be expressed as follows: 499 ℎ𝑠𝑠(𝛾𝛾𝑠𝑠)=�𝑓𝑓𝑗𝑗 2 𝑗𝑗=1 ·𝑒𝑒𝑒𝑒𝑒𝑒�−𝑛𝑛𝑗𝑗𝛾𝛾𝑠𝑠�; where 𝑓𝑓1=𝑓𝑓 and 𝑓𝑓2= 1 −𝑓𝑓 (19) 500 This equation includes two well-known damping function models: 501 The Wagner model,where 𝑓𝑓= 1 and 𝑛𝑛1=𝑛𝑛 502 The Laun model, where 0 < 𝑓𝑓< 1 and 𝑛𝑛1,𝑛𝑛2 > 0 503 Moreover, a generalized sigmoidal expression, the Soskey-Winter model, has been widely 504 used as a representation of the damping function: 505 ℎ𝑠𝑠(𝛾𝛾𝑠𝑠)=1 1 + 𝑎𝑎𝛾𝛾𝑠𝑠𝑏𝑏 (20) 506 It is worth mentioning that the experimental values of the damping function for the O/W 507 interface have been calculated in the same way as those of the bulk, i.e. from the linear to non-508 linear interfacial relaxation modulus ratio: 509 ℎ𝑠𝑠(𝛾𝛾𝑠𝑠)=𝐺𝐺𝑠𝑠�𝛾𝛾𝑠𝑠,𝑡𝑡� 𝐺𝐺𝑠𝑠(𝑡𝑡) (21) 510 23 Thus, experimental data and fitting from models are shown in Fig. 7 for the three pH values 511 studied: 2.5, 5.0 and 7.5 (A, B and C, respectively). 512 This figure reveals a remarkable strain softening behaviour for all studied systems. 513 Consequently, the non-linear behaviour seems to appear at much smaller deformations 514 compared to those predicted by the Doi-Edwards tube model theory for entangled linear 515 polymers [74] or the force-balanced network model by Marrucci et al. [75]. Interestingly, the 516 non-linear viscoelastic behaviour of the O/W interface is similar to the one reported previously 517 for plant protein-stabilized emulsions, since the parameters of the damping function for the 518 Soskey-Winter model are similar in values [70]. Regardless of the pH value at the water 519 subphase, the damping function for the interfacial layer fits fairly well to either the Soskey-520 Winter model, described by Eq. (20), or the Laun model (Eq. 20), both of them describing a 521 clear strain softening behaviour. This strain dependence is higher at pH 5.0, according to the 522 value of parameter “a” from the Soskey-Winter model, which is similar for the interfacial layers 523 at pH 2.5 and 7.5. Strain softening has been explained for protein-stabilized emulsions in terms 524 of shear-induced deflocculation (physical) phenomena. By analogy, strain softening of protein 525 adsorbed interfacial layers may be regarded as the result of shear-induced disruption of physical 526 interactions among protein chains. The extent of this effect depends on pH since the interactions 527 are different. 528 Fig. 8 displays the experimental interfacial steady state viscosity obtained at the three pH values 529 studied: 2.5, 5.0 and 7.5 (A, B and C, respectively). A power-law decay for the interfacial 530 viscosity as a function of shear rate can be observed for the three pH values. 531 As previously outlined, this interfacial steady state viscosity may be predicted by means of a 532 suitable constitutive equation involving time-strain separability. According to Rolón-Garrido 533 and Wagner [64], the application of time-strain factorability has been widely used for a wide 534 variety of polymeric systems, including protein-stabilized emulsions. Thus, some studies on 535 24 protein-based concentrated O/W emulsions have applied time-strain separability by means of a 536 non-linear viscoelastic model such as the Wagner-I constitutive equation [68,70,76–78]. 537 The apparent interfacial viscosity at constant shear rate, 𝛾𝛾󰇗𝑠𝑠𝑠𝑠, can be obtained from the Wagner-I 538 constitutive equation (Eq. 17) either for stress growth tests, as a function of time, 𝜂𝜂𝑠𝑠 +(𝛾𝛾󰇗𝑠𝑠𝑠𝑠,𝑡𝑡)=539 𝜏𝜏𝑠𝑠 +(𝑡𝑡)𝛾𝛾󰇗𝑠𝑠𝑠𝑠 ⁄, or for steady state flow, where the total strain is 𝛾𝛾𝑠𝑠=𝛾𝛾󰇗𝑠𝑠𝑠𝑠 · (𝑡𝑡−𝑡𝑡′) for ∞<𝑡𝑡′<𝑡𝑡. 540 The steady state interfacial viscosity is a function of the imposed shear rate but is no longer a 541 function of time and can be calculated as follows: 542 𝜂𝜂𝑠𝑠�𝛾𝛾󰇗𝑠𝑠𝑠𝑠�=� 𝑚𝑚𝑠𝑠(𝑡𝑡−𝑡𝑡′)·ℎ𝑠𝑠(𝛾𝛾𝑠𝑠)·(𝑡𝑡−𝑡𝑡′)𝑑𝑑𝑡𝑡′ (22) 𝑡𝑡 −∞ 543 On the other hand, according to the definition of the memory function by the GM model (Eq. 7) 544 and the damping function for the Laun model (Eq. 19), the final expression for the Wagner-I 545 equation at constant 𝛾𝛾󰇗𝑠𝑠𝑠𝑠 is given by Eq. (23): 546 𝜂𝜂𝑠𝑠�𝛾𝛾󰇗𝑠𝑠𝑠𝑠�=� �𝐺𝐺𝑠𝑠,𝑘𝑘 𝜆𝜆𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒�−𝑡𝑡−𝑡𝑡′ 𝜆𝜆𝑘𝑘�·�𝑓𝑓𝑗𝑗𝑒𝑒𝑒𝑒𝑒𝑒�−𝑛𝑛𝑗𝑗𝛾𝛾󰇗𝑠𝑠𝑠𝑠(𝑡𝑡−𝑡𝑡′)� 2 𝑗𝑗=1 𝑛𝑛 𝑘𝑘=1 (𝑡𝑡−𝑡𝑡′)𝑑𝑑𝑡𝑡 (23) 𝑡𝑡 −∞ 547 This equation can be rearranged in the form: 548 𝜂𝜂𝑠𝑠�𝛾𝛾󰇗𝑠𝑠𝑠𝑠�=��� 𝐺𝐺𝑠𝑠,𝑘𝑘 𝜆𝜆𝑘𝑘𝑒𝑒𝑒𝑒𝑒𝑒�−𝑡𝑡−𝑡𝑡′ 𝜆𝜆𝑘𝑘�·𝑓𝑓𝑗𝑗𝑒𝑒𝑒𝑒𝑒𝑒�−𝑛𝑛𝑗𝑗𝛾𝛾󰇗𝑠𝑠𝑠𝑠(𝑡𝑡−𝑡𝑡′)�(𝑡𝑡−𝑡𝑡′)𝑑𝑑𝑡𝑡 𝑡𝑡 −∞ 𝑗𝑗 (24) 𝑘𝑘 549 Which can be integrated, obtaining the following solution: 550 𝜂𝜂𝑠𝑠�𝛾𝛾󰇗𝑠𝑠𝑠𝑠�=��⎣ ⎢ ⎢ ⎡ 𝐺𝐺𝑠𝑠,𝑘𝑘·𝑓𝑓𝑚𝑚 𝜆𝜆𝑘𝑘·�1 𝜆𝜆𝑘𝑘+𝑛𝑛𝑗𝑗𝛾𝛾󰇗𝑠𝑠𝑠𝑠�2⎦ ⎥ ⎥ ⎤ 𝑗𝑗 (25) 𝑘𝑘 551 An obvious limitation for this model is that it is not able to predict a high shear rate limiting 552 viscosity. Thus, 𝜂𝜂𝑠𝑠(∞)→0 when 𝛾𝛾󰇗𝑠𝑠𝑠𝑠 →∞. 553 On the other hand, when the damping function is represented by the Soskey-Winter analytical 554 expression, the Wagner-I equation has to be numerically solved for each case. 555 25 Steady state interfacial viscosity values calculated from Eq. (25) for the Wagner and Laun 556 models are included in Fig. 8, as well as data estimated numerically using the Wagner-I model 557 in combination with the memory function for the GM model and the Sokey-Winter damping 558 function. As may be deduced, the Wagner-I constitutive equation with Laun damping function 559 provides a fairly well prediction of the experimental interfacial flow behaviour. Some 560 deviations from experimental data can be only appreciable for the protein-adsorbed interfacial 561 layer at pH 5.0 (Fig. 8B). This deviation is an error propagation from i-SAOS fitting carry out 562 at pH 5.0, using the GM model (Fig. 6B). 563 Moreover, the values of the interfacial complex viscosity for each pH studied are also displayed 564 in Fig. 8 as a function of frequency. This figure indicates that the Cox-Merz rule, which involves 565 an equivalence between complex and steady state viscosity for a variety of polymers, cannot be 566 applied in its original form for these O/W interfaces. This occurs even though the slope for both 567 interfacial complex and steady state viscosities are quite similar, as may be seen in Table 3, 568 which also shows the reduction rate (RR) obtained by shifting from linear viscoelasticity 569 (𝜂𝜂𝑠𝑠 ∗(𝜔𝜔)) to steady state flow conditions (𝜂𝜂𝑠𝑠(𝛾𝛾󰇗𝑠𝑠)). These negative slopes, being not far from unity 570 (i.e. 0.92±0.01) regardless of pH, indicate that the O/W interface shows a very shear-thinning 571 behaviour. 572 This very shear-thinning behaviour, with similar slopes, has been also reported for highly 573 flocculated emulsions and has been associated to a shear-induced deflocculation process 574 [18,70]. 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Y). 47 (2003) 897–910. 831 36 832 833 37 Figure Captions 834 Fig. 1: Values for the interfacial pressure (𝛱𝛱) at the O/W interface at different pH values (2.5, 5.0 and 835 7.5) after reaching the apparent equilibrium (i.e. after 24 h) as a function of protein concentration for 836 the aqueous phase (𝑐𝑐𝑊𝑊) measured using a Wilhelmy plate. 837 Fig. 2: Protein adsorption kinetics at the O/W interface at different pH values (2.5, 5.0 and 7.5), recorded 838 for the concentration of the aqueous phase at which the O/W interface becomes saturated: (A) Values 839 for the interfacial pressure (𝛱𝛱) as a function of adsorption time (𝑡𝑡); (B) Initial values of the interfacial 840 pressure (𝛱𝛱) as a function of the square root of time �𝑡𝑡1 2 ⁄� for the diffusion stage; (C) Dimensionless 841 interfacial pressure �𝛱𝛱𝑓𝑓−Π(𝑡𝑡) 𝛱𝛱𝑓𝑓−𝛱𝛱0� as function of time (𝑡𝑡) after the diffusion stage. 842 Fig. 3: Evolution of the linear dilatational moduli (𝐸𝐸’𝑠𝑠(𝜔𝜔) and 𝐸𝐸"𝑠𝑠(𝜔𝜔)) at a strain amplitude of 5 % and 843 different pH values (2.5, 5.0 and 7.5), obtained for the concentration of the aqueous phase at which the 844 O/W interface becomes saturated: (A) As a function of adsorption time (at a constant frequency of 0.1 845 Hz); (B) As a function of frequency after reaching the pseudo-equilibrium (i.e. after 180 min). 846 Fig. 4: Evolution of the interfacial shear elastic modulus �𝐺𝐺’𝑠𝑠(𝜔𝜔)� and loss tangent �tan 𝛿𝛿𝑠𝑠(𝜔𝜔)� at a 847 strain amplitude and of 0.05% and three different pH values (2.5, 5.0 and 7.5), obtained for the 848 concentration of the aqueous phase at which the O/W interface becomes saturated: (A) As a function of 849 adsorption time (at a constant frequency of 0.1 Hz); (B) As a function of frequency after reaching the 850 pseudo-equilibrium (i.e. after 180 min). 851 Fig. 5: Evolution of the linear interfacial shear mechanical spectra obtained at different time intervals 852 during protein adsorption at the O/W interface until the pseudo-equilibrium state, at a strain amplitude 853 and of 0.05% and different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the protein concentration 854 at the bulk aqueous phase was the one at which the O/W interface becomes saturated. 855 Fig. 6: Experimental values of the relaxation modulus, 𝐺𝐺𝑠𝑠�𝛾𝛾𝑠𝑠,𝑡𝑡� and calculated values of the linear 856 relaxation modulus 𝐺𝐺𝑠𝑠�𝛾𝛾𝑠𝑠� from the generalized Maxwell (GM) model, obtained for the concentration 857 of the aqueous phase at which the O/W interface becomes saturated, at three different pH values: (A) 858 38 2.5; (B) 5.0; (C) 7.5. In all the cases, the measurements were carried out after reaching the pseudo-859 equilibrium state (i.e. after 180 min). 860 Fig. 7: Experimental and calculated damping function values (ℎ𝑠𝑠�𝛾𝛾𝑠𝑠�) from the Wagner, Laun and 861 Soskey-Winter models, obtained for the concentration of the aqueous phase at which the O/W interface 862 becomes saturated, at three different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the 863 measurements were carried out after reaching the pseudo-equilibrium state (i.e. after 180 min). 864 Fig. 8: Experimental and predicted interfacial steady state viscosity from the Wagner-I model, obtained 865 for the concentration of the aqueous phase at which the O/W interface becomes saturated, at three 866 different pH values: (A) 2.5; (B) 5.0; (C) 7.5. In all the cases, the measurements were carried out after 867 reaching the pseudo-equilibrium state (i.e. after 180 min). 868 869 39 Table 1 870 871 pH k D · 103 (mN/m·s -1/2 ) k A · 104 (s -1 ) 2.5 51200* ± 520a -3.52 ± 0.02A 5.0 2.07 ± 0.06b -2.61 ± 0.04B 7.5 36800* ± 739c -3.04 ± 0.01C 872 Table 1: values of kD and kA for protein adsorption as a function of pH value. Superscript indicates apparent 873 diffusion rate constant (𝑘𝑘𝐷𝐷 ∗). Different letters within a column indicate significant differences (p < 0.05). 874 Table 2 875 876 Dilatational Shear pH tan 𝛿𝛿𝑠𝑠(0.1) 𝐸𝐸′𝑠𝑠(0.1) (mPa·m) tan 𝛿𝛿𝑠𝑠(0.1) 𝐺𝐺′𝑠𝑠(0.1) (mPa·m) 2.5 0.07 ± 0.01α 27.1 ± 0.3a 0.17 ± 0.03Г 17.1 ± 0.2A 5.0 0.14 ± 0.02β 21.6 ± 0.4b 0.19 ± 0.01П 8.0 ± 0.5B 7.5 0.02 ± 0.01γ 13.2 ± 0.6c 0.23 ± 0.02Ф 8.6 ± 0.3B 877 Table 2: parameters obtained from both, dilatational rheology and interfacial shear rheology obtained at 0.1 Hz. 878 Different letters within a column indicate significant differences (p < 0.05). 879 880 Table 3 881 882 pH 1 - n 1 - n* B RR (%) 2.5 0.94 ± 0.01a 0.91 ± 0.02A 31.4 ± 0.3α 95.9 ± 0.2Γ 5.0 0.91 ± 0.02a 0.93 ± 0.02A 22.3 ± 0.2β 94.3 ± 0.4Π 7.5 0.92 ± 0.01a 0.93 ± 0.01A 12.9 ± 0.2γ 90.6 ± 0.3Φ 883 Table 3: parameters obtained from fitting interfacial steady state viscosity curves. Different letters within a 884 column indicate significant differences (p < 0.05) 885 40 Figure 1 886 887 888 0123456 8 10 12 14 16 18 20 22 pH 2.5 pH 5.0 pH 7.5 Π (mN/m) c W (wt. %) 41 Figure 2 889 890 891 892 02000 4000 6000 8000 10000 4 6 8 10 12 14 16 18 20 22 Time (s) pH 2.5 pH 5.0 pH 7.5 Π (mN/m) A