Rheology of protein-stabilised emulsion gels envisioned as composite networks. 2 -- Framework for the study of emulsion gels
RRheology of protein-stabilised emulsion gels envisionedas composite networks.2 - Framework for the study of emulsion gels
Marion Roullet a,b, ∗ , Paul S. Clegg b , William J. Frith a a Unilever R&D Colworth, Sharnbrook, Bedford, MK44 1LQ, UK b School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road,Edinburgh, EH9 3FD, UK
Abstract
Hypothesis
The aggregation of protein-stabilised emulsions leads to the formation ofemulsion gels. These soft solids may be envisioned as droplet-filled matrices.Here however, it is assumed that protein-coated sub-micron droplets con-tribute to the network formation in a similar way to proteins. Emulsion gelsare thus envisioned as composite networks made of proteins and droplets.
Experiments
Emulsion gels with a wide range of composition are prepared and theirviscoelasticity and frequency dependence are measured. Their rheologicalbehaviours are then analysed and compared with the properties of pure gelspresented in the first part of this study.
Findings
When the concentrations of droplets and protein are expressed as aneffective volume fraction, the rheological behaviour of emulsion gels is shownto depend mostly on the total volume fraction, while the composition of thegel indicates its level of similarity with either pure droplet gels or pure protein ∗ Current address: BioTeam/ECPM-ICPEES, UMR CNRS 7515, Universit´e de Stras-bourg, 25 rue Becquerel, 67087 Strasbourg Cedex 2, France
Email addresses: [email protected] (Marion Roullet), [email protected] (Paul S. Clegg), [email protected] (William J. Frith)
Preprint submitted to Journal of Colloid and Interface Science October 6, 2020 a r X i v : . [ c ond - m a t . s o f t ] O c t els. These results help to form an emerging picture of protein-stabilisedemulsion gel as intermediate between droplet and protein gels. This justifies a posteriori the hypothesis of composite networks, and opens the road forthe formulation of emulsion gels with fine-tuned rheology. Keywords:
Colloidal gel, Rheology, Emulsion, Sodium caseinate,Viscoelasticity, Protein-stabilised droplet, Formulation, Mixture
Graphical abstract1. Introduction
Emulsion gels are materials of great interest, because of their many appli-cations in foods, drug-release pharmaceutical products, and novel personalcare products [1, 2, 3]. Emulsion gels are soft solids that contain a liquidphase, usually water, trapped within the pores of a network comprised ofemulsion droplets [4]. However, this general description conceals the verydifferent structures that emulsion gels can have, depending on their compo-sition [5]. Despite the increased efforts in relating the mechanical propertiesof emulsion gels to their composition, the full understanding of these links isstill lacking.Traditionally, for emulsion gels, the distinction is made between emulsion-filled gels - in which the droplets act as fillers in a viscoelastic gel matrix - andemulsion particulate gels - in which aggregated droplets form a gel network of2heir own [4, 5]. Emulsion-filled gels have been studied widely, and a meanfield theoretical approach has been used to model the gel matrix, that isoften a protein gel, as a continuous medium [6, 7]. In that framework, theemulsion droplets are elastic inclusions that can be deformed upon stressingthe emulsion gel [8], and that present interactions with the matrix that areeither attractive (active fillers) or repulsive (passive fillers) [9, 10, 11, 12, 13,14]. Emulsion particulate gels have attracted less attention, and they wereconsidered to be similar to other colloidal gels [15, 16, 17]. An exception is thefirst part of this series, in which pure gels made of protein-stabilised emulsiondroplets have been studied and their rheological properties characterised [18].At this point, it is useful to note the difference between emulsion gelsand concentrated emulsions like mayonnaise, which also display a solid-likebehaviour. Emulsion gels present a solid gel network, that can be relativelydilute, and that traps a significant amount of solvent within its pores. Bycontrast, concentrated emulsions are made of jammed repulsive droplets,that are limited in their mobility by the presence of the other droplets [19].Such jammed systems are often refered to as colloidal glasses [20], and arecomparable to other glasses made of soft particles, such as star polymers andmicrogels [21, 22, 23, 24]. The present study will focus on emulsion gels, andthe emulsions used to prepare the gels will thus be kept at concentrations forwhich a low-shear viscosity can be defined.The binary distinction between emulsion-filled gels and emulsion partic-ulate gels is however limited by the strong assumptions that are made whendefining these two situations. First, the approximation of a continuous ma-trix, in which the droplets are embedded, does not always apply. Indeed,this matrix is often a protein gel, which is a ramified network with a meshsize of a few microns [25, 26], so it is assumed that the droplets are muchlarger. Yet, sub-micron droplets are widely used in commercial products, astheir production is made easier by the advances in emulsification techniques,and notably the use of microfluidizers [27, 28]. There can thus be emulsiongels in which the droplets are smaller than the pores of the matrix, whichcannot then be approximated by a continuous medium.Furthermore, it is worth noting that the formation of large aggregates andnetworks of attractive droplets would make a significant contribution to theoverall viscoelasticity of the emulsion gel, but this is generally not consideredin the emulsion-filled gel model, while it is central to the existence of emulsionparticulate gels. Previous efforts to account for droplet aggregation, and itscontribution to the viscoelasticity, in the emulsion-filled gel model, have not3et lead to an accurate estimation of the changes in viscoelasticity inducedby droplet aggregation [29]. It thus appears necessary to fill the gap betweenthese two models of emulsion gels, to define a more accurate framework forthe study of these materials.This study focuses on the gels produced by destabilising protein-stabilisedemulsions, in which proteins - more specifically sodium caseinate - act bothas surface-active emulsifier, to form sub-micron oil droplets stabilised bysteric and electrostatic repulsion at neutral pH, and as gelling agent. Whenthe emulsion is acidified, the electrostatic repulsion is decreased, and at theprotein isoelectric point, attractive van der Waals interactions lead to thegelation of the proteins and of the protein-coated droplets [7]. In order toensure a sufficient surface coverage of the droplets in real systems, and thusa good stability of protein-stabilised emulsions, it is common to work witha protein excess, so a mixture of protein-coated droplets and of unadsorbedproteins is obtained after emulsification [30]. In summary, the gels studiedhere are made of sub-micron droplets covered with proteins, and of sodiumcaseinate, structured into self-assembling aggregates of around 20 nm. Theoil droplets are part of the network, as they exhibit an attractive interactionbetween them mediated by the adsorbed proteins at their interface. Theprotein-stabilised droplets and caseinate assemblies presented here have beenthoroughly characterised in a previous study [31].In the first paper of this pair, pure gels of caseinate assemblies and puregels of caseinate-stabilised sub-micron droplets were prepared and charac-terised [18]. It was shown that the gelation of protein suspensions and ofpurified suspensions of droplets led to gel networks with a characteristiclength-scale of the order of a few microns. The emulsions studied here arethus characterised by droplets that are smaller than the length-scale of thenetworks, and these droplets aggregate extensively to form a space-spanningfractal network, even at low concentration.In addition, it was shown that the concentrations of the suspensions ofproteins, and of protein-stabilised droplets, could be scaled by the effectivevolume fraction φ eff , and their viscosity could be analysed in the frameworkdeveloped for soft colloids [31]. This parameter φ eff represents the volumeoccupied by the particles in the sample divided by the total volume. It iscalculated by multiplying the concentration by a parameter k , derived byapproximating protein aggregates and protein-stabilised droplets to modelhard spheres when in semi-dilute suspensions. This same framework wasused to study the gels formed by the two types of suspensions in the first4art of this series, and the scaling by the effective volume fraction φ eff madeit possible to emphasise the similarities between the two types of gels at fixed φ eff , both in terms of microstructural features and of rheological properties[18].The present work envisions protein-stabilised emulsion gels as compos-ite networks made of un-adsorbed protein assemblies and protein-coateddroplets. This approach relies on the hypothesis that there is little distinc-tion between droplets and un-adsorbed proteins in the way each contributesto the properties of the gel of mixture. This is because the most relevantlength-scale to study the rheological and microstructural features of colloidalgels appears to be the length-scale of strands of particles [32, 33, 34, 35]. Con-sequently, the systems are examined at a much larger scale than of the singleparticles, and the discrepancy in size and structure of the protein aggregatesand protein-stabilised droplets is thus assumed not to be critical.Here, protein-stabilised emulsion gels with a wide range of protein anddroplet content are prepared, and their rheological properties are charac-terised and analysed as a function of the composition of the sample. Theemulsion gels are then compared to the pure gels of proteins and droplets, toidentify the contribution of each of the components to the rheological prop-erties of the composite networks. The emulsion gels are shown to displayan intermediate behaviour between those of pure gels of proteins and puregels of droplets, thus confirming that the framework of composite networks ismore relevant for these systems than the two models identified in the existingliterature.
2. Materials & Methods
Suspensions of pure sodium caseinate and of pure sodium caseinate-stabilised droplets were prepared as described in a previous study [31], ata range of concentrations. They were then used as sols for the preparationof acid-induced gels.
Sodium-caseinate emulsions of well-characterised compositions were pre-pared by mixing precise amounts of the protein suspension and of the paste ofpurified droplets. A wide range of compositions of mixtures was explored. In5he following, the terms mixture and emulsion will be used without distinc-tion to indicate the samples prepared in this section (as opposed to a standardemulsion where the amount of un-adsorbed protein is uncontrolled).
To prepare emulsions with a controlled amount of proteins in suspension,the paste of purified droplets at (0 . ± . − was re-suspended ina protein suspension. The protein suspension was prepared as describedpreviously at 45 mg mL − and diluted to the desired concentration. As forthe suspensions of pure droplets, the paste was first roughly homogenisedwith a spatula in the vial, and then gently mixed using a magnetic stirrer.The mixing time required to obtain a visibly homogeneous sample rangedfrom 5 min to 2 h. The re-dispersion required longer stirring times at highconcentration of droplets and at high concentration of proteins. At a givendroplet concentration, significantly more stirring was required to disperse thedroplets in a protein suspension than in water. It is useful to think about protein-stabilised emulsions as ternary mix-tures, made of water and of two sorts of colloidal particles: droplets andprotein aggregates. Table S1, in the supplementary material, gives the com-position of all the mixture samples. The concentrations were calculated fromthe dilution of the stocks of pure proteins and pure droplets, while volumefractions were calculated from the concentrations as detailed in a previousstudy [31].
The gels were prepared as described in the first part of this study [18]. Thedecrease in pH required for the gelation of the sols to occur was induced bythe slow hydrolysis of glucono δ -lactone (Roquette). The amount of glucono δ -lactone was calculated appropriately for the protein and droplet contents ofeach sample, using the following weight ratios: for protein glucono δ − lactoneprotein =0 . glucono δ − lactonedroplet = 0 . . . ° C, in order to accelerate the phasetransition. Indeed, over long time scales, adverse phenomena such as cream-ing or bacterial growth may occur in the samples. Following this protocol,6he gelation of the suspensions takes between 30 min and 2 h , depending onthe type of sample and concentration.The sols containing glucono δ -lactone were placed in the rheometer cupjust after preparation, and the measurements were started immediately. Oscillatory rheology measurements were performed using a stress-controlledMCR 502 rheometer (Anton Paar) and a Couette geometry (17 mm diam-eter profiled bob and cup CC17-P6, inner radius 16 .
66 mm, outer diameter18 .
08 mm yielding a 0 .
71 mm tool gap, gap length 25 mm). To avoid slip atthe wall during shearing, profiled bob and cup (serration width 1 . . ° C during the entire measurement sequence.To prevent evaporation, a thin layer of silicon oil of low viscosity (10 cSt)was deposited on the surface of the sample.The measurements were started immediately after mixing of the samplewith glucono δ - lactone and subsequent loading in the instrument. First,small-amplitude oscillations (superposition of sinusoids of amplitude γ =0 . . . γ = 4 . f = 0 . . . .
50 Hz for the base frequency) at fixedamplitude ( γ = 4 %). For each sample, 3 measurements were performed andthe values were averaged.
3. Results & Discussion
In order to achieve a thorough study of emulsion gels, it is importantto study the full range of what is described as an emulsion, and thus tovary the contents of droplets and un-adsorbed proteins, both in terms of thetotal concentration and also the ratio of the two components. The choice ofparameters for the composition of the gels is a core part of the frameworkapplied to the problem of the study of mixtures.Previous studies of emulsion gels have focused on the contribution of thedroplets [36, 12], or of the matrix [3] to the properties of the gels. Because7he role of these two components were considered distinct and studied sep-arately, the individual concentrations were used in the literature to describethe composition of the gels.However, in the present study, the emulsion gels are envisioned as compos-ite networks, similar to the gels formed by the pure gels made of proteins orof droplets. Thus, in order to make possible the comparison of emulsion gelswith pure gels, the focus of the new framework has to be changed, from theindividual content of each component in the mixture φ eff,prot and φ eff,drop ,to the total content φ eff,tot = φ eff,prot + φ eff,drop and their relative amounts,described here as φ eff,drop / ( φ eff,prot + φ eff,drop ). This choice of parameters ispresented in Figure 1. Figure 1: Composition of the emulsion gel samples prepared in this study. The gelsare envisioned as composite networks, and thus described by their total volume fraction φ eff,prot + φ eff,drop (coded by the size of the symbols) as a function of the ratio of dropletsover the total volume fraction φ eff,drop / ( φ eff,prot + φ eff,drop ) (colour coded). As can be seen, these two parameters make the distinction between gelsthat are similar to protein gels ( φ eff,drop / ( φ eff,prot + φ eff,drop ) (cid:39)
0) and gelsthat are closer to droplet gels ( φ eff,drop / ( φ eff,prot + φ eff,drop ) (cid:39) The rheological properties of the emulsion gel samples, whose composi-tions are presented in Figure 1, were measured during and after gelation.To compare the viscoelasticity of the gels at similar ageing state, the differ-ences in gelation kinetics between samples were taken into account followingthe same protocol as in the first part of this series [18]. In short, the gela-tion curves were first shifted horizontally and vertically in logarithmic scaleto achieve collapse onto a master curve [37, 38, 39]. The storage and lossmoduli were then measured at a given scaled time on the master curve, aspresented In Figure S1 of the supplementary material. The storage and lossmoduli of emulsion gels can be compared with the moduli of the gels of purecomponents presented in the first part of this study [18]. These results aredisplayed in Figure 2.As can be seen, the moduli of the emulsion gels are of the same order ofmagnitude as for the pure gels and they follow the same trend with the vol-ume fraction. The elastic and viscous aspects of the network are thus mainlydetermined by the total effective volume fraction φ eff,droplet + φ eff,protein , andonly moderately by the composition. As can be seen in Figure S2 in the sup-plementary material, this finding is not visible when the weight concentrationis used. This result demonstrates that the use of the effective volume fractiondeveloped for suspensions of pure components in Ref.[31] is also relevant forthe description of emulsion gels, despite the approximations used.9 Fit droplet gels S t o r age m odu l u s G ’ ( P a ) (a) Ratio f droplet /f protein +f droplet Lo ss m odu l u s G ’’ ( P a ) Effective volume fraction f eff
Gels of mixture
Figure 2: Storage ( G (cid:48) , (a)) and loss ( G (cid:48)(cid:48) , (b)) moduli at 1 Hz of protein-stabilised dropletgels (circles, cyan), of protein gels (squares, navy blue), and of gels of mixtures (diamond,colour-coded by the value of φ eff,drop / ( φ eff,prot + φ eff,drop )) as functions of the effectivevolume fraction of the gel (respectively φ eff,drop , φ eff,prot and φ eff,prot + φ eff,drop , scalingderived in Ref.[31]). A power-law fit was performed for each system in the first part ofthis study, and the model as well as the 95 % confidence band are displayed on each graph.The horizontal and vertical error bars are calculated using the error propagation theory.
10n addition, small variations in the viscoelastic properties of emulsiongel samples with similar volume fractions but different compositions seemto imply that the nature of the elementary particles forming the networkmust be taken into account for a more detailed description. Two differentapproaches for the analysis of the storage moduli, shown in Figure 2 (a), aretherefore suggested here to emphasise the influence of the composition andthe reinforcement of the gels.
First, the classical droplet-filled gel approach can be used for the analysisof the influence of the composition of emulsion gels on their viscoelasticity.In this way, emulsion gels can be considered either as protein gel matricesfilled with droplets, or as droplet gel matrices filled with proteins. In thisframework, it is interesting to look at the change in rheological propertiesof the matrix gel upon addition of fillers. The presence of attractive vander Waals interactions between protein-stabilised droplets and proteins whengelation occurs indicates that the addition of filler probably has a reinforcingeffect [9].This reinforcing effect of the component chosen as filler, droplets for ex-ample, on the strength of the matrix of the other component, here the proteingel, can be expressed by the ratio of storage moduli between mixture andmatrix: G (cid:48) expmixture G (cid:48) modelprotein ( φ protein ) (1)Where G (cid:48) expmixture is the experimental storage modulus of the mixture, as pre-sented in Figure 2. G (cid:48) modelprotein is the modulus of a hypothetical protein gel,containing the same volume fraction of protein φ protein as the mixture, andcalculated using the model developed in the first part of this series: G (cid:48) ( φ eff ) = G (cid:48) ,φ × φ αeff (2)The values of the parameters G (cid:48) ,φ and α found in the first part of the seriesare summarised in Table 1 [18].Alternatively, if any emulsion gel is seen as a protein-filled droplet gelmatrix, then the reinforcing role of the proteins can be expressed by G (cid:48) expmixture G (cid:48) modeldroplet ( φ droplet )11 able 1: Parameters to calculate G (cid:48) modelprotein and G (cid:48) modeldroplet using Equation 2. Gel type G (cid:48) ,φ α Droplet gels (4 . ± .
22) kPa 3 . ± . . ± .
19) kPa 2 . ± . G (cid:48) modeldroplet is also calculated using thecharacterisation of pure droplet gels as a function of the volume fraction.The two scenarios, droplet-filled protein gels and protein-filled dropletgels, are used for the analysis of the gels of mixtures presented in Figure 2,and the reinforcement in both cases is shown in Figure 3. The reinforcementof the gel is represented as a function of the proportion of droplets in themixture, rather than the volume fraction of droplets, in order to facilitatecomparisons of gels at different concentrationsAs can be seen, there is a collapse of the reinforcing effects for matricesof different volume fraction to a single master curve in both cases. For thetwo scenarios, the elastic modulus is doubled when the amount of filler addedis 25 % of the matrix volume fraction ( i.e. φ filler / ( φ filler + φ matrix ) = 0 . i.e. φ filler / ( φ filler + φ matrix ) = 0 . atrix FillerMixtureMatrix FillerMixture (a)(b) φ droplet / φ protein + φ droplet Figure 3: Reinforcement of a protein gel upon addition of droplets G (cid:48) expmixture /G (cid:48) modelprotein ( φ protein ) (top, from left to right), and of a droplet gel upon ad-dition of proteins G (cid:48) expmixture /G (cid:48) modeldroplet ( φ droplet ) (bottom, from right to left) as a function ofthe relative amount of droplet added φ eff,drop / ( φ eff,prot + φ eff,drop ). The miscellaneousvolume fractions of matrices are indicated by x%, and the values can be found in TableS1. The two graphs represent the same samples of gels of mixtures, as shown in Figure 2,but differ by the arbitrary role of the components: the proteins form the matrix in thetop graph while they are the fillers in the bottom graph, and vice-versa for the droplets,as depicted in the cartoon. In this second approach to the viscoelastic behaviour of emulsion gels,they are envisioned as composite colloidal gels of total volume fraction φ eff,prot + φ eff,drop and for which the composition indicates how similar theyare to pure gels of droplets and of proteins. The focus is thus moved fromthe reinforcement of a matrix with the addition of another colloidal species,to the comparison of the composite networks with pure gels at the same totalvolume fraction.The storage modulus G (cid:48) expmixture of the gels formed by the mixtures can becompared to the weighted mean of the storage moduli of the gels formed bytheir pure components. This can be achieved using the power law dependenceon the volume fraction identified in the first part of this study for pure gels[18]. A theoretical storage modulus G (cid:48) modelmixture for the emulsion gels can thusbe expressed by a linear rule of mixture: G (cid:48) modelmixture = φ droplet φ protein + φ droplet × G (cid:48) modeldroplet ( φ protein + φ droplet )+ (cid:18) − φ droplet φ protein + φ droplet (cid:19) × G (cid:48) modelprotein ( φ protein + φ droplet ) (3)Where G (cid:48) modelprotein and G (cid:48) modeldroplet designate the modulus of a hypothetical proteingel (resp. droplet gel), containing the same total volume fraction φ protein + φ droplet as the mixture, and calculated using Equation 2 and the values pre-sented in Table 1.The ratio between experimental and theoretical storage moduli G (cid:48) expmixture /G (cid:48) modelmixture is shown in Figure 4 as a function of the composition,described by the ratio φ eff,drop / ( φ eff,prot + φ eff,drop ). Schematically, this figurecan be interpreted as the change in gel strength in a network of fixed volumefraction when its composition goes from a pure protein gel to a pure dropletgel.As can be seen, Equation 3 provides a good approximation of the storagemodulus of emulsion gels over a large part of the composition range, as theratio G (cid:48) expmixture /G (cid:48) modelmixture ≈
1. A noticeable increase of this ratio is observed forthe mixtures with 50 % < φ eff,drop / ( φ eff,prot + φ eff,drop ) <
70 %, for which the14 .0 0.2 0.4 0.6 0.8 1.00.51.01.52.0
Gels of pure components Protein gels Droplet gels Gels of mixtures
Ratio φ droplet / φ protein + φ droplet Figure 4: Ratio between the experimental storage modulus G (cid:48) expmixture and the theoreticalstorage modulus G (cid:48) modelmixture , defined in Equation 3 as the weighted mean of the pure gelsmoduli, as a function of the relative amount of droplets φ eff,drop / ( φ eff,prot + φ eff,drop )illustrated in the cartoon. The size of the data points indicates the total volume fraction φ eff,drop + φ eff,prot . This graph represents the same gel samples than shown in Figure 2.The error bars arise from error propagation upon calculation of the theoretical storagemodulus, and take into account the errors of the models for each pure component. φ eff,drop + φ eff,prot . It is then corrected for the composition of the mixtureby using the trend for the normalised storage moduli displayed in Figure 4. Similarly to the pure protein and droplet gels presented in the first partof this study, the frequency dependence of emulsion gels was measured aftergelation, and is represented in Figure S3 of the supplementary material [18].The dependence of the storage modulus of emulsion gels on frequency can bemodelled by a power law, as was done for pure gels: G (cid:48) = G (cid:48) ,ω × ω β Where the exponent β describes the dynamic behaviour of the networks.Here β is estimated for each emulsion gel and presented as a function of thecomposition in Figure 5.This representation of the frequency dependence of the network as a func-tion of the ratio φ eff,drop / ( φ eff,prot + φ eff,drop ) demonstrates that there is acontinuous transition between that of droplet gels, at the lower end of thehorizontal axis, and of protein gels, at the upper end of the horizontal axis.Indeed, the frequency dependence of mixtures presents some variations withthe total volume fraction, represented by the size of the data points, butvaries overall between β droplet ≈ . β protein ≈ . .0 0.2 0.4 0.6 0.8 1.00.100.150.200.25 P o w e r l a w e x ponen t β Ratio φ droplet / φ protein + φ droplet Figure 5: Comparison of frequency dependence for gels of mixtures (diamonds, colour-coded), of protein stabilised droplets (circles, in cyan) and of protein (squares, in darkblue): power-law exponent β as a function of the ratio φ eff,drop / ( φ eff,prot + φ eff,drop ).The size of the data points indicates the total volume fraction φ eff,drop + φ eff,prot . Theshaded area is a guide for the eye. protein increases in the mixture. This is in good correspondence with previ-ous studies in which a decrease in frequency dependence was observed uponaddition of casein-coated droplets in a casein gel [9].Therefore, it seems that the difference in dynamics between droplets andproteins is reflected linearly in the mixtures as a function of their composi-tion. This result reinforces the hypothesis that emulsion gels are compositenetworks that are best described as intermediate between protein gels anddroplet gels.
4. Conclusion
The choice of the parameters used for the description of protein-stabilisedemulsion gels with sub-micron droplets is the first step in giving shape to anew framework for these systems. Here, based on qualitative argumentsabout the structure of colloidal gels, it is suggested that this category of softsolids can be viewed as composite networks made of droplets and proteinassemblies. The composition of these systems was thus defined by their totalvolume fraction φ eff,prot + φ eff,drop and composition ratio φ eff,drop / ( φ eff,prot +17 eff,drop ). These parameters were calculated by using a previous study onthe viscosity of pure suspensions of proteins and of droplets [31]. This twodimensional composition range of emulsion gels was explored in this study.The analysis of the rheological properties of emulsion gels in this frame-work confirmed the relevance of this choice. Indeed, it was found that thestorage modulus is mostly determined by the total volume fraction of theemulsion gel φ eff,prot + φ eff,drop . In addition, when the strength of the emul-sion gels is scaled in order to account for the variations in volume fraction,it varies continuously between the behaviour of pure protein gels and puredroplet gels following a simple rule of mixture. Similarly, the frequencydependence varies continuously between the behaviour of protein gels anddroplet gels, linearly with the composition ratio φ eff,drop / ( φ eff,prot + φ eff,drop ).Notably, the decoupling of total volume fraction and relative composition forthe rheological properties justifies a posteriori the choice of parameters.In addition, the viscoelasticity of the emulsion gels presented here wasalso analysed using the classical approach of droplet-filled matrix [4, 5]. Itwas shown that the total volume fraction is more important than the absoluteamount of fillers, as the reinforcing effect of fillers collapsed onto a master-curve when scaled by the density of the matrix. This finding shines a newlight on previous studies of the rheology of attractive droplet-filled emulsiongels [9, 10, 11, 12, 13, 14]. In addition, the symmetric role of the compo-nents may reinforce the idea of composite networks, where the stress-bearingstrands are formed by the proteins and protein-stabilised droplets alike. Theclassical approach for these systems thus yields results that seem to reinforcethe image of protein-stabilised emulsion gels as intermediate colloidal gels.The implications of these results are multiple. A first obvious applicationis the formulation of dairy products with a more refined control of their rheo-logical properties, as the present study offers a more precise characterisationof the contributions of un-adsorbed proteins and of sub-micron droplets. Thisfalls within the emerging framework of dairy products, like milk and cheese,envisioned as soft colloidal systems [31, 41].More generally, the description of emulsion gels as intermediate colloidalgels could offer a model for the formulation of emulsion gels of fine-tunedrheology. Indeed, the study of emulsion gels of any composition could beperformed in two steps. First, pure gels of the two components are char-acterised over a wide range of volume fraction, in what could be describedas a calibration step. Then, using the quantification of the variation in theintermediate zone between the two limit systems, the properties of any gel18f mixture can be calculated using their composition. Such an analyticalapproach to formulation would present the advantage of identifying a smallrange of possible composition to reach the required mechanical properties,rather than using a more common “trial and error” process.Finally, in a broader picture, mixture systems are not commonly studiedin academic research, despite being ubiquitous in industrial products. Herea simple framework for thinking about emulsion gels is suggested. In this,they are first deconstructed into their components, protein-stabilised dropletsand un-adsorbed proteins, and then compared to these primary systems.This approach may be valid for a larger range of ternary mixtures in whichtwo components play a similar role in building up the viscoelasticity, whilethe solvent plays none. Further investigations are needed to identify othersystems that can be modelled as composite networks.
5. Acknowledgements
This project forms part of the Marie Curie European Training NetworkCOLLDENSE that has received funding from the European Union’s Horizon2020 research and innovation programme Marie Sk(cid:32)lodowska-Curie Actionsunder the grant agreement No. 642774