# Interfacial protein-protein displacement at fluid interfaces

Emma B.A. Hinderink, Marcel B.J. Meinders, Reinhard Miller, Leonard Sagis, Karin Schroën, Claire Berton-Carabin

► To cite this version:

Emma B.A. Hinderink, Marcel B.J. Meinders, Reinhard Miller, Leonard Sagis, Karin Schroën, et al. Interfacial protein-protein displacement at fluid interfaces. Advances in Colloid and Interface Science, 2022, 305, pp.102691. 10.1016/j.cis.2022.102691. hal-04698364

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## Historical Perspective

# Interfacial protein-protein displacement at fluid interfaces

Emma B.A. Hinderink<sup>a,b,1,*</sup>, Marcel B.J. Meinders<sup>b,c</sup>, Reinhard Miller<sup>d</sup>, Leonard Sagis<sup>e</sup>, Karin Schroën<sup>a</sup>, Claire C. Berton-Carabin<sup>a,f</sup>

<figure><img src="image_3.png" /></figure>

## ARTICLE INFO

### Keywords:

- Interfacial rheology

- Competitive adsorption

- Protein-stabilised emulsion

- Brownian dynamics simulations

- Adsorption model

- Surface equation of state

## ABSTRACT

Protein blends are used to stabilise many traditional and emerging emulsion products, resulting in complex, non-equilibrated interfacial structures. The interface composition just after emulsification is dependent on the competitive adsorption between proteins. Over time, non-adsorbed proteins are capable of displacing the initially adsorbed ones. Such rearrangements are important to consider, since the integrity of the interfacial film could be compromised after partial displacement, which may result in the physical destabilisation of emulsions. In the present review, we critically describe various experimental techniques to assess the interfacial composition, properties and mechanisms of protein displacement. The type of information that can be obtained from the different techniques is described, from which we comment on their suitability for displacement studies. Comparative studies between model interfaces and emulsions allow for evaluating the impact of minor components and the different fluid dynamics during interface formation. We extensively discuss available mechanical physical models that describe interfacial properties and the dynamics of complex mixed systems, with a focus on protein in-plane and bulk-interface interactions. The potential of Brownian dynamic simulations to describe the parameters that govern interfacial displacement is also addressed. This review thus provides ample information for characterising the interfacial properties over time in protein blend-stabilised emulsions, based on both experimental and modelling approaches.

## 1. Introduction

A broad range of biological materials and manufactured products contain oil droplets dispersed in an aqueous phase, called emulsions, as for example in plant energy storage organs, milk, mayonnaise, paints and cosmetics. Various emulsifiers are commonly found in such systems, of which proteins are paramount representatives for food applications. Interfacial protein layers are usually thin (2–6 nm) and electrically charged [1,2], and a (two-dimensional) network may be formed driven by in-plane protein interactions, which protects droplets against coalescence [3–5]. Since emulsions are interface-dominated systems (e.g. more than 3 m² interfacial area per gram of oil for droplets having radii

of 1 µm), their stability strongly depends on the physicochemical properties of their interfacial layers [6].

In real life applications, protein isolates, which contain a variety of proteins, are often used as ingredients to stabilise emulsions. An example is whey protein isolate that contains at least two variants of β-lactoglobulin and α-lactalbumin as major proteins, as well as various minor fractions such as bovine serum albumin and immunoglobulins. Upon emulsification, different proteins may compete for adsorption [7–11], and possibly displace each other over time [11–15]. The overall composition does thus not reflect the interfacial composition due to the inequivalent protein partitioning between the continuous phase and the interface, which also changes as function of time. Competitive

<footnote><sup>a</sup> Laboratory of Food Process Engineering, Wageningen University and Research, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands</footnote>

<footnote><sup>b</sup> TiFN, P.O. Box 557, 6700 AN Wageningen, the Netherlands</footnote>

<footnote><sup>c</sup> Food and Biobased Research, Bornse Weilanden 9, Wageningen University and Research, 6708 WG Wageningen, the Netherlands</footnote>

<footnote><sup>d</sup> TU Darmstadt, Department of Physics, 64289 Darmstadt, Germany</footnote>

<footnote><sup>e</sup> Laboratory of Physics and Physical Chemistry of Foods, Wageningen University and Research, Bornse Weilanden 9, 6708 WG Wageningen, the Netherlands</footnote>

<footnote><sup>f</sup> INRAE, UR BIA, F-44316 Nantes, France</footnote>

<footnote>* Corresponding author at: Delft University of Technology, Faculty of Applied Sciences, Department of Chemical Engineering, van der Maasweg 9, 2629 HZ, Delft, The Netherlands.</footnote>

<footnote>E-mail address: e.hinderink@tudelft.nl (E.B.A. Hinderink).</footnote>

<footnote n="1">¹ Current address: Delft University of Technology, Faculty of Applied Sciences, Department of Chemical Engineering, van der Maasweg 9, 2629 HZ, Delft, The Netherlands.</footnote>
adsorption and interfacial displacement of protein mixtures has been systematically studied and published in various papers for binary protein mixtures as summarised in Dickinson, 2011 and Fainerman et al., 2020 [11,16]. In those papers competitive adsorption and interfacial displacement were characterised using model interfaces (e.g. Langmuir-trough, drop tensiometer) or real emulsion systems and sometimes linked to physical adsorption models.

Even though experiments using model interfaces are extremely relevant to assess the properties of e.g. aging interfacial layers around droplets, the actual composition of the interface will be rather different from that formed during industrial processes where the hydrodynamic conditions are turbulent and adsorption times extremely short [11,17]. Therefore, measurements on actual complex emulsion systems are needed for verification and comparison purposes. Emulsion characterisation typically involves assessing the emulsion droplet size and physical stability over time. This, in combination with the surface load (i.e. the mass of proteins adsorbed at the oil-water interface, usually denoted $\Gamma$ and expressed in $mg/m^2$), constitute the important parameters underlying the emulsifying capacity [10]. The surface load gives information about the thickness of the layer, and through compositional analysis of the adsorbed proteins in time, also about the contribution of the individual proteins, and interfacial displacement.

Without considering any mass transfer effects, at the basic thermodynamic level, the protein with the greatest capacity to lower the free energy dominates the interface [11]. In protein-surfactant mixtures, the displacement of proteins is driven by the lower interfacial tension achieved through surfactant adsorption. However, for protein blends, the interfacial tension as well as favourable in-plane protein interactions play a role in the overall energy of the system [11,13]. Any factor that restricts the interfacial mobility (e.g. due to aggregation/ in-plane protein aggregation) increases the resistance against displacement and vice versa. It was also reported that enhanced flexibility of the proteins in the bulk increases their ability to displace adsorbed proteins [11,18]. These findings may seem contradictory, since flexible proteins would displace other proteins more easily, but in turn form weak interfacial layers that are more prone to displacement resulting in non-equilibrated systems. This discrepancy may be due to the fact that only a few proteins were considered in previous competitive adsorption and interfacial displacement studies, with measurement techniques varying amongst the different studies. Interfacial properties such as in-plane protein interactions and surface loads depend on a range of system conditions including ionic strength, pH, and temperature but also the proteins' conformational state and supramolecular structure as a result of preprocessing [11]. This makes it difficult to reach generic conclusions and pinpoint the underlying mechanisms. For this, theoretical mechanical models and simulations are essential tools to link and translate experimental observations to more generic insights.

In this review, we will describe experimental techniques available to assess interfacial properties and protein displacement using model interfaces or emulsions. Furthermore, we will discuss mechanistic physical models to describe interfacial properties and the dynamics of complex

mixed systems, with a focus on protein in-plane and bulk-interface interactions. Also, the potential of coarse-grained Brownian dynamic (BD) simulations to describe the parameters that govern interfacial displacement will be reviewed. Although theoretical models describe very simple systems well, emulsions are highly complex both at the molecular level and at larger scales (Fig. 1), which comes with additional challenges. We will connect model parameters and experimental results as much as possible in order to reach a more generic and fundamental understanding for protein displacement phenomena.

## 2. Experimental techniques

### 2.1. Model interfaces

Model interfaces, which are interfaces with well-defined components, are widely studied to get insights in the structure and rheological behaviour of protein-stabilised interfaces [5], including competitive adsorption and interfacial displacement. Table 1 highlights the variety of techniques used to prepare such interfacial layers, the involved time scales and subsequent characterisations. Next to the adsorption time and type of apolar phase as reported in Table 1, also other variables play a role in protein adsorption, such as protein concentration, temperature, pH and ionic strength [19,20]. During simultaneous adsorption of two proteins (also referred to as co-adsorption or complementary adsorption) from an aqueous mixture, displacement might be possible due to differences in adsorption rate and surface activity, e.g. when one of the species adsorbs faster, while the other lowers the surface tension to a larger extent. During sequential exposure, a primary interfacial layer is first formed, after which a second emulsifier is added and the interfacial composition and properties are followed over time. About half of the interfacial studies in Table 1 involve macroscopic observations (e.g. $^{14}$C surface radioactivity, as described in section 2.1.1.1) in combination with interfacial tension measurements (e.g. using a Wilhelmy plate). These observations are very useful to determine to what extent displacement occurs and how this relates to the surface tension. To better understand the interfacial layers formed, interfacial rheology measurements are essential. In the following sections we will first summarise how interfacial displacement can be detected using model interfacial layers in combination with optical techniques, after which we will describe the relevant interfacial rheological measurements.

#### 2.1.1. Langmuir monolayers

A Langmuir trough consists of a flat trough filled with an aqueous phase [35,36]. The aqueous phase can be covered with oil to measure at the oil-water interface [37]. In a Langmuir trough, a layer can be formed in several ways. A known amount of emulsifier can be spread on the interface, which allows control over the interfacial concentration [6]. Traditionally these monolayers are formed by dissolving surfactants in volatile organic solvents that evaporate after spreading. The solubility of proteins in such solvents is usually very low and solvents may induce conformational changes/aggregation, therefore it is preferred to

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** The system (i.e. ingredient and parameter) complexity in the techniques used to characterise interfacial displacement. Black spheres and stars represent proteins, and light and dark grey spheres different isolated proteins.</figcaption></figure>
<caption>**Table 1**</caption>

Overview of competitive adsorption and dynamic exchange experiments in model interfaces using binary mixtures of food proteins.

<table><thead><tr><th>Proteins</th><th>Primary layer</th><th>Second layer</th><th>Adsorption time</th><th>Apolar phase</th><th>Methods</th><th>Reference</th></tr></thead><tbody><tr><td>Lyophilized α<sub>51</sub>- and β-casein and 1:1 mixture</td><td>(Co-) adsorption</td><td>Injection (after 24 h)</td><td>24 h</td><td>Air</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[21]</td></tr><tr><td>BSA, lysozyme</td><td>(Co-) adsorption</td><td>Injection (after 24 h)</td><td>24 h</td><td>Air</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[22]</td></tr><tr><td>BSA, β-casein</td><td>(Co-) adsorption</td><td>Injection</td><td></td><td>Air</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[23]</td></tr><tr><td>Lysozyme, β-casein</td><td>(Co-) adsorption</td><td>Injection (after 10 h)</td><td>14 h</td><td>Air</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[24]</td></tr><tr><td>7S soy protein and β-casein</td><td>(Co-) adsorption</td><td>Injection (after 20 min)</td><td>15 min – 30 h</td><td>Air</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[25]</td></tr><tr><td>Soy proteins, BSA, β-, α-casein, lysozyme, ovalbumin, β-lg, α-lac IgG (hydrophobized)</td><td>(Co-) adsorption</td><td>Injection (after 2 h)</td><td>18 h</td><td>Air</td><td><sup>14</sup>C surface radioactivity, glass container, Wilhelmy plate</td><td>[26]</td></tr><tr><td>BSA, β-casein</td><td>Co-adsorption</td><td>–</td><td>4 days</td><td>Air</td><td>Epifluorescence (LS-films), <sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[27]</td></tr><tr><td>β-, α-casein and 1:1 mixture</td><td>Adsorption</td><td>Injection</td><td>20 h</td><td>Triolein</td><td><sup>14</sup>C surface radioactivity, Langmuir trough, Wilhelmy plate</td><td>[28]</td></tr><tr><td>ovalbumin, lysozyme and 1:1 mixture</td><td>Adsorption</td><td>Injection, washing and subsequent injection</td><td></td><td>Air</td><td>Langmuir sample trough + ellipsometry, surface shear rheometer</td><td>[29]</td></tr><tr><td>β- and α-casein</td><td>Adsorption</td><td>Injection</td><td></td><td>n-Tetradecane</td><td>Surface shear rheometer</td><td>[30]</td></tr><tr><td>β-casein, α-lac, β-lg, β-lg*</td><td>Adsorption</td><td>Injection (after 24 h)</td><td>5, 30 min, 4, 24 h</td><td>n-Tetradecane</td><td>Surface shear rheometer</td><td>[31]</td></tr><tr><td>Casein, gelatin, α-lac and lyszoyme and 1:1 mixture</td><td>Adsorption</td><td>Injection (after 24 h)</td><td></td><td>n-Hexadecane</td><td>Surface shear rheometer</td><td>[32]</td></tr><tr><td>β-lg and bovine submaxillary mucin and 1:1 mixtures</td><td>Co-adsorption</td><td>–</td><td>2.5 h</td><td>Air</td><td>Surface shear rheometer</td><td>[33]</td></tr><tr><td>β-casein, β-lg and mixtures</td><td>Co-adsorption</td><td>–</td><td>3 h</td><td>Sunflower oil</td><td>Drop tensiometer</td><td>[34]</td></tr><tr><td>β-casein, β-lg and mixtures</td><td>Co-adsorption</td><td>–</td><td>2 h</td><td>Air</td><td>Drop tensiometer</td><td>[16]</td></tr><tr><td>WPI, PPI</td><td>Adsorption</td><td>Prefusion</td><td>1 h</td><td>Stripped sunflower oil</td><td>Drop tensiometer</td><td>[13]</td></tr></tbody></table>

IgG, immunoglobulin; BSA, bovine serum albumin; β-lg, β-lactoglobulin; α-lac, α-lactalbumin; LS, Langmuir-Schaeffer. * β-lg chemically modified to cleave and block the -SH groups; S-carboxymethyl-β-lactoglobulin and amidoethyl- β-lactoglobulin

<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Schematic representation of the Langmuir trough with a) spreading or infusion of the emulsifier. Langmuir trough equipped with a dipper to construct b) Langmuir-Blodgett or Langmuir-Schaeffer films.</figcaption></figure>
dissolve and spread proteins through an aqueous solution using an
microliter volume syringe or using the Trurnit method [38,39]. Next to
spreading, proteins can diffuse to and adsorb at the interface when
infused into the clean subphase. In this case, there is less control of the
interfacial composition and the adsorbed amount.

After the formation of a primary layer, the second protein can be
introduced in various ways (Fig. 2A). The second emulsifier can be
injected underneath the subphase, ideally via a tube that is permanently
dipped trough the subphase to not disturb the primary layer or at the
outside of the barrier with a L-shaped needle. The protein can also be
injected trough the side of the trough [28] and subsequently mixed with
a magnetic stirring bar without disturbing the interfacial layer. To
prevent protein interactions in the bulk (e.g. aggregation of the
sequentially introduced proteins) complete perfusion of the subphase
can be employed [40].

Surface pressure isotherms, i.e. plots of the surface pressure as a function of the available surface area, can be obtained to provide information about the intermolecular interactions within the layer and related interfacial organisations [41]. These isotherms can be converted into plots of the mean molecular area as a function of the molar ratio of two surfactants at a certain surface pressure, which provides information about the repulsive and attractive interactions between the adsorbed molecules [42]. This approach has proved useful in verification of repulsive interactions in binary low molecular weight (LMW) surfactant-stabilised interfaces [43]. For well-defined protein systems, i.e. binary protein mixtures with known molecular weights, these plots can be useful to assess the interaction type and strength.

An advantage of the Langmuir trough is that it can be easily com-
bined with other techniques to obtain information about interfacial
layer properties such as thickness, morphology, and composition [41].
This can be done either in situ or by loading the interfacial layer onto a
solid substrate which then can be characterised by a variety of tech-
niques, as discussed in the following paragraphs. It remains questionable
whether the obtained information is relevant for droplets with sizes
much smaller than the typical domains probed in model interfaces [6],
but as with any complex puzzle; information from various length and
time scales needs to be combined to understand the complex displace-
ment phenomena.

2.1.1.1. Radioactive labelling. In order to allow for protein detection, radioactive labelling can be used. Although the question remains whether the label influences the behaviour of the component [44], labelling does facilitate localisation of various proteins. To quantify the protein concentration at the air- or oil-water interface, a radiotracer method with ¹⁴C labelled proteins can be used [26,45,46]. The method has been successfully applied in competitive adsorption and displacement studies of binary protein mixtures (Table 1), using a calibration curve to convert the radioactive signal (in counts per minutes) into a surface load (in mg/m²). It was found that the radioactive signal, and thus the quantification of the rate and extent of adsorption of the proteins, was different when using a calibration curve based on lysozyme (globular protein), β-casein (disordered protein) or stearic acid [47]. Stearic acid and β-casein formed stable interfacial films, but the ¹⁴C nuclide of the β-casein was buried deeper (  >  > 3.5 Å) into the aqueous phase than that of the stearic acid, resulting in a lower measured surface radioactivity. Lysozyme did not form a stable interfacial film i.e. desorbed over time. Since proteins differ considerably in their conformation, quantification in competitive adsorption and displacement studies are dependent on the choice of the calibration method [47]. The fact that various calibration curves were used in the different displacement studies, means that translation and comparison of the results has to be done cautiously, and that further verification through e.g. ellipsometry is particularly useful.

**2.1.1.2. Ellipsometry.** Ellipsometry is a non-destructive optical

technique to characterise interfacial films. Linearly polarized light is
reflected at an interface and collected by a detector. The change in po-
larization upon reflection is measured and expressed as the ellipsometric
angles (Δ and ψ). The signal depends on the material properties (e.g.
refractive index) and the film thickness. The lateral resolution of
ellipsometry is down to 1μm and the perpendicular resolution is in the
nanometer range. The outcomes are thus the average thickness of the
film and the characteristic size of phase separated areas, that is, if they
are comparable to or larger than the lateral resolution. Ellipsometry in
combination with a Langmuir trough allows the simultaneous recording
of the film thickness and surface pressure to construct surface pressure
vs film thickness plots [29,48]. Furthermore, the surface loads can be
calculated using the refractive index of the interface and the refractive
index increment of proteins (0.185 mL/g [49]).

Ellipsometry can be a powerful tool to quantify displacement in mixed protein-surfactant systems when large differences in adsorbed layer thickness occur [50]. To measure interfacial displacement in protein blends, the technique is expected to be less useful due to the relatively small differences in protein size and surface pressure and the lower degree of displacement; e.g. surfactants can fully displace pre-adsorbed proteins [51,52] whereas protein-protein displacement occurs to a limited degree [13,14,31] and mostly not in phase-separated fashion. In some cases, the displaced protein may interact with the displacing proteins at the interface, resulting in multilayer formation. The increase in film thickness can be quantified and in combination with the surface pressure, conclusions can be drawn about the type of protein present at the interface [29].

2.1.1.3. *Brewster angle microscopy (BAM).* Brewster angle microscopy (BAM) is an optical technique that provides information about the two-dimensional organisation of emulsifiers at a planar interface at the micrometre scale. BAM has been widely used to visualise protein and surfactant-stabilised interfaces [53] e.g. mixed protein-monoglyceride-based interfaces [54]. An imagining ellipsometer combines the principles of BAM and ellipsometry to allow for characterisation of the thickness and lateral organisation simultaneously [55]. The lateral resolution of BAM (~2 µm, [56]) is not high enough to study the interfacial nano-structures formed by protein blends and thus never used for this purpose. Finer structural details can be assessed using Langmuir-Blodgett (LB) or Langmuir-Schaeffer (LS) films in combination with atomic force microscopy (AFM), which will be discussed later.

2.1.1.4. Infrared reflection absorption spectroscopy. Infrared reflection absorption spectroscopy (IRRAS) is a characterisation method providing chemical information about the secondary structure of the proteins. From the obtained spectra, the molecular behaviour of proteins at and near the air-water interface can be derived [39,57]. The amide I band is a result of the vibration of the C=O bond in the protein, which represents the geometry of the polypeptide chain backbone whereas the amide II band represents the NH₂ vibration in the primary amides [58]. IRRAS allows to directly monitor the adsorption process by following the intensity of characteristic infrared bands of the proteins as a function of time. Due to the considerable difference in chemical structure of surfactants and proteins, the technique was effectively used to measure the displacement in these mixed systems [59,60]. The intensity of the amide bands reduced upon displacement by the surfactant, whereas antisymmetric and symmetric CH₂ stretching vibrational bands of the surfactant fatty acyl chains appeared. It is good to mention that the width and maximum wavelength of the amide bands vary between proteins, and that these bands are sensitive to the protein concentration and interfacial protein rearrangements over time (e.g. in-plane protein interactions) [39,57]. This makes the method not sensitive enough to distinguish between proteins with comparable secondary structures, and thus challenging to use in protein-protein competitive adsorption and displacement studies.
## 2.1.2. Transfer of Langmuir films onto solid substrates

The Langmuir-Blodgett or Langmuir-Schaefer techniques (Fig. 2b) involve the formation of a monomolecular layer in the Langmuir trough and subsequent transfer onto a solid substrate [61]. A LB film is constructed by moving the substrate perpendicularly trough the interface, whereas in the LS setup the substrate is lowered parallel to the interface. The substrate is typically a solid plate that is atomically flat. Mica and glass are commonly used as substrate for protein films. LB or LS-films can be used to further characterise the top or bottom (hydrophobic or hydrophilic side) of the interfacial film, respectively due to the different way of protein loading (see Fig. 2b for a schematic representation). Since the films are prepared in a Langmuir trough it allows the formation of films over a range of surface pressures.

### 2.1.2.1. Atomic force microscopy.
Atomic force microscopy (AFM) is able to scrutinize a protein film at the micrometre (lateral) and nanometer scale (z-direction), thus giving information on the topography of the sample (in case of protein-based interfacial films, often LB or LS film). The method has been successfully used to quantify the displacement of adsorbed proteins by surfactants introduced in the subphase [40,52,62]. The films containing surfactants (e.g. Tween 20) and proteins were imaged under butanol to desorb the surfactants form the substrate. This resulted in a high contrast between the phase separated domains. In depth characterisation of the images led to the development of the orogenic displacement model [52]. Furthermore AFM images allowed the determination of the protein-to-surfactant ratio in the film confirming the presence of phase-separated domains were used to determine the protein-to-surfactant ratio in the film [40,52,62]. After the pioneering work by Mackie, the technique and theory has been used in various groups and for different topics, including substantial work on digestion [63].

Results obtained with LB and LS films may not be directly comparable, as reported by [64] who found different displacement patterns of β-lactoglobulin and sodium dodecyl sulfate (SDS). The LB-films showed large circular holes during the late stages of displacement whereas LS-films had non-circular and smaller holes. In LB films, the holes may represent the adsorption and spreading of SDS via the substrate while exposed to the subphase.

AFM images of protein films present relevant data about the structural heterogeneity of the interface [61,65–67], which can be linked to in-plane protein aggregation (section 2.1.3), an important aspect of resistance against displacement. Although in principle one could differentiate between small and large proteins, interfacial protein aggregation hinders differentiation between the individual proteins [66].

### 2.1.2.2. Fluorescence microscopy.
LB and LS-films can be prepared using fluorescently labelled proteins to characterise lateral phase separation of binary protein films [27,40,68,69], although for fluorescence labelling the question remains whether it may alter the proteins' interfacial behaviour [70]. Fluorescence micrographs of protein blend-based LB films showed heterogeneity (i.e. phase separation) at length scales in the submicron range as a result of the different adsorption rates and interactions between the proteins [68], and phase-separated domains larger than 100 µm were reported in LS films after four days in the trough [27,69]. It is unclear if the difference in domain sizes is a result of the substrate preparation (simple glass slide or modified glass slides to fix the proteins and reduce the lateral diffusion of the proteins), the transfer method (LB vs LS), or a combination of the two, or a difference between experimental settings or even experimentalists. In both cases, the lateral resolution (~100 nm-100 µm) achieved was relatively low and films were constructed under pseudo-equilibrium conditions (e.g. after a period of four days). It is unlikely that the resolution is high enough to capture (very local) phase separation at short time scales, which, according to BD-simulations is a pre-requisite for displacement to occur [71,72]. For this, the higher resolution (~50 nm) feasible by near

field scanning fluorescence microscopy [73,74] is recommended.

### 2.1.3. Interfacial rheology

Protein adsorption leads to reduction of the interfacial tension, thereby reducing the total energy of the system. After adsorption, full phase separation in binary protein mixtures with the same molecular properties (charge) has been reported to be the result of self-association of one of the protein types, rather than thermodynamic incompatibility [75]. Furthermore, proteins can form viscoelastic interfacial networks that can impose a significant resistance against deformation. Both phenomena are related to in-plane protein interactions. The strength of the interfacial interactions can be assessed through interfacial rheology [76] that monitors the interfacial stress response as a result of a shear or dilatational deformation of the interface [5].

In the following sections we will discuss how interfacial displacement and its impact on the interfacial rheology can be measured using shear rheology or dilatational rheology. For a complete overview of characterisation methods for fluid interfacial layers, the reader is referred to [77].

#### 2.1.3.1. Interfacial shear rheology.
Interfacial shear rheology probes the surface stress and deformation of the interfacial layer upon shearing, i.e. it measures the mechanical strength of the layer upon shear deformations. Surface viscosities of films can be measured at the air-water or oil-water interface in a surface shear viscometer. Interfacial films can be formed by adsorption from the bulk phase, or manual spreading at the interface. For sequential introduction, a glass tube is placed through the air-water interface, before forming the initial layer [32] or by a modified measuring cell that allows for exchange via several inlets and outlets at the bottom [78,79]. The added volume should be chosen such that it does not change the viscous drag, and the ratio between surface stress and bulk stress, i.e. the Boussinesq number should be >1 [80]. The surface viscosity during binary protein blend displacement studies typically has an error of ±5%, which confirms the reproducibility of the method [31].

#### 2.1.3.2. Interfacial dilatational rheology.
A drop tensiometer is often used to characterise adsorption of proteins (i.e. their ability to reduce the interfacial tension) and the dilatational rheological properties of the interfacial layers. In brief, a small drop or bubble (10–40 µL) is formed at the tip of a needle and its shape captured with a camera. Dilatational rheology can be performed by pumping liquid into and out of the droplet. Sequential introduction is typically achieved by exchanging either the internal phase of the drop, or the outer continuous phase (Fig. 3A and B, [16,66]). When using a coaxial double needle, the inner capillary is used to control the droplet size during the whole experiment whereas the outer capillary is used for the exchange of the droplet solution. The second water phase is continuously injected into the droplet while its size is simultaneously controlled by removing water from the droplet via the inner capillary. In this way, the droplet size remains constant during the exchange. Care has to be taken that the inner flow does not lead to desorption of the initially adsorbed protein [81,82] or loss of the droplet at the tip of the needle.

Sequential introduction has, amongst others, been used in digestion studies to monitor how proteins were displaced by surfactants present in digestive fluids [83–85], and also in a pioneering study to investigate displacement of proteins by proteins [13]. A disadvantage of exchange of the aqueous phase is that the interfacial composition cannot be measured, and thus the dominating protein cannot be determined. Maldonado-Valderrama et al. [86] spread a protein solution at the droplet interface using a mini glass rod, and in principle, this technique may also be considered for sequential adsorption since it allows for better control of the interfacial composition compared to spontaneous adsorption.

To obtain insights into the rheological properties of the interface,
<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Schematic representation of two drop tensiometer configurations that allow for sequential introduction of proteins: A) using a coaxial double needle or B) using bulk phase exchange. C) Classical amplitude sweep and interfacial tension response (middle); an example of the representation of these data as a Lissajous plot, showing a viscoelastic response (left); and a step dilatational measurement (right).</figcaption></figure>

oscillatory dilatational experiments can be performed in which the interfacial area of the droplet is changed in a sinusoidal way as a function of oscillation frequency and strain amplitude. Typically, two types of experiments are performed at i) constant amplitude (within the linear viscoelastic regime) and varying frequency (so-called frequency sweeps) and at ii) constant frequency and varying amplitude (amplitude sweeps) [87]. An amplitude sweep is typically (partly) measured outside the linear viscoelastic regime, therefore, expressing the results as Lissajous plots is useful. It reveals the in-plane mechanical properties and highlights the non-linear response of the interface, such as strain softening or jamming, which are typical for structurally heterogeneous layers [87]. Interfacial protein aggregation can also be approached using step dilatational measurements where the area of the droplet is suddenly expanded or compressed. Relaxation of the interfacial stress can then be analysed using a Kohlrausch-Williams-Watt stretched exponential function (Eq. 1, [88]),

$$ \gamma(t) = ae^{-(t/\tau_1)^\beta} + be^{-t/\tau_2} + c \quad (1) $$

with $\gamma(t)$ the change in surface stress over time, $\tau_1$ and $\tau_2$ relaxation times, $\beta$ a stretch exponent, and $a, b$ and $c$ constants. The $\tau_2$ accounts for the aging of the interfacial microstructure, which is typical for protein-stabilised interfaces, as interfacial tension often does not reach equilibrium within the timespan of a typical experiment (i.e. hours). Protein-stabilised interfaces generally have $\beta$-values of 0.4–0.6 in extension, and of 0.5–1 in compression [88]. This implies two things: i) such layers have an asymmetric behaviour, shown in the differences in response between compression and extension, and ii) the relaxation behaviour cannot be described by a single relaxation time, but rather by a normal distribution of relaxation times indicative of interfacial structural heterogeneity. The link between low $\beta$-values and heterogeneous structures at the interface has been experimentally validated by AFM images of LB films showing structural heterogeneity at the micrometre scale

**Table 2**

Score overview of the suitability of model interfaces for competitive adsorption and interfacial displacement studies. Scores represent: ++ very suitable, + suitable, +/- suitable under certain circumstances to - not suitable.

<table><caption>Measurements related to model interfaces</caption><thead><tr><th></th><th></th><th>Ellipsometry</th><th>BAM</th><th>IRRAS</th><th>AFM</th><th>Fluorescence</th><th>Rheology</th></tr></thead><tbody><tr><td>Model system</td><td>Langmuir-trough</td><td>Langmuir-trough</td><td>Langmuir-trough</td><td>Langmuir-trough</td><td>LB-/LS-film</td><td>LB-/LS-film (Langmuir-trough)</td><td>Langmuir trough Drop tensiometer Shear rheometer</td></tr><tr><td>Surface load</td><td>+</td><td>++</td><td>-</td><td>+</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Surface composition</td><td>++</td><td>-</td><td>-</td><td>+/-</td><td>-</td><td>+</td><td>-</td></tr><tr><td>Interface structure</td><td>+ (signal could be a measure of penetration depth of <sup>14</sup>C into the aqueous phase)</td><td>-</td><td>+</td><td>+ (secondary structure of the proteins)</td><td>++</td><td>+</td><td>+/- (indirectly)</td></tr><tr><td>Competitive adsorption</td><td>++</td><td>-</td><td>-</td><td>+</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Displacement</td><td>++</td><td>-</td><td>-</td><td>-</td><td>-</td><td>+</td><td>+</td></tr><tr><td>Time resolution</td><td>min-hours</td><td>min-hours micro scale</td><td>min-hours micro scale</td><td>min-hours</td><td>min-hours nano scale (z-direction), micro scale (x,y-direction)</td><td>min-hours micro scale</td><td>sec-hours nano scale (indirectly)</td></tr><tr><td>Spatial resolution</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

BAM, Brewster angle microscopy; AFM, atomic force microscopy; IRRAS, infrared reflection absorption spectroscopy.
[65,88,89] and is also confirmed by lateral diffusion measurements [90].

To summarise, model interfaces have been used to gain information about the structural properties of fluid interfaces. Many of these techniques have also been used for interfacial displacement studies involving protein-surfactant and protein-protein mixtures. An overview of the advantages and disadvantages of the various methods is highlighted in Table 2.

## 2.2. Emulsions

Studies on model interfaces give insights in the structural and rheological properties of the interfacial layers, including displacement at the micrometre scale, but they are not necessarily good predictors for emulsion stability. For that, inter-droplet interactions and destabilisation phenomena such as coalescence and flocculation also need to be investigated. This can be done using a droplet micro-manipulator in which two droplets are brought together [91]. Detailed information about the drainage and coalescence of isolated thin films can be measured using a Sheludko cell [92]. Alternatively, a large number of droplets can be allowed to interact in microfluidic tools, and coalescence can be observed with high-speed imaging [93], allowing measurement at the microsecond scale, although this has not yet been used to study the effect of displacement on coalescence.

Measurements at model interfaces involve dilute protein solutions, and can therefore significantly be influenced by minor components (e.g. polar lipids) that are much smaller than proteins and thus diffusing faster to and adsorb at the interface. In emulsion studies, these effects are in most cases negligible due to the high protein concentration used and convection-dominated adsorption. Ideally, insights obtained through measurements performed on model interfaces and on emulsion systems should lead to an overview of effects associated with interfacial displacement at various length- and time scales. Competitive adsorption and interfacial displacement studies in emulsion systems are summarised in Table 3, and those that report results both for emulsion systems and model interfaces are highlighted. When analysing competitive adsorption and displacement in protein-stabilised emulsions, the first step is to determine the surface load ($Γ$, mg/m²) in time, to distinguish between additional adsorption and interfacial displacement. This is conventionally done by physically separating the aqueous and creamed phases of the emulsion by moderate centrifugation, followed by

quantification of the components present in both phases [10]. Subsequently, the surface load and interfacial composition are measured directly via the (washed) creamed phase, or indirectly via the serum phase and calculated by subtraction from the total protein present (as summarised in Table 3). The applied procedure can substantially influence the measured surface load [13]; for instance, an aggregated protein fraction that was not accounted for in the continuous phase concentration due to sedimentation may lead to an overestimation of the adsorbed protein amount, whereas washing the creamed phase prior to determining the adsorbed protein amount tends to reduce the measured surface load, and may also affect the measured interfacial composition. It is important to keep in mind that to investigate competitive adsorption, both proteins are present pre-emulsification whereas for sequential adsorption the second protein is added post-emulsification (Table 3), either to the emulsion or to the (washed) creamed phase, and this needs to be considered when comparing displacement studies.

### 2.2.1. Surface load measured in the separate emulsion phases

#### 2.2.1.1. Surface load determination via the serum phase.
The surface load can be quantified directly from the proteins in the water phase (also often called ‘serum’) through a mass balance [10,99–101] (Fig. 4). The surface load $Γ$ (mg/m²) can be calculated with eq. 2.

$$Γ = \frac{C_s \cdot d_{3,2}}{6\varphi} \qquad (2)$$

Where $C_s$ (mg/L) is the adsorbed protein concentration calculated by subtracting the protein concentration in the serum phase from the initial protein concentration of the solution used for emulsion preparation, $d_{3,2}$ the surface-weighed mean droplet diameter (in the absence of flocs), and $\varphi$ the dispersed phase volume fraction. Alternatively, adsorbed proteins can be quantified using the creamed phase (Fig. 4). Measurements via the serum are relatively simple and contain fewer steps compared to the measurements via the creamed phase.

The proteins in the serum phase are considered the non-adsorbed fraction, whereas those in the cream are the adsorbed fraction [6]. Still, for emulsions with small droplet sizes (~$d_{3,2} < 0.4$ µm), the serum phase may contain many small droplets that cannot be removed by extensive centrifugation or filtration [10,102]. Proteins adsorbed at the interface of these small droplets falsely contribute to the non-adsorbed protein fraction which leads to underestimation of the surface load.

<caption>**Table 3**</caption>

Overview of studies dealing with competitive adsorption and sequential protein introduction in emulsions prepared with mixtures of food proteins. Studies highlighted in bold combine measurements in both emulsion systems and model interfaces.

<table><thead><tr><th>Proteins</th><th>Pre-/post-emulsification</th><th>Probed time scale</th><th>Analysed phase</th><th>Method for concentration measurement</th><th>Method for composition determination</th><th>Reference</th></tr></thead><tbody><tr><td>β-casein, α-casein</td><td>Post (washed cream)</td><td>1–24 h</td><td>Serum</td><td>FPLC</td><td>FPLC</td><td>[30]</td></tr><tr><td>β-Ig, α-lac</td><td>Post (washed cream)</td><td>1–32 h</td><td>Serum</td><td>FPLC</td><td>FPLC, electrophoretic mobilities</td><td>[14]</td></tr><tr><td>SC and heated SPI</td><td>Pre and post</td><td>0</td><td>Washed cream<br>Serum</td><td>–<br>Lowry method</td><td>SDS-PAGE<br>SDS-PAGE</td><td>[94]</td></tr><tr><td>β-Ig in a 1:1 mixture with β-casein, α-lac or ovalbumin</td><td>Post (washed cream)</td><td>48 h</td><td>Serum</td><td>FPLC</td><td>FPLC</td><td>[15]</td></tr><tr><td>WPI, SC</td><td>Post</td><td>10 (min)</td><td>Cream</td><td>SDS-PAGE</td><td>SDS-PAGE</td><td>[95]</td></tr><tr><td>Phosvitin, β-casein</td><td>Post (washed cream)</td><td>48 h</td><td>Serum</td><td>FPLC</td><td>FPLC</td><td>[96]</td></tr><tr><td>β-Ig, α-lac in 1:1 mixture</td><td>Pre</td><td>1–18 h</td><td>Washed cream</td><td>SDS-PAGE</td><td>SDS-PAGE</td><td>[18]</td></tr><tr><td>β-Ig, α-lac</td><td>Post (washed cream)</td><td>1–18 h</td><td>Serum</td><td>Lowry method</td><td>SDS-PAGE</td><td>[97]</td></tr><tr><td>Sodium caseinate</td><td>Pre</td><td>1–24 h</td><td>Serum</td><td>FPLC</td><td>FPLC</td><td>[97]</td></tr><tr><td>WPI, egg yolk lipoproteins</td><td>Post (washed cream)</td><td>0–1 h</td><td>Cream<br>Serum</td><td>Lowry method</td><td>SDS-PAGE</td><td>[98]</td></tr><tr><td>WPI, SC, PPI and 1:1 WPI-PPI or SC-PPI</td><td>Pre</td><td>0–72 h</td><td>Cream<br>Serum<br>(Washed) cream</td><td>–<br>BCA</td><td>SDS-PAGE<br>BCA</td><td>[12]</td></tr><tr><td>WPI, PPI and 1:1 mixture</td><td>Pre and post</td><td>0–72 h</td><td>Serum</td><td>BCA</td><td>SDS-PAGE</td><td>[13]</td></tr></tbody></table>

FPLC, fast protein liquid chromatography; SDS-PAGE, sodium dodecyl sulfate polyacrylamide gel electrophoresis.
<figure><img src="image_7.png" /><figcaption>**Fig. 4.** Overview of the procedures to determine the droplet surface load in protein-stabilised emulsions via the serum, creamed or washed cream phases, for monodisperse and polydisperse O/W emulsions.</figcaption></figure>

This can be compensated by measuring the oil quantity and droplet size in the subnatant, which allows the calculation of the total surface area of remaining oil [10]. Next to the classic lipid extraction methods based on organic solvents, nuclear magnetic resonance (NMR) spectroscopy is very suitable to measure the size and lipid concentration of submicron-sized emulsion droplets [102]. On the other hand, sedimentation of non-adsorbed and insoluble proteins may lead to overestimation of the surface load. For dairy proteins, this effect may be limited due to their high solubility in aqueous media, but needs to be taken into account for plant proteins that are typically less soluble and are present as supramolecular assemblies in water. In general, measurements via the creamed phase should be preferred when dealing with (partly) insoluble proteins [10,13].

#### 2.2.1.2. Surface load determination via the creamed phase.
The protein concentration in the cream can be determined either by directly mixing a known amount of cream with a component that displaces adsorbed proteins, such as SDS, or by first applying a washing step (to remove proteins that are loosely bound at the interface, or captured in the voids of the creamed phase; [13]). A washing step is considered especially relevant for sequential adsorption and/or when high amounts of proteins have been used to prepare the emulsion [13]; yet, the question remains whether only loosely bound material is removed, or the actual equilibrium is somewhat altered by this step.

To determine the surface load, the cream may be dried (e.g. on a filter paper or in a climate chamber) after which the protein concentration in the cream can be directly quantified using either total nitrogen determination [103], or SDS-PAGE [10,95]. In case of protein colorimetric assays (e.g. BCA assay [104]), the adsorbed proteins have to be desorbed from the interface into the water phase by e.g. re-dispersing the cream in SDS-solution (1–5 wt%) [10,105] (Fig. 4). The total surface area can be calculated based on the $d_{3,2}$ and the oil content of the cream, and used to calculate the surface load [13,106].

### 2.2.2. Interfacial composition

To determine interfacial composition (Table 3), mostly sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) in combination with a calibrated densitometer [10,13,107] or chromatography techniques (e.g. fast protein liquid chromatography; FPLC [15,30]) are used. SDS-PAGE densitometry has been shown to be reproducible for sodium caseinate stabilised emulsions when analysing the serum phase, leading to deviations from the average of 5% for α-casein, 4% for β-casein and 9% κ-casein from (n = 9) [108]. Similar results were reported when using the dried cream of sodium caseinate- and whey protein isolate-stabilised emulsions, leading to variations

from the average of 4% for α-casein, 4% for β-casein, 5% for κ-casein, 4% for α-lac, and 4% for β-lg (n = 12) [109]. Densitometry analysis thus seems reproducible, and it would be interesting to compare compositions determined from the analyses of the serum and the creamed phases.

For compositional analysis of protein blends with overlapping molecular weights, e.g. plant protein blends, more advanced techniques are needed such as proteomics that have been successfully applied to pea protein-stabilised emulsions [110], and are expected to be a future trend in such compositional analysis.

### 2.2.3. Direct, non-destructive measurements

#### 2.2.3.1. Front-surface fluorescence.
The aforementioned analytical measurements rely on the separation of the creamed and serum phases, which may induce uncertainties in the measured values, and are time-consuming due to the various centrifugation steps. Alternatively, protein partitioning can be measured in situ using front-surface fluorescence which relies on the variable spectral fluorescence characteristics of the tryptophanyl residues in aqueous or hydrophobic environments [111,112]. The technique has been used for surface load quantification in protein blend-stabilised emulsions (skim milk powder) [111], and to non-destructively monitor the interfacial displacement of a protein (bovine serum albumin (BSA)) by a surfactant (Tween 20) [113]. The method has not yet been used to characterise interfacial composition in protein blend systems but could be promising for plant-dairy protein blends [114]. Furthermore, front-surface fluorescence measurements are useful to confirm surface loads as measured via methods that involve emulsion phase separation.

#### 2.2.3.2. Electrophoretic mobility measurements.
Electrophoretic mobility measurements rely on the electrostatic surface charge of the outer layer of a particle (component) surface [11]. This method can be used in emulsion systems to estimate the charge of the proteins in the outer layer and hence the potential predominance of a given protein in this outer layer: for instance, if the mobility of a droplet covered by a layer of protein A and an added layer of protein B, is close to that of droplets coated with protein B only [14]. It is important to consider that electrophoretic mobility must be measured in very dilute conditions, and at low ionic strength. Dilution in water or a low ionic strength buffer is thus needed, which raises the question whether this can truly be considered a non-invasive method. Dilution of the continuous phase protein (i.e. the concentration of displacing protein in this phase) may affect the interfacial composition [13]. To summarise, the results may provide some
insights on the interface composition, and can confirm the presence of additional protein, but without further information on the interfacial structures and concentrations.

2.2.3.3. Fluorescence microscopy. Although standard light microscopy techniques can be used to assess the structure of emulsions at various scales, they are less suited to obtain information on the properties of a thin (nanometer-scale) interfacial layer, unless labelled components are used. Mesoscopic structures of protein-based interfaces may be visualised using e.g. fluorescent labelling in combination with visualisation by CLSM; this was applied to emulsions prepared using WPI, SC or PPI covalently stained with fluorescein isothiocyanate (FITC) prior to emulsion preparation (Fig. 5). The left column shows images of emulsions stabilised with a single protein, and a bright yellow ring can be seen around the droplets, indicative of a homogeneous protein distribution at the interface. For PPI, the yellow dots in the continuous phase and at the interface indicate that the protein was present as so-called "soluble aggregates". Blending stained PPI with non-stained WPI or SC led to an inhomogeneous interfacial film with bright patches combined with unstained areas. In the emulsions stabilised with stained WPI or SC and non-stained PPI, a homogeneous interfacial dairy protein layer was visible, indicating that these proteins were homogeneously present at the interface. Due to the small size of the dairy proteins, CLSM images do not provide information about the local structure; this is only possible using techniques that have a much higher spatial resolution, such as AFM (Section 2.1.3.2). As mentioned, at model interfaces coexisting regions were identified, albeit in the order of 10²–10³ µm of which it is doubtful if it is relevant for emulsions [9,11]. Optical microscopy (e.g., light and fluorescence) is a rapidly evolving field with substantial recent progress to scrutinize nano-structures [115,116], which opens perspectives for probing relevant scales for such complex interfaces in a near future.

To wrap up, interfacial displacement in emulsions can be measured using invasive (e.g. measurements in separate phases) or in situ measurements, as summarised in Table 4, including their pros and cons. Direct measurements using the creamed phase are most appropriate for the invasive methods since they provide direct information about the interface composition and surface load; assuming that the concentration process did not influence these values. In situ measurements give general insights on the interfacial protein composition and load, but do not allow for differentiation between individual proteins and their subunits. Both invasive and in situ measurements provide information about the composition, but often overlook the corresponding interfacial

<figure><img src="image_8.png" /><figcaption>Fig. 5. CLSM images of protein-stabilised emulsions with either SC, PPI or WPI covalently stained with FITC, and used as single protein or in blends with non-stained proteins. Excitation was at 488 nm, scale bar represents 25 µm. Unpublished results (Hinderink et al., personal communication, 2018).</figcaption></figure>

organisation and structure. Yet, the latter are believed to be at least as important for emulsion stability as the interfacial composition. Both influence the interfacial rheological properties as well as the repulsive/ attractive interactions between droplet interfaces. For example, in casein-whey protein-stabilised emulsions, a small fraction of caseins can prevent the emulsions from flocculation upon heating, due to the formation of a low-density outer layer that provides steric interactions [117].

A major disadvantage of measurements on emulsion systems rather than model interfaces is the fact that the first measurements are typically performed a few minutes after emulsion formation. This is especially the case for invasive methods where a long centrifugation step is applied (typically >30 min, depending on the droplet size). Within such a period, interfacial displacement may occur, which makes it impossible to measure competitive adsorption only.

### 3. Theoretical models

Theoretical models and comparison with experimental data are needed to understand protein adsorption and interfacial behaviour in much greater detail. Various reviews are available for surfactants and proteins as well as mixtures, including competitive adsorption [11,118–124].

#### 3.1. Equilibrium thermodynamic models

Equilibrium thermodynamics of multiphase systems, as described by Gibbs and Guggenheim [124–126], starts from two bulk phases between which a boundary region with finite thickness is present. In this interfacial region, bulk fields change rapidly (and smoothly) from their value in one bulk phase to their value in the other bulk phase. This region is typically represented by a sharp interface, also referred to as a dividing surface. Bulk properties are extrapolated up to this dividing surface, and the differences between extrapolated fields and actual fields are accounted for by associating excess properties to this interface. For example, species that accumulate in this interface region will result in an interfacial excess $Γ$ (in number when using Boltzmann constant or moles when using universal gas constant per area). It has been shown that protein adsorption can be reversible, which is a prerequisite for this approach, whereas true equilibrium is intrinsically hard to prove for interacting protein layers, which thus would take away from the theory being valid for proteins at an interface. This debate is still ongoing; for now, we report on results obtained. One of the most simple relations between interfacial tension, interfacial excess and temperature is the 2D analogue of the equation of state of an ideal gas, giving the surface equation of state (SEOS):

$$ \Pi = \Gamma k_B T \quad (3) $$

With

$$ \Pi = \gamma_0 - \gamma \quad (4) $$

Here $π$ is the interfacial pressure, $γ_0$ and $γ$ are the interfacial tensions of the bare interface, and that with interfacial excess $Γ = n/A$, respectively, $n$ is the number of molecules adsorbed at area $A$, $k_B$ is Boltzmann's constant and $T$ is the temperature. The adsorption isotherm, which is the relation between the adsorbed amount $c$, is found from the equality of chemical potentials at the surface and in the bulk. This gives the Gibbs isotherm:

$$ \Gamma = \frac{1}{k_B T} \frac{\partial \gamma}{\partial \ln c} \quad (5) $$

Substituting the equation of state of the ideal 2D gas, and integrating gives the Henry isotherm:

$$ \Gamma = kc \quad (6) $$
<caption>**Table 4**</caption>

Score overview of the suitability of emulsion characterisation techniques for competitive adsorption and interfacial displacement studies. Scores represent: ++ very suitable, + suitable, +/- suitable under certain circumstances to - not suitable.

<table><caption>Measurements related to emulsion systems</caption><thead><tr><th rowspan="2"></th><th colspan="3">Invasive methods</th><th colspan="3">In situ measurements</th></tr><tr><th>Serum (after centrifugation)</th><th>Cream (after centrifugation)</th><th>Front surface fluorescence</th><th>Electrophoretic mobility measurements</th><th>Microscopy (fluorescent labelling proteins)</th></tr></thead><tbody><tr><td>Surface load</td><td>+</td><td>++</td><td>++</td><td>-</td><td>-</td></tr><tr><td>Surface composition</td><td>+</td><td>++</td><td>+</td><td>+/- (can be affected by dilution step)</td><td>+/-</td></tr><tr><td>Interface structure</td><td>-</td><td>-</td><td>+/- (fourth derivative of spectra could provide information about tertiary protein structure)</td><td>-</td><td>+</td></tr><tr><td>Competitive adsorption</td><td>+</td><td>++</td><td>-</td><td>-</td><td>+/-</td></tr><tr><td>Displacement</td><td>+</td><td>++</td><td>+</td><td>+/-</td><td>+/-</td></tr><tr><td>Time resolution</td><td>Hours-weeks</td><td>Hours-weeks</td><td>Min-weeks</td><td>Min-weeks</td><td>Min-weeks Macro scale</td></tr><tr><td>Spatial resolution</td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

with *k* an adsorption constant related to the adsorption energy of the species. In principle, the Henry isotherm and corresponding 2D ideal gas SEOS is only valid for ideal bulk and interface behaviour. Common protein and surfactant systems often do not comply with this, therefore the model needs to be extended to include interactions. The SEOS of a 2D gas including interactions and excluded volume equals that of a van der Waals gas, containing constants for the adsorption energy (*k*), lateral interactions (α), and molecular adsorbed area (ω₀)

$$ \Pi = \frac{k_B T}{(\omega_a - \omega_0)} - \frac{\alpha}{\omega_a^2} \quad (7) $$

$$ kc = \frac{\theta}{1 - \theta} \exp \left( \frac{\theta}{1 - \theta} - \frac{2\alpha}{\omega_a k_B T} \theta \right) \quad (8) $$

with ϖ = 1/Γ and θ = ϖ₀Γ.

By defining the system on a 3D or 2D lattice, excluded volumes are automatically taken into account, because atoms need to be at a unique site. The basic lattice model is of Langmuir who considered a fixed number of adsorption sites of which a fraction θ was occupied and 1 - θ not. Assuming that the molecules can adsorb and desorb, results in the following kinetic equation (excluding interaction between the adsorbed species):

$$ \frac{d\theta}{dt} = k_a c(1 - \theta) - k_d \quad (9) $$

with *c* the bulk concentration and *k*<sub>a</sub> and *k*<sub>d</sub> adsorption and desorption rate constants. At equilibrium, when *dθ/dt* = 0, and *k* = *k*<sub>a</sub>/*k*<sub>d</sub> is the associated equilibrium constant, this leads to the Langmuir adsorption isotherm:

$$ \theta = \frac{kc}{1 + kc} \quad (10) $$

Substituting into the Gibbs SEOS and integrating gives the Langmuir SEOS:

$$ \Pi = - \frac{k_B T}{\omega} \ln(1 - \theta) \quad (11) $$

Various versions have been published that include interactions between compounds. In random sequential adsorption models, the surface filling effect of hard spheres adsorbed on solid surfaces is included [127,128]. Comprehensive reviews on equilibrium adsorption models, including those of ionic surfactants are given by Peng et al. [121,122].

The Langmuir model can be extended for a binary mixture or more adsorbing components to describe competitive adsorption. For two components 1 and 2 it follows that:

$$ \theta_1 = \frac{k_1 c_1}{1 + k_1 c_1 + k_2 c_2} \quad (12) $$

$$ \theta_2 = \frac{k_2 c_2}{1 + k_1 c_1 + k_2 c_2} \quad (13) $$

with θ<sub>b</sub>, *k*<sub>i</sub>, and *c*<sub>i</sub> the adsorbed fraction, adsorption rate constant, and bulk concentration of component *i* = 1 or 2, respectively. The SEOS is the same as eq. 11, with θ = θ<sub>1</sub> + θ<sub>2</sub>. The Langmuir adsorption isotherm was used to model the co-adsorption of lysozyme and β-casein [24], and Dickinson showed that such models fit well with experimental data of α<sub>s1</sub>-casein and β<sub>s1</sub>-casein (the latter being more surface-active and displacing α<sub>s1</sub>at the oil-water interface) [11,21]. Yet, the agreement with experiments on other globular food proteins is not as good. For example, β-lactoglobulin cannot displace α-lactalbumin and vice versa, which also holds for other proteins: β-casein and lysozyme, lysozyme and BSA, β-casein and BSA, while this did not directly follow from modelling work. An interesting clue was that increasing the flexibility of an adsorbed protein in models increases its ability to exchange with other proteins and that interfacial aggregation decreases such exchanges. Equilibrium thermodynamics of flexible polymers, including flexible proteins such as caseins at interfaces, can be modelled well using the self-consistent-field (SCF) theory, which is based on the work of Scheutjens and Fleer [129,130]. The polymer is modelled as a chain of monomers, and the distribution in the lattice is calculated from a self-consistent set of equations based on the monomer adsorption energy and lattice occupancy. The SCF theory has been applied to describe mixed protein-polysaccharide interfacial layers [131] as well as to predict the adsorption and interfacial behaviour of a α<sub>s1</sub>-β<sub>s1</sub>-casein mixture at different pH values, which corresponds well with experimental data [132,133].

Competitive adsorption on solid surfaces has been investigated using blood and blood plasma. Initially, small proteins with high mobility adsorb, whereas at a later stage these are replaced by proteins with higher adsorption energies. This is known as the Vroman effect [134,135]. It turned out that the ability to be displaced from the interface by another protein also depends on the age of the adsorbed protein layers. This implies that reorganizations and/or in-plane interactions occur, that increase protein adsorption energy, and thus would need to be incorporated in models when targeting relatively long time scales. The Langmuir model can be extended for multiple components that adsorb in multiple states and can aggregate, by including rate constants between the different states and diffusion. In principle, this allows discrimination between the effect of protein size, composition, surface-protein interactions and protein conformational changes. The model parameters are generally obtained by fitting experimental adsorption data. In general, good fits between experimental data and models can be obtained. It is good practice to make models as simple as possible, so with as few as possible fitting parameters (Ockhams' razor).
## 3.2. Interfacial adsorption models based on thermodynamic solution theory

An important class of theoretical models for adsorption and interfacial properties of surfactants and proteins are those based on solution theory, developed by Diamant and Andelman, who used a free energy approach [119,136,137], and by Fainerman, Miller and co-workers who used the generalized Butler equation [16,138,139]. The latter group contributed greatly to the understanding and modelling of proteins and surfactants at fluid-fluid interfaces.

### 3.2.1. Free energy approach

Diamant and Andelman used a free energy approach to describe the adsorption and interfacial properties of non-ionic and ionic surfactants [136,137]. A three-dimensional lattice is used, of which each site of size $a_0^3$ can be occupied by a solvent molecule, surfactant, or ion. The interface is assumed flat and sharp, with thickness $a_0$ and located at $x = 0$. At large distance from the interface, the solvent volume fraction $\phi_1$ is assumed constant, equal to $\phi_{1\infty}$. The excess free energy per unit area at the interface is the interfacial tension, which for a simple system of a non-ionic surfactant and solvent can be written as:

$$ \Pi = \int_{0}^{\infty} \Delta f[\phi_1(x)] dx + f_s(\phi_{1\infty}) \quad (14) $$

with $\phi_1(x)$ the volume fractions of the surfactant in the bulk at $x > 0$, $\Delta f$ the excess free energy per unit volume in the bulk, and $f_s$ the free energy per unit area interface. Furthermore, full lattice occupancy applies both in the bulk and the interface (s) so $\phi_0(x) + \phi_1(x) = \phi_{0s} + \phi_{1s} = 1$, with $\phi_0(x)$ and $\phi_{0s}$ the bulk and interfacial solvent volume fractions, respectively. Regular lattice solution theory includes entropic ($k_B T \ln \phi_i$), lateral interaction and interfacial adsorption terms, and the chemical potentials of the species $\mu_i(x)$ can be calculated as a function of $x$ using the derivative of the free energy with respect to the species' volume fractions. At equilibrium these are all equal, and for the equilibrium adsorption isotherm it follows that:

$$ \phi_{1s} = \frac{\phi_{1\infty}}{\phi_{1\infty} + (1 - \phi_{1\infty}) \exp\left(-\frac{\alpha_1 + \beta_1 \phi_{1s}}{k_B T}\right)} \quad (15) $$

with $\alpha_1$ and $\beta_1$ the surfactant adsorption, and lateral interaction energies, respectively, expressed in $k_B T$. For the SEOS this leads to:

$$ \Pi = \frac{k_B T}{a_0^2} \left( \ln(1 - \phi_{1s}) + \frac{\beta_1}{2k_B T} \phi_{1s}^2 \right) \quad (16) $$

For a dilute bulk regime ($\phi_{1\infty} \ll 1$) the equations correspond to the Frumkin isotherm, and further neglecting the lateral interactions ($\beta = 0$) leads to the Langmuir isotherm. The formalism can rather straightforwardly be extended to a mixture consisting of $n$ components. For a mixture of three components, one solvent (index 0) and two non-ionic surfactants (indices 1 and 2), the equilibrium isotherms and SEOS are given by:

$$ \phi_{1s} = \frac{\phi_{1\infty}(1 - \phi_{2s})}{\phi_{1\infty} + \phi_{0\infty} \exp\left(-\frac{\alpha_1 + \beta_{11} \phi_{1s} + \beta_{12} \phi_{2s}}{k_B T}\right)} \quad (17) $$

$$ \phi_{2s} = \frac{\phi_{2\infty}(1 - \phi_{1s})}{\phi_{2\infty} + \phi_{0\infty} \exp\left(-\frac{\alpha_2 + \beta_{22} \phi_{2s} + \beta_{21} \phi_{1s}}{k_B T}\right)} \quad (18) $$

$$ \Delta\gamma = \frac{k_B T}{\omega_{tot}} \left( \ln(1 - \phi_{1s} - \phi_{2s}) + \frac{\beta_{11}}{2k_B T} \phi_{1s}^2 + \frac{\beta_{22}}{2k_B T} \phi_{2s}^2 + \frac{\beta_{12}}{k_B T} \phi_{1s} \phi_{2s} \right) \quad (19) $$

with $\phi_{0\infty} = 1 - \phi_{1\infty} - \phi_{2\infty}$ the solvent volume fraction at large $x$, $\alpha_i$ the adsorption energies of surfactant $i$, and $\beta_{ij}$ the lateral interaction energies between emulsifiers $i$ and $j$.

Adsorption dynamics, and diffusion of the components follow from

the gradients in chemical potential of the components [137,140,141] that allow for calculation of a time-dependent dynamic surface pressure and volume fractions of the components at the surface by numerically solving differential equations. This allows for systematic evaluation of the adsorption $\alpha_i$ and lateral interaction $\beta_{ij}$ energies, which are relevant for competitive protein adsorption at solid surfaces [119]. It is also possible to take conformational changes of the proteins into account by assuming the probability of certain conformational states, and protein transport through a diffusion equation based on chemical potential differences. This formalism can be further extended to include surfactant charge and ionic strength [136], and can be used to describe the adsorption dynamics of colloidal particles [142].

It was thought that typical theoretical protein surface interaction energies are in the order of 20 to 80 $k_B T$; however, the work of Vogler concluded that the apparent free energy of adsorption is about $-5 \pm 1k_B T$ and decreases with increasing hydrophilicity (see e.g. [124] and references therein). If the latter is true, these energies are not extremely large compared to their thermal energy, and competitive adsorption and displacement of a protein with lower interfacial adsorption energy by proteins or surfactants with higher adsorption energies seems likely. In practice, it is known that proteins form aggregates and aggregated networks at the interface, which in turn will increase the desorption energy tremendously. To wrap-up, although protein displacement could, at first sight, seem possible owing to the low adsorption energies involved, the propensity of lateral interactions established post-adsorption largely hampers this. In order to have a complete overview of all effects involved in protein adsorption including lateral interactions, they would need to be incorporated in the free energy formalism, which is far from trivial.

### 3.2.2. Multistate adsorption model

The model developed by Fainerman, Miller and co-workers is based on 2D solution theory [16,138,139,143–146]. Their starting point is the generalized Butler equation describing the chemical potential of non-ionic components $i$ at the surface and in bulk:

$$ \mu_i^s = \mu_i^{0s} + k_B T \ln f_i^s x_i^s - \gamma \omega_i \quad (20) $$

$$ \mu_i^b = \mu_i^{0b} + k_B T \ln f_i^b x_i^b \quad (21) $$

with the superscripts $s$ and $b$ indicating the surface and bulk, respectively, $k_B$ the Boltzmann's constant, $T$ the temperature, $\gamma$ the surface tension, $f_i^{s/b}$ the activity coefficient of component $i$, $x_i^{s/b} = N_i^{s/b} / \sum N_i^{s/b}$ the molecular number fraction and $N_i^{s/b}$ the number of component $i$, and $\omega_i$ the partial molar interfacial area of component $i$. The solvent is usually described by the subscript 0.

For a binary mixture of molecules with equal area and considering a first order enthalpic correction for the activity coefficient (thus only including lateral interaction energies proportional to the number fraction), a Frumkin SEOS and isotherm follow. A protein is considered a flexible polymer consisting of a number of $n_1$ elements that can adsorb in a number of states on an area that varies between a minimum value $\omega_{min} \ge \omega_0$ and a maximum value $\omega_{max} \le n_1 \omega_0$. From this it follows that:

$$ \Pi = - \frac{RT}{\omega_0} \left( \ln(\theta_0) + \left(1 - \frac{\omega_0}{\omega}\right)(1 - \theta_0) + \beta(1 - \theta_0)^2 \right) \quad (22) $$

with $\omega$ the averaged area of an adsorbed protein molecule. At higher coverage and/or surface energies, the area of the adsorbed protein can decrease due to desorption of segments, which is characteristic for proteins. The interfacial protein coverage equals:

$$ \theta_1 = 1 - \theta_0 = \omega \Gamma_1 = \sum_{i=1}^{n_1} \omega_{1i} \Gamma_{1i} \quad (23) $$

The adsorption isotherm for the protein adsorbed in state $i$ is then given by:
$$kc = \sum_{i \ge 1} k_i c = \sum_{i \ge 1} \frac{\omega \Gamma_i}{(\theta_0)^{n_i}} \exp(-2\beta n_i'(1 - \theta_0)) \quad (24)$$

with c the bulk protein concentration, $k_i$ the adsorption equilibrium coefficient for each adsorbed protein state, which is assumed to scale the minimum area $\omega_1 = \omega_{min}$ for the protein at $b_i = (\omega_i/\omega_1)^{a}b_1$.

Multilayer adsorption is taken into account by assuming that the total amount of adsorbed protein is given by:

$$\Gamma = \Gamma^{(1)} \sum_{j=1}^{N} \left( \frac{b_j c}{1 + b_j c} \right)^{j-1} \quad (25)$$

with $b_x$ the equilibrium constant for the protein adsorbed in the sub-surface layers.

Protein aggregation is taken into account by assuming that when the adsorbed amount of protein exceeds a critical value $\Gamma^*$, the surface tension is given by:

$$\Pi = \Pi^* \left( 1 + \frac{\Gamma - \gamma^*}{n_a \Gamma^*} \right) \quad (26)$$

with $n_a$ the aggregation number (size) of the protein.

Adsorption dynamics is based on fast diffusion from the bulk to the interface [146], similar to what is considered in the Ward and Tordai model [124]. Protein conformational changes can be taken into account, and kinetics between different adsorbed protein conformations are described using adjustable rate constants. Fainerman and Miller extended this formalism to mixtures of different proteins as well as mixtures of proteins and surfactants to include mixed, sequential and competitive adsorption. In general, fair comparison with experiments could be obtained. Experiments and modelling of protein (β-casein, human serum albumin) and nonionic surfactant mixtures show that an increased surfactant concentration decreases interfacial protein concentration and that displacement is most pronounced for flexible proteins [144]. Studies on a mixture of β-lactoglobulin and CTAB showed that proteins interact with surfactants, resulting in protein-surfactant complexes and/or alteration of the protein's conformational structure [146]. Another example is a mixture of lysozyme, positively charged at neutral pH, with non-ionic (decyl dimethyl phosphine oxide ($C_{10}DMPO$)) and ionic surfactant SDS, negatively charged at neutral pH. Adsorption properties, including interfacial rheology, were well described through modelling, and showed that competitive adsorption depends on the charge of the surfactant [145,147]. A similar study was performed by Kotsmar et al. on mixtures of milk proteins and surfactants [50,148], and good agreement between the theoretical model and experiments could be obtained. In this study, binding of surfactants to proteins led to a decrease in the hydrophobicity of proteins and thus in their adsorption energy, which in turn allowed those complexes to desorb.

Competitive adsorption of β-lactoglobulin and β-casein was investigated by Fainerman et al. [16], who showed that both proteins can displace each other from the air-water interface. Equilibrium and dynamic calculations were performed with ten adjustable fitting parameters that were the same for both calculations. The model of the protein mixture revealed good alignment with experimental findings, although some parameters needed adjustment, and the fitted protein diffusion coefficients were lower than expected based on physical grounds, which was attributed to an adsorption barrier.

The Fainerman and Miller approach has therefore shown useful to describe interfacial properties of various surfactant and protein systems, including their lateral interactions. It is good to point out that many adjustable parameters are involved and these need careful validation.

### 3.3. Modelling interfacial rheology

Besides dynamic surface tension and equations of state, also the

response of the surface to deformation (e.g. interfacial rheology) is an important characteristic that can provide information about in-plane intermolecular interactions between the adsorbed proteins. The interface is a concentrated region where proteins have various degrees of freedom, coupled to bulk chemical potential, and can change orientation and conformation. This leads to interacting networks and complex non-linear viscoelastic rheological responses when the interface is deformed (as described in section 2). In general, the interfacial stress response to deformations is described using the tensor formalism, including shear and dilatational components, and is very challenging to model [149–152].

Drop and bubble tensiometry measure purely the dilatational component of the interfacial rheological response whereas a superposition of the dilatational and shear modulus is measured in a Langmuir through where the interface is uni-axially deformed. Here we will focus on the dilatational rheology of flat interfaces.

An important and often studied parameter to characterise the in-plane rheological properties of interfaces is the interfacial dilatational modulus $E$, which can be assessed using drop and bubble tensiometry. According to Gibbs it is equal to:

$$E = \frac{\partial \gamma}{\partial \ln A} \quad (27)$$

with A the total interfacial area and $\gamma(t)$ the interfacial tension of the interface at constant $\Gamma$.

To get insights in the rheological response of the interface as a function of the change in the interfacial area, often the interfacial area is changed periodically:

$$A = A_0 + \Delta A e^{i\omega t} \quad (28)$$

with $\Delta A$ the amplitude of area variation and $\omega$ the radial frequency. For small $\Delta A$, in the linear regime, the response $\gamma(t)$ will be periodical with the same frequency but phase shifted (Fig. 3). Then the modulus can be assessed through a Fourier transformation, and in general the interfacial dilatational modulus will be complex:

$$E^*(\omega) = E'(\omega) + i E''(\omega) \quad (29)$$

with $E'$ the storage modulus and $E''$ the loss modulus, corresponding to elastic storage and viscous dissipation of energy during deformation, respectively. In the non-linear regime, $E^*$ will also depend on $\Delta A$ and it may depend on time and history (thixotropy). Furthermore, $E^*$ can depend on adsorption and desorption phenomena induced by the deformation [153].

For soluble surfactants, the interfacial coverage will change with surface area due to adsorption and desorption of the emulsifiers. This was firstly modelled by Lucassen and van den Tempel, who considered a diffusional flux [154]. The complex interfacial dilatational modulus $E^*$ can then be written as:

$$E^* = \frac{\partial \gamma}{\partial \Gamma} \frac{\partial \Gamma}{\partial \ln A} = E_0 \frac{1 + \zeta + i\zeta}{1 + 2\zeta + 2\zeta^2} \quad (30)$$

with $\zeta = \sqrt{1/\omega\tau_D}$, corresponding to the ratio of the time scale of the experiment and the diffusion time $\tau_D = (2/D)(\partial\Gamma/\partial c)_\text{eq}$. This approach can be extended with the thermodynamic models described earlier that express the dynamic interfacial tension as a function of the interfacial coverage, which itself depends on adsorption and desorption [155].

In general, for proteins and polymers at interfaces, interactions and network formation are important and interpretation of the complex modulus is possible using phenomenological constitutive models, similar as often applied in 3D. These consist of pure elastic spring and pure viscous dashpot elements, combined in series (e.g. Maxwell model) and/or in parallel (e.g. Kelvin-Voigt model). The Kelvin-Voigt model consists of a dashpot with viscosity $\eta$ and spring with elasticity $E$ in parallel and the relation between deformation $\epsilon$ and stress $\sigma$ is given by:
$$ \sigma = E\epsilon + \eta \frac{d\epsilon}{dt} \qquad (31) $$

The Maxwell model consists of a spring and dashpot in series, with relation between deformation and stress

$$ \frac{1}{E} \frac{d\sigma}{dt} = E\epsilon + \eta \frac{d\epsilon}{dt} \qquad (32) $$

The characteristic time of retardation after application of a sudden change in stress (Kelvin-Voigt) or relaxation after a sudden change in strain (Maxwell) is given by $\eta/E$.

In the linear regime, for small strain, the model parameters (the elasticities and viscosities of the springs and dashpots) are assumed constant. Non-linear behaviour at the interface can be modelled by introducing nonlinear versions of (32), such as the upper-convected Maxwell model [156], or introducing elements that depend on e.g. strain (rate), shear (rate), or on a structure parameter [157–159]. This allows modelling of yield stress, shear thinning, thickening and thixotropy [158]. Such a structure parameter can be coupled to the network or aggregates that are formed in time at the interface. In such a way, a mean field theory can be developed in terms of a set of ordinary differential equations that can be solved numerically. They contain various parameters for diffusion rates of the ingredients, interaction and adsorption energies, rearrangement and aggregation rates, as well as parameters for the elements used to describe the constitutive relations. Parameters can be estimated from interfacial adsorption and rheological experiments on individual components as well as mixtures, at different ingredient concentrations, ionic strength and pH. The model can then be used to predict e.g., properties of interfaces that are formed by subsequent addition of ingredients. In addition, model validation and parameter estimation can be improved when comparing model outcomes with molecular and Brownian dynamic simulations.

### 3.4. Brownian dynamics simulations

Interfacial displacement has been simulated using BD [71,72,75,160], which provided useful information on the mechanisms involved and showed good comparison with experimental data Fig. 6A. Wijmans and Dickinson simulated an adsorbed protein monolayer as bonded particles and introduced non-interacting displacer particles with a stronger affinity for the interface. They showed that if the initially adsorbed particles form a strongly bonded network, very few displacer particles succeed in adsorbing at the interface. In case of less strong network interactions at the interface, the displacer particles could adsorb, when present in sufficiently large numbers, and thus produce a closely packed monolayer with a lower interfacial tension (Fig. 6B and C) [71,72]. A generic conclusion was drawn, according to which for displacement to occur in the BD simulations, three criteria need to be met:

1) The cross-linked interfacial layer needs to have small holes through which the displacing molecules can penetrate.

2) The cross-linked film has to be flexible enough to allow compression prior to displacement.

3) Short-range repulsive interactions between the adsorbed and displacer components need to occur, which enhances local phase separation and subsequent growth of the areas occupied by displacer particles.

Furthermore, the simulations confirmed that proteins were not simply displaced per molecule but as ‘gel like’ structures (Fig. 6C, [161]), highlighting the effect of lateral in-plane interactions. Repulsive interactions between displacer particles and bonded monolayer were investigated by Pugnaloni, Ettelaie, & Dickinson (2003) [75], and ultimately, the BD simulations were compared to experimental data on displacement of a protein layer by surfactants [51,162] in a semi-quantitative way, because the interactions within the layers varied

<figure><img src="image_9.png" /><figcaption>Fig. 6. A) Comparison of a Brownian dynamic simulation of a protein film partially displaced by a surfactant (left) with an AFM image of a β-lactoglobulin film displaced by Tween 20 (right). The image is 0.8 × 0.8 µm. Light particles represent the protein film, adsorbed surfactants are not displayed. “Reprinted from [162] with permission from Elsevier”. B) Snapshots of the interfacial plane during a displacement simulation. “Adapted with permission from [71]. Copyright 2022, American Chemical Society”. C) Schematic representation of the side-on profile of the same interfaces represented in B. In both B and C the dark particles represent the initially adsorbed particles and the light particles the displacer particles.</figcaption></figure>
greatly between β-lactoglobulin and β-casein. This could be taken into account in a fairly simple coarse-grained manner. Furthermore, the interactions between the proteins and low molecular weight components were not taken into account which if they were, are expected to reduce the surface activity of the proteins due to reduced hydrophobicity [50].

The outcomes of BD simulations highlight the importance of the interfacial rheological properties of the pre-adsorbed monolayer and of the surface activity of the displacing particle, and thus illustrates strategies for displacement of adsorbed proteins by low molecular weight emulsifiers (e.g. SDS, Tween 20). It is presumable that similar mechanisms play a role in displacement mechanisms in protein blends, although the interfacial tension differences are much smaller. Furthermore, the nature and strength of in-plane protein interactions of the pre-adsorbed and displacing protein would need to be included to make the BD simulations even more relevant.

## 4. Summary and outlook

When using protein blends, non-equilibrated interfacial structures are formed that change over time due to interfacial displacements and rearrangements. It is therefore essential to characterise competitive adsorption and interfacial displacement in these systems at the relevant length scales (and ideally also time scales). Visual observations in model interfaces (e.g. AFM) and protein partitioning in emulsions are useful to determine whether displacement occurs, but do not allow for mechanistic understanding; for this latter perspective, the determination of interfacial rheological properties is essential. The use of theoretical models including iterative parameter fitting and phenomena prediction will strongly increase insights in the behaviour, competitive adsorption and interfacial properties of complex protein mixtures. This review thus provides ample information for characterising the interfacial properties over time, and presents both experimental and modelling techniques.

It is clear that there are still considerable challenges in trying to explain the behaviour of such systems as would happen in practice especially for emerging protein sources (e.g. plant protein isolates), which often contain much more than proteins in their native conformation. Until now, the majority of displacement characterisation has been done using dairy proteins (Table 1, Table 3), that typically have a high solubility in aqueous media. Plant protein ingredients have gained considerable interest in food research [163,164] and in industrial applications. Plant protein isolates typically contain insoluble proteins, soluble proteins and non-proteinaceous components (e.g. lipids, phenolic compounds, fibres, etc.). When used to stabilise emulsions, the soluble and insoluble proteins may compete for adsorption and displace each other over time [165], in a comparable manner to mixtures of Pickering particles and LMW surfactants [166,167]. The fact that the proteins are insoluble implies that they exist in a supramolecular, particulate form and may act as Pickering particles [168]. These particles can only anchor at the interface when they have enough kinetic energy to exceed the adsorption energy barrier (which exceeds diffusion energy by orders of magnitude) [169]. This makes interface characterisation challenging since the particles would not diffuse to the interface or desorb due to gravitational forces in model interfaces (e.g. drop tensiometer or Langmuir-trough). For experiment to get closer to practice, mass transfer would need to be incorporated, and promising methods for this are microfluidic tools. The stability of emulsions stabilised by silica nanoparticles [170] or solid lipid particles [171] have been studied using microfluidics, so the proof of principle has been delivered. As a next step, the interfacial rheological properties of such particle-stabilised droplets could be assessed with the microfluidic rheology chips [93]. This would open new perspectives to study the interfacial rheological properties of droplets stabilised by plant protein ingredients, even at very short time scales.

# Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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