Rheological approaches as a tool for the development and stability behaviour of protein-stabilized emulsions

Food Hydrocolloids 104 (2020) 105719

Contents lists available at ScienceDirect

Food Hydrocolloids journal homepage: http://www.elsevier.com/locate/foodhyd

Rheological approaches as a tool for the development and stability behaviour of protein-stabilized emulsions Manuel F� elix , Cecilio Carrera , Alberto Romero , Carlos Bengoechea , Antonio Guerrero * Departamento de Ingeniería Química, Universidad de Sevilla, Facultad de Química, Calle Profesor García Gonz� alez 1, 41012, Sevilla, Spain

A R T I C L E I N F O

A B S T R A C T

Keywords: Complex interfaces Emulsion Modelling Rheology

Emulsion stability is the primary requirement for the industrial applications of many commercial food products. This work analyses the importance of rheology on the characterisation of protein-adsorbed systems, from complex fluid-fluid interfaces to bulk emulsions, as well as their relationship to the stability behaviour of the final emulsion. To accomplish this aim, three case studies involving protein-adsorbed systems at different scales are discussed: bulk rheological properties of protein-stabilized emulsions, interfacial rheology of proteins adsorbed at O/W interface, and the links between interfacial and bulk rheology of proteins/polysaccharide mixtures. The knowledge of the interfacial behaviour on a nanoscale is essential for the development of optimal properties on both the microscale (droplet size distributions and microstructure) and the macroscale (bulk rheology and stability). This work presents linear and nonlinear rheology of complex interfaces, including a discussion on recent progress available for analysing and modelling nonlinear interfacial rheology data. In addition, a similar rheological analysis for protein-stabilized emulsions is reviewed, with the aim of exploring possible links between interfacial shear rheology and emulsion rheology, as well as their connections to emulsion microstructural parameters and emulsion stability. This approach, which mainly relies on the characterization of the interface, might be regarded as very useful to tailor interfaces for the development of optimal emulsion microstructure and stability.

1. Introduction The stability of an emulsion is related to its rheological properties at different levels since macro and microscopic properties are particularly important when characterizing bulk phases; however, a nanoscale level is generally required for the description of the existing interfaces. Much has been discussed on the relationship between emulsions properties at a macroscopic (i.e. emulsion rheology and stability) and microscopic level (i.e. emulsion microstructure), which, in turn, de­ pends on the formulation but also on the emulsification process (i.e. a high amount of energy is required to disperse small droplets of one phase within a continuous phase). Classical approaches are available that have contributed to the understanding of this relationship (e. g. Derkach, 2009; Dickinson, 1998, 2019; Tadros, 2004). Nevertheless, the present analysis is focused on the behaviour of the interface at a nanoscale level, and more specifically on the rheology of complex fluid-fluid interfaces regarding interfacial microstructures and stability, which are also linked to emulsion stability and rheology. It is well known that the emulsification process is not favoured from

a thermodynamic point of view due to the large interfacial area gener­ ated, which tends to destabilize the emulsion through different mecha­ nisms (e.g., creaming, flocculation). Thus, from an industrial point of view, the primary target to be considered is to enhance kinetic stability. More specifically, an emulsion may be considered to be kinetically stable when droplets remain unchanged over time in number, size, size dis­ tribution or even in their spatial arrangement, (Gallegos & Franco, 1999). There are two main ways of achieving this target. The first one consists in increasing the rheology of the continuous phase, even forming a gel network (Bengoechea, Cordob�es, & Guerrero, 2006). This can be achieved either by adding a stabilizer (i.e. a polysaccharide), by promoting physical interactions among different proteins chains (changes in pH and ionic strength, thermal treatment …) or by increasing the protein content (Huang, Kakuda, & Cui, 2001; Raikos, 2010). In the former case the polysaccharide tends to form a gel under the appropriate conditions, as observed in gel networks formed by chi­ tosan in the continuous phase of a protein-stabilized O/W emulsion ~ oz, Cox, Heuer, & Guerrero, 2013), whereas an increase in (Calero, Mun protein content would produce a great excess that may lead to the

* Corresponding author. Departamento de Ingeniería Química, Universidad de Sevilla, Facultad de Química, 41012, Sevilla, Spain. E-mail address: [email protected] (A. Guerrero). https://doi.org/10.1016/j.foodhyd.2020.105719 Received 18 October 2019; Received in revised form 24 January 2020; Accepted 27 January 2020 Available online 30 January 2020 0268-005X/© 2020 Elsevier Ltd. All rights reserved.

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

formation of a gel matrix, as has been previously observed in gluten-based emulsions (Bengoechea et al., 2006). The second way consists in increasing the energy barrier for destabilization using a suitable emulsifier, such as a protein. The case study 1 shows the in­ fluence of emulsion microstructure on bulk properties of protein-stabilized emulsions. Proteins are the most important emulsifiers used in food products. Hence, they are remarkably efficient in stabilizing emulsions by a sharp reduction of interfacial tension, which facilitates the breakup of droplets during emulsification and by the formation of viscoelastic films that helps to stabilize the newly formed droplets against coalescence. In such a case, the interfacial rheology of the protein adsorbed layer has a key role in obtaining this kinetic stability. A special case refers to the adsorption of particles to the interface, also known as Pickering emul­ sions. These systems have gained significant interest since particle and/ or particle-protein systems hardly suffer destabilization phenomena such as coalescence and Ostwald ripening due to a high desorption en­ ergy (Araiza-Calahorra & Sarkar, 2019). This interest is derived from the delaying lipid digestion since bile salts cannot displace from interfaces, involving a wide range of systems. However, Pickering emulsions are out of the scope of the present study, and those interested readers are referred to different articles covering the stabilization of A/W (Li, Murray, Yang, & Sarkar, 2020), O/W (Araiza-Calahorra & Sarkar, 2019) and W/O interfaces (Araiza-Calahorra, Akhtar, & Sarkar, 2018), where not only particle-proteins (Sarkar, Zhang, Murray, Russell, & Boxal, 2017), but also particle-particle can be used (Zembyla, Lazidis, Murray, & Sarkar, 2019). Interfacial rheology may play an essential role in maintaining physical stability and has been typically measured by applying dilata­ tional or shearing deformations. According to Benjamin and LucassenReinders (Benjamins & Lucassen-Reynders, 1998), dilatational mea­ surements are more relevant for short-term stability, whereas interfacial shear rheology provides more valuable information of middle or long-term stability. Unfortunately, the interpretation of results obtained from the interfacial rheological measurements is not always straight­ forward (e.g. the dynamics of rheologically complex fluid-fluid in­ terfaces is often difficult to analyse) and some precautions have to be taken into consideration, particularly for dilatational measurements, in order to deliver the right interfacial properties. Finally, a further chal­ lenge that is still far from being solved is the application of models being able to describe properly the dynamics of complex interfaces, particu­ larly at the nonlinear regime at which a better understanding of the interfacial microstructure behaviour seems to be essential. The aim of this work is to analyse the importance of rheology on the characterisation of protein-adsorbed systems, from complex fluid-fluid interfaces to bulk emulsions, as well as their relationship to the stabil­ ity behaviour of the final emulsion. In this context, two complementary sections are considered. The first section will be devoted to reviewing the recent progress available for the modelling of linear viscoelastic properties of complex fluid-fluid interfaces including data from inter­ facial dilatational or shear rheology and the limitations found in these measurements, either under linear or nonlinear conditions. Subse­ quently, some case studies will be discussed. Modelling of nonlinear viscoelastic behaviour of protein-stabilized systems will be analysed, first at the bulk and later at the oil/water interface, using in both case a similar approach, aiming for exploring possible links between interfacial shear rheology and emulsion rheology, both of which are considered to be closely related to emulsion microstructural parameters and emulsion stability. The last case will be focused on the effect of adding a poly­ saccharide and how it may affect the rheology of the complex fluid-fluid interface.

has a decisive influence on the macroscopic behaviour of the dispersed system (formation, stability and rheology), being essential their under­ standing to create emulsions-based foods (McClements, 2015). Due to their amphiphilic character, proteins can be adsorbed at the O/W interface forming interfacial films which reduces the interfacial tension and provides stability against destabilization phenomena such as coa­ lescence and creaming (Tadros, 2013). The complexity and functionality of O/W interfaces have a key role in the design of emulsions. However, the methods currently available for the characterisation of these nano­ metric layers and, particularly, their modelling are very limited. Despite their limitations, this challenge has been recently addressed by inter­ facial rheological measurements (Leonard M C Sagis & Scholten, 2014).

2. Fluid-fluid interfaces

All of these contributions may be important even in the absence of rheological complexity, where the gradient is related to Marangoni stress. Therefore, the surface stress tensor of the interface after the appli­

2.1. Soft interface dominated materials (SIDM) Although fluid-fluid interfaces are very thin (manometer scale), their large interfacial area confers them an essential role in many materials. Typical examples of SIDM include a wide variety of food products, such as emulsions and foams, or biological fluids, such as the lipid bilayers that form cell membranes, tear films, which protect our eyes (formed by a mucin film, an aqueous layer and a lipid layer), and the lung walls, which are covered with surface active agents (proteins and phospho­ lipids) and allow the exchange of oxygen to blood cells by expanding and contracting. The interfacial film of some of these materials may be classified as simple interfaces when they are stabilized by low molecular weight (LMW) surfactants which do not self-assemble into mesophases. In contrast, complex fluid-fluid interfaces are stabilized by active-agents which tend to form 2D microstructures, including gels (formed by pro­ teins or colloidal particles), soft glasses (proteins, colloidal particles or glycolipids), liquid crystalline phases (protein fibrils) and composites. The dynamics of such complex interfaces, which are generally dominated by the surface rheological properties, are typically charac­ terized by nonlinear relationships between stress and strain or strain rate. A typical evidence of rheological complexity can be detected on pendant drop tests by the formation of wrinkles upon deflation. Two different approaches can be used to account for the difference in properties across the interface: a) The diffuse-interface approach, which admits a finite thickness for the interface and a gradient of properties across the fluid-fluid interface; b) The so-called Gibbs dividing surface, which can be assumed when the thickness is very small as compared to the significant length scale (e.g. a droplet diameter). This very thin interfacial layer supports the difference between the two fluid phases (i. e. excess surface properties). In any case, continuity of velocity or stress across the interface must be imposed as required from fluid mechanics where the Navier-Stokes equations can be applied for each phase. Equation (1) (Eq. (1)) describes the stress (τÞ obtained using this requirement: �

τð1Þ ij

�

nj þ τð2Þ ij

∂Τ sij ∂nk ¼ Τ sij nj ∂xj ∂xk

(1)

where the first term on the left side refers to the stress difference be­ tween the two bulk fluids ((1) and (2)) that are supported by the interface, and the second one to the gradient of the surface extra stress tensor, including isotropic and anisotropic components. The term on the � right side (Τ sij nj ∂∂nxkk arises from the existence of normal stresses. The gradient of the surface extra stress tensor ðΤ sij Þ may be expressed in terms of the surface stress tensor ðτsij Þ and the surface pressure (Πδij ): Τ sij ¼ τsij

In any emulsion there is a thin region separating the oil phase from the aqueous phase, which is known as the O/W interface. This thin layer 2

Πδij

(2)

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

cation of deformation (σsij Þ is related to the interfacial tension (σ ), which

is a function of the surface concentration (ΓÞ and temperature (T), and the deviatoric stress tensor (τsij ), which differs from the previous inter­

facial extra stress tensor by the 2D isotropic surface pressure (Hermans, Saad Bhamla, Kao, Fuller, & Vermant, 2015), according to the following expression:

the deformed (A) and undeformed surface areas ðA0 Þ. Equation (11) separates the dilatational contributions from the shear contributions. If A is equal to A0, then J is equal to 1, and the dilatational term is cancelled from the equation. It is worth emphasizing that the importance of this model does not reside in its capacity to reproduce the behaviour of real interfaces, but in its ability to separate the effect of shear and dilation. This fact enables using this model as a limiting equation for pure elastic interfaces that can be applied in combination with the limit for pure viscous interfaces (i.e. the Boussinesq-Scriven equation) as building blocks for the development of more realistic viscoelastic interfaces. This was the successful approach followed in bulk rheology when viscous (Newtonian) and elastic (Hookean) ele­ ments were combined to develop a range of predictive models for a wide variety of viscoelastic materials.

For complex interfaces we need a constitutive equation to capture the response of the interfacial stress to a deformation or rate of defor­ mation of the interface (Jaensson & Vermant, 2018). The simplest equation is obtained for a purely viscous interface where the stress can be described by the Boussinesq-Scriven equation. It may be noticed, even in such a simple case, that not only the surface shear viscosity contributes to the stress but also the surface dilatational viscosity.

∂vk δ þ 2 μs Dsij ∂xk ij

(4)

κs and μs are the surface dilatational and shear viscosities, respec­ tively, v is the velocity vector on the interface and Dsij is the surface rate of deformation tensor. This tensor can be described in terms of the ve­ locity gradient for planar interfaces (Eq. (5)), although it may also need an extra term to account for the projection of normal components onto the interface. � � 1 ∂vi ∂vj Dsij ¼ þ (5) 2 ∂xj ∂xi

2.2.1. Surface dilatational rheology When a drop is deformed by dilatation/compression, this general expression for the surface stress gives rise to a generalization of the Young-Laplace equation, where the Laplace pressure ΔP ðPð2Þ Pð1Þ Þ can be written as a function of different terms (Sagis, 2013): � � Pð2Þ Pð1Þ ¼ 2σðΓ; TÞH þ 2Htr τsij (12) κC0 K

It is worth mentioning the similarity between Eq. (4) and the Newton equation for the bulk fluid: � � 2 ∂vk τij ¼ κ μ δ þ 2μDij (6) 3 ∂xk ij

where 1 refers to the outer phase and 2 to the inner phase; σ is the surface tension; H is the mean curvature between 1=R1 and 1=R2 ½L 1 �, thus representing the trace of the surface stress tensor, which is the contribution from in-plane viscoelastic stresses; κ ½ML2 T 2 � is the contribution of the bending rigidity of the interface to an applied deformation; C0 is the spontaneous curvature ½L 1 �; and K is the Gaussian curvature ½L 2 �. For a quasi-spherical drop of radius R, the equation can be reduced to an expression that capture the influence of the drop size (Sagis, 2013). . . � � κC0 2R (13) σ eff ¼ ΔP 2H ¼ σ þ tr τsij

The difference here is that liquids, unlike highly deformable in­ terfaces, can be generally assumed to be incompressible and then the equation reduces to the well-known expression of Newton’s law: � � ∂vi ∂vj ¼ μγ_ ij τij ¼ 2μDij ¼ μ þ (7) ∂xj ∂xi On the other hand, for a purely elastic interface, the surface (or interfacial) stress can be described in terms of the surface dilatational and shear modulus (Es ​ and Gs , respectively), the divergence of the displacement vector ðuÞ and the surface infinitesimal stress tensor (Usij Þ (Verwijlen, Imperiali, & Vermant, 2014):

τsij ¼ ðEs

Gs Þ

∂uk δ þ2 ∂xk ij

Gs U sij

(10)

where J is determined as detðFsij Þ, thereby representing the ratio between

2.2. Models in complex fluid-fluid interfaces

μs Þ

∂xi ∂XJ

where xi and xJ are the position vectors in the deformed and reference configuration, respectively. In this way, a “neo-Hookean” constitutive equation has been recently derived by Pepicelli, Verwijlen, Tervoort, and Vermant (2017): � � � � � � 1 1 1 s 1 1 Bij tr Bsij δij τsij ¼ Es ln J δij þ Gs (11) J J J 2 J

In the absence of rheological complexity, the equation gives rise to the Young Laplace equation, such that the first term includes Gibbs elasticity, Marangoni effects and capillary phenomena. The second term comprises all the rheological material functions, which makes it responsible for the rheological complexity of the interface.

τsij ¼ ðκs

(9)

F sij ¼

(3)

σ si ¼ σ ðΓ; TÞδij þ τsij

� �T Bsij ¼ Fsij Fsij

As a consequence, experiments carried out at different drop sizes and deformation amplitudes may be useful to identify which of these terms is dominant. According to Sagis (L M C Sagis, 2013) if the response is in­ dependent of R 1 and δR, the interface is dominated by surface tension; if the response is independent of δR, but decreases proportional to R 1, a bending rigidity dominated interface is defined; and if the response is proportional to both R 1 and δR, then the interface is dominated by the deviatoric stresses. In all these experiments, the dilatational modulus is calculated from the transient response (after Fourier analysis) in terms of the difference between deformed and undeformed surface tension (σ eff and σ nd , respectively) and of the relative deformation. However, the apparent modulus depends on the nature of the dominant term of the interface. For interfaces dominated by surface tension, the modulus is the thermodynamic dilatational modulus.

(8)

In the case of planar interfaces, the surface infinitesimal strain tensor � � ∂u may be expressed again as Usij ¼ 12 ∂∂uxji þ ∂xji . However, for curved in­ terfaces with normal components in the interfacial displacement, a tensor projection onto the interface is required. A further limitation is that Usij is only valid for infinitely small deformations and should be replaced for finite deformations. An alternative, representing an appropriate finite deformation, is given by the left-Cauchy-Green surface strain tensor Bsij , which may be readily obtained from the 2D surface deformation gradient tensor, Fsij :

3

M. F�elix et al.

σ eff ðtÞ � σ nd ðtÞ ​ ⇒Eapp � Ed0 ¼

Food Hydrocolloids 104 (2020) 105719

σ eff

σnd

dlnA

(14)

E’s ¼ Ese þ

The deformation applied to the interface changes the surface con­ centration (Γ) and Ed0 is determined by the rate of exchange of the emulsifier with the adjoining phases. In any case, the interface is not complex and the moduli (E’s and E”s ) can be properly described by the well-known Lucassen-Van den Tempel model (Lucassen & Van Den Tempel, 1972) as a function of frequency (ω) for soluble surfactants, assuming the diffusion from/to the bulk as unique relaxation process. pffiffiffiffiffiffiffiffiffiffiffiffi ωD =ω . E’s ¼ Ed0 (15) pffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 2 ωD =ω þ 2ωD ω

E”s ¼ Ed0

pffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ωD =ω . pffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 2 ωD =ω þ 2ωD ω

E”s ¼

In systems with ultralow interfacial tension, bending rigidities might become important and could play a role in interfacial phenomena, such as phase separation. From earlier calculations, the bending rigidities were estimated to be a few hundred times the thermal energy term (kbT, with kb being the Boltzmann constant and T the temperature) for nearcritical systems with a very large interfacial thickness (Scholten, Sagis, & van der Linden, 2004). These calculations showed that bending rigidities become important at droplet sizes smaller than a certain critical radius, Rc¼(k/σ)0,5. Taking realistic values for k (100 kbT) and σ (1 μN/m), the critical diameter of approximately 1.3 μm. In any case, the contribution of bending rigidity will be in most cases negligible, with some exceptions, such as some membranes (Danov, Kralchevsky, & Stoyanov, 2010), lipid vesicle bilayers (Smeulders, Mellema, & Blom, 1992) and interfaces with phase separated biopolymer mixtures (Scholten et al., 2004) or with densely packed particles (Yunker et al., 2012). In those cases, the relevant property is not a dilatational modulus, but a rigidity term. The response is dominated by deviatoric stresses when the defor­ mation does not alter surface tension (σ ¼ σ nd Þ and the rigidity is neglected. � � σ σ nd σ eff ðtÞ � σnd þ tr τsij ðtÞ ⇒Eapp � Ed þ Gs ¼ eff (17) dlnA

(18)

E”s ¼

Es λd ω 1 þ λ2d ω2

(19)

(21)

2.2.2. Interfacial shear rheology The measurement of interfacial shear properties is also challenging, not only because the torque values associated with the deformation of an interface will be small, but also because the flow and deformation of an interface will entail the deformation and flow of the adjoining bulk phases. The intimate coupling between the flow in bulk and at the interface is often complex to analyse. The Boussinesq number (Bq ) provides an index of the contribution of the surrounding phases to the interfacial measurements: Bq ¼

ηsurface Surface drag ¼ Subphase drag ηsubphase ⋅L

(22)

where η corresponds to viscosity and L is a characteristic length scale. Bq values much higher than 1 are required to detect the interface alone in the presence of the adjoining fluids. Therefore, small values of the characteristic length scale (L) are required and, consequently, a surface geometry has to minimize the ratio between the contact area with the adjoining phases and the perimeter in contact with the interface. In this sense, several measuring geometries have been proposed to fulfil these requirements, including, among others: a Du Noüy ring, whose main drawbacks are the large gap and the undefined contribu­ tions of the central part of the ring; the bicone, which has overcome these problems, although it entails a large contact area with the adjoining phase that leads to relatively low values of Bq (Erni et al., 2003); the double-wall ring (DWR) geometry, which is a modification of the Du Noüy ring that minimizes the contact surface/perimeter, elimi­ nates the central region with the double wall that also contributes to increase the torque, and facilitates aiming at the interface by using a diamond shape for the ring (Vandebril, Franck, Fuller, Moldenaers, & Vermant, 2010). Finally, it is worth mentioning the interfacial stress rheometer, which uses a magnetized needle freely suspended at the interface (Reynaert, Brooks, Moldenaers, Vermant, & Fuller, 2008). Among them, the latter two alternatives stand out for the following reasons:

The response to a dilatational deformation may involve significant values for Gs in addition to Ed : In this case, surface shear tests must be also determined to obtain the surface shear modulus. A simple model, such as the linear Maxwell model can be used to represent the viscoelastic response of the interface (Barnes, 1994). This model uses a combination of one elastic element and one viscous element, representing the elastic modulus (E’s ) and viscous (E”s ) modulus, respectively. Es λ2d ω2 1 þ λ2d ω2

n X Esk λdk ω 2 2 k¼1 1 þ λdk ω

(20)

In summary, we can identify the dominant contribution by per­ forming droplet size variations, strain sweeps, and frequency sweeps. The problem arises when there is no single dominant mechanism. Generally, the separation of these contributions cannot be carried out with dilatational experiments alone. A combination with surface shear, structural analysis methods, and mesoscopic simulations may then be needed to unravel the dynamics of the interface. As stated by Sagis (L M C Sagis, 2013) this is an unsolved problem that requires significant progress, particularly for the latter two types of techniques. These models involving the frequency dependence can also be used for small amplitude oscillatory interfacial shear measurements in terms of the surface shear elastic and viscous moduli (G’s and G}s ). The case study 2 compares results from dilatational and interfacial shear rheology to put forward the importance of both techniques for a proper interfacial characterisation. In this case, the multimode Maxwell model has been used for modelling the linear viscoelastic interfacial shear behaviour. This strategy has been extrapolated from the Generalized Maxwell Model used to reproduce the LVE behaviour of bulk emulsions, as described in the case study 1.

(16)

E’s ¼

n X Esk λ2dk ω2 1 þ λ2dk ω2 k¼1

At frequencies (ωÞ, much lower than the reciprocal of the relaxation time (λd Þ, the surface viscous modulus is dominant, and the model represents a fluid-like behaviour. At high frequencies, the response is dominated by E’s and is predominantly elastic. Unfortunately, the above models are very limited and other alter­ natives are required in order to provide more realistic responses. Among these alternatives, a surface multimode Maxwell model, which combines different Maxwell elements in parallel, has been proposed. The scaling for both surface elastic and viscous moduli is typically given by expo­ nents ranging between 0.05 and 0.2.

- The development of specific geometries such as the DWR fitted to a high sensitive rheometer benefiting for the great advance in sensi­ tivity undergone in recent years. In this case, a sinusoidal shear stress 4

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

wave is applied at the interface and the sinusoidal shear strain response is recorded. The interfacial viscoelastic functions (G’s and G}s ) are obtained from the stress and strain amplitudes and the phase angle. - The use of specialized measurement devices, such as the Interfacial Stress Rheometer (ISR) with a magnetic rod freely suspended at the interface and subjected to a magnetic field gradient. The viscoelastic properties of the interface (G’s and G}s ) are measured from the amplitude and phase shift of the needle displacement driven by the application of a periodic magnetic field gradient. This is the system that provides the highest sensitivity for the measurement of the interfacial viscoelastic properties. Its main drawbacks are that ex­ periments are difficult and time consuming, and that it is limited to the air/water interface. The importance of interfacial shear measurements in protein and protein-polysaccharide emulsions are evidenced in the case studies 2 and 3, respectively. The former is based on the use of the DWR geometry, whereas the later compares the results obtained using both the DWR and the ISR measuring systems.

Fig. 1. Sauter diameter and plateau modulus (d32 and G0N, respectively) ob­ tained from droplet size distribution (DSD) and small amplitude oscillatory shear (SAOS) profiles for emulsions stabilized by wheat gluten (WG) or soya protein (SPI).

2.2.3. Nonlinear viscoelasticity of complex fluid-fluid interfaces In general, most studies on the interfacial rheology of complex in­ terfaces focus on the linear response regime. However, complex in­ terfaces tend to have a nonlinear response, even at relatively small deformations, as a consequence of changes in the interfacial micro­ structure. This is a quite important issue that has been recently reviewed by Sagis and Fischer (2014). There are different ways to study nonlinear viscoelasticity for complex interfaces, including:

deviations from elliptical shape are smaller. Quantification of the nonlinear behaviour may be carried out by using a Nonlinearity parameter as a function of two elastic moduli: one at minimum deformation (G’M), obtained from the tangent at zero strain, and one at large deformation (G’L), from the secant at maximum strain. SðγÞ ¼

- Large amplitude oscillatory shear or dilatation (LAOS/LAOD) - Measurements of transient viscoelastic functions at large de­ formations, such as the relaxation modulus. - Parallel superposition by combining SAOS and steady shear.

G’L

G’M G’L

(23)

For the linear region, either the slopes or the moduli are equal and S is zero. S is positive for strain hardening interfaces and negative for strain softening layers. A similar treatment has been carried out for dilatational measure­ ments, which require two parameters, one for extension and one for compression. To our knowledge, no examples of parallel superposition using a combination of SAOS and steady flow measurements have been used to describe the non-linear rheology of complex fluid-fluid interfaces. Similarly, the characterisation of nonlinear viscoelasticity through transient viscoelastic functions at large deformations has been limited to the use of 2D relaxation tests reported in the case study 2. In this way, it is possible to extrapolate the use of nonlinear constitutive equations used in bulk rheology, such as the Wagner model (Wagner, 1976) to model the nonlinear rheological behaviour at the complex fluid-fluid interface.

However, most of the studies found in the literature on the charac­ terization of the nonlinear viscoelastic behaviour of the interface have been carried out using LAOS/LAOD measurements. Surface stress or strain sweep tests have been generally used to qualitatively analyse the effect of applying large deformations and to delimit the linear visco­ elastic regions. In the linear viscoelastic (LVE) region, the response is a perfect sinusoidal wave with the contribution of only the first harmonic. Outside of the LVE region, additional higher harmonics will appear, for instance, in surface shear, only odd harmonics will contribute, whereas in surface dilatational both even and odd may be observed. Lissajous curves have been used to represent the nonlinearities in oscillatory surface shear and dilatational experiments (Sagis & Fischer, 2014). In both experiments we can create such curves by plotting the time-dependent output signal versus the input sinusoidal wave.

3. Case studies At this point, some examples involving the rheological study of O/W emulsions and O/W interfaces stabilized by proteins will be discussed. In the first two cases, we will include the characterization of the linear viscoelasticity and nonlinear measurements at the bulk or the interface, whereas the third case illustrates the links between interfacial and bulk rheology of proteins/polysaccharide mixtures.

- In surface shear experiments we can create curves by plotting the time-dependent surface stress signal versus strain (or alternatively, versus the strain rate). - In dilatational rheological experiments, we typically plot the timedependent surface tension or surface pressure versus deformation (or rate of deformation). For purely viscous interfaces, the response is a circle, whereas for purely elastic interfaces, the response is a straight line. Viscoelastic in­ terfaces will generate an elliptical profile in the linear range. In surface shear, the response may be strain softening or strain hardening, but Lissajous curves are always symmetrical with respect to the origin. However, the behaviour of the interface in extension may be different from the behaviour in compression and then dilatational Lis­ sajous curves are always asymmetrical. In any case, the nonlinearities in dilatational tests tend to be much smaller than in surface shear and the

3.1. Case study 1: rheology of (wheat gluten and soya) protein-stabilized O/W emulsions In this first case study, the linear viscoelastic properties of concen­ trated O/W emulsions stabilized by wheat gluten (WG) or soya protein (SPI) as the only emulsifier are examined (Bengoechea et al., 2006). The mechanical spectra of both emulsions show a gel-like behaviour corre­ sponding to the plateau region of the relaxation spectrum, characterized by a predominant elastic response where G0 shows a weak frequency 5

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

Fig. 2. Experimental mechanical spectra and generalized Maxwell model (GM) fitting (A) and continuous relaxation spectrum (B) of emulsions stabilized by wheat gluten (WG) or soya protein (SPI).

dependence and a minimum value in G’’ (data not shown). This fact allows defining the plateau modulus (G0N) as the value of G’ corre­ sponding to this minimum. Fig. 1 shows two parameters (Sauter diam­ eter, d32 and plateau modulus, G0N) obtained from droplet size distribution (DSD) and small amplitude oscillatory shear (SAOS) profiles as a function of protein content. However, the interesting issue in this case is the possibility of using this parameter together with the average droplet size (d32) to model the behaviour of the emulsion, taking into account the volume fraction of the dispersed phase (φ) as well as φm , which corresponds to the closepacking volume fraction that has a value of 0.64 for randomly packed monodisperse spheres. In this figure (Fig. 1), the plateau modulus is plotted using a universal master relationship proposed by Mason et al. (1997) for highly concentrated emulsions. This approach is based on a functional dependence between rheological parameters subjected to small deformations (e.g. the static modulus) and the interfacial tension (σ ), d32 and φ, similar to an equation first reported by Princen & Kiss (Princen & Kiss, 1986). Therefore, the elastic shear modulus obtained from small deformations can be reproduced by Eq. (24) for polydisperse emulsions G’∝

2σ φðφ d32

φm Þ

different energy inputs (N), oil and protein concentrations and tem­ peratures (Tp). As may be seen, there is an enhancement of the plateau value with increasing protein content. Moreover, the fitting is fairly good except at the highest concentration of gluten. That difference can be explained by observing the confocal laser scanning microscopy (CLSM) images for both protein-stabilized emulsions (Fig. 1). With SPI, the microstructure can be enhanced but always reflect the behaviour of a highly flocculated network. The same behaviour may be observed for gluten-stabilized emulsions up to 1% protein. However, for 2% WG (or higher) there is a change in the microstructure. The elasticity of the emulsion seems, in this case, to be dominated by the gel network formed by the excess protein located at the aqueous phase, being the oily phase embedded into the gel matrix. The rheological behaviour of those emulsions including linear and nonlinear viscoelasticity was modelled by means of a constitutive equation (C. Bengoechea, Puppo, Romero, Cordob�es, & Guerrero, 2008). For the linear viscoelasticity behaviour, a generalized Maxwell model, similar to previously shown for interfacial models (Eqs. (20) and (21)), was used that consider a superposition of n relaxation processes, each one having a relaxation time and strength as can be observed in Fig. 2A.

(24)

G’ðωÞ ¼ Ge þ

n X

Gk k¼1

In this way, Fig. 1 includes results from emulsions processed at

ω2 λ2k 1 þ ω2 λ2k

(25)

Fig. 3. Experimental values and generalized Maxwell (GM) values of the relaxation moduli, G(γ,t) for an emulsion stabilized by wheat gluten (WG) (A) and experimental and predicted damping function (h(γ)) for emulsions stabilized by wheat gluten (WG) or soya protein (SPI). 6

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

Fig. 4. Stress-growth experiments at constant shear rate performed to emulsions stabilized by wheat gluten (WG) (A) or soya protein (B).

G”ðωÞ ¼

n X

Gk k¼1

ωλk 1 þ ω2 λ2k

Relaxation tests were carried out at different strains to represent the nonlinear viscoelastic response of these emulsions and plotted in Fig. 3A. The linear response calculated from oscillatory measurement by the GM model is rather coincident with the relaxation modulus at low strain (Fig. 3A). After some time, the relaxation modulus becomes par­ allel such that the modulus (ðGðγ; tÞÞ can be separated by shifting the linear function with a proper value that depends on the strain (γ). The experimental values obtained for the shift factor (i.e. the dumping function, h(γ)) are shown in Fig. 3B and reveal a remarkable strainsoftening behaviour for both emulsions studied. The non-linear damp­ ing function (h(γ)) can be fitted to the Soskey-Winter equation (Soskey & Winter 1984):

(26)

The linear discrete relaxation spectrum can be obtained by plotting each relaxation strength value (Gk ) vs. its corresponding relaxation time (λk ), as may be observed in Fig. 2B. These results may be fitted by means of a continuous relaxation spectrum model such as the BSW model (Baumgaertel, Schausberger, & Winter 1990) (Fig. 2B), which delimits the onset and the end of the plateau region. The Wagner constitutive equation can be applied to describe the nonlinear viscoelastic behaviour of the O/W emulsions (C. Bengoechea et al., 2008). Z t τðtÞ ¼ mðt t’Þ⋅hðγÞ⋅γðt t’Þdt’ (27)

hðγÞ ¼

∞

This equation assumes time-strain separability for the relaxation modulus ðGðγ; tÞ, such that it can be separated into two functions: the linear relaxation modulus (GðtÞÞ and the damping function (hðγÞÞ, which represents the nonlinear part of the relaxation modulus. The linear memory function (mðt t’Þ) can be obtained from the time derivative of the linear relaxation modulus, which, in turn, may be calculated from the GM model as follows: � � n X t t’ GðtÞ ¼ Ge þ Gk exp (29) λk k¼1 mðt

t’Þ ¼

dGðt t’Þ ​ ¼ dt’

n X k¼1

Gk exp λk

�

t

t λk

� ’

(31)

where a and b are dimensionless parameters, related to the nonlinear viscoelastic properties of the materials. Stress-growth experiments at a constant shear rate can be used to validate the Wagner model that in principle can be used to reproduce any nonlinear rheological property for the O/W interface. It is inter­ esting to highlight that the model can reproduce the enveloped curve for the LVE behaviour of both emulsions, as well as any of their transient responses, even those showing a stress overshoot typically obtained at high shear rate (Fig. 4).

(28)

Gðγ; tÞ ¼ GðtÞ⋅hðγÞ

1 1 þ a⋅γb

3.2. Case study 2: rheology of (chickpea and fava bean) protein-adsorbed O/W interfaces

(30)

Dilatational measurements can be used to analyse protein adsorption kinetics, recording the evolution of dilatational or shear moduli (Felix,

Fig. 5. Evolution of both the interfacial shear elastic and viscous moduli (G’s and G’’s) after chickpea (A) and fava bean (B) protein adsorption at the O/W interface and generalized Maxwell (GM) values obtained for the interfacial layer. 7

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

Fig. 6. Experimental values and generalized Maxwell (GM) values of the relaxation moduli, G(γ,t) for chickpea interfacial film at pH 2.5 (A) and 7.5 (B), and experimental and predicted damping function (h(γ)) for chickpea interfacial film at pH 2.5, 5.0 and 7.5 (B).

Romero, Carrera-Sanchez, & Guerrero, 2019a; Felix, Romero, Sanchez, & Guerrero, 2019b). However, i-SAOS, as compared to dilatational rheometry, shows the advantage of directly reflecting the true visco­ elastic response (G’s and G}s ) of the interface. Fig. 5 shows the final mechanical spectra for chickpea and fava bean as a function of pH values (2.5, 5.0 and 7.5). The mechanical spectra exhibit similar shape, yielding higher values at pH 2.5, which again puts forward the relevance of electrostatic repulsions between positively charged protein segments. It may be noted that fava bean protein concentrate at pH 7.5 also leads to high values of the viscoelastic moduli. Once again, a generalized Maxwell model can be used to reproduce linear viscoelastic functions of each complex O/W interface (Fig. 5). Note that in this case (interface) the elastic and viscous moduli correspond to G’ s and G}s , respectively. G’s ð

ωÞ ¼ Gs;e þ

n X k¼1

ω2 λ2k Gs;k 1 þ ω2 λ2k

G}s ðωÞ ¼

n X

Gs; ​ k k¼1

ωλk 1 þ ω2 λ2k

(33)

On the other hand, interfacial shear rheology can also be used to obtain information about the non-linear VLE behaviour of the interface by relaxation tests (Fig. 6A). As may be observed, the linear relaxation modulus obtained from oscillatory tests by means of the GM model (Eq. (35)) agrees well with the experimental relaxation modulus at low strain. In addition, regardless of the strain applied to the interface, the slope of the relaxation modulus is rather constant. As a result, the sur­ face model can be separated into linear modulus and the damping function which accounts for the nonlinear response of the interface (Eq. (34)). (34)

Gs ðγ; tÞ ¼ Gs ðtÞ⋅hs ðγÞ

(32)

n X

Gs ðtÞ ¼ Gs;e þ k¼1

� Gs;k exp

t’

t

�

λk

Fig. 7. Experimental and predicted interfacial steady state viscosity of chickpea interfacial film at pH 2.5 (A), 5.0 (B) and 7.5 (C). 8

(35)

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719

Fig. 8. Evolution of interfacial elastic modulus of crayfish (CFPI)/chitosan (CH) interfacial film obtained by means double-wall-ring geometry (DWR) and magnetic rod interfacial stress (ISR) rheometers at 1 rad/s (G0 s,1) as a function of surface pressure (A) and chitosan molecular weight.

hs ðγÞ ¼

1 1 þ a⋅γb

(36)

As may be seen in Fig. 6B, the damping function fits the SoskeyWinter model (eq. (36)) fairly well. The Wagner constitutive equation (Eq. (22)), which also involves time-strain separability, can be applied to describe the nonlinear viscoelastic behaviour of the O/W interface. Z t τs ðtÞ ¼ ms ðt t’Þ⋅hs ðγs Þ⋅γs ðt t’Þdt’ (37) ∞

The memory function can be obtained from the GM model (Eq. (38)): � � n X dGs ðt t’Þ Gs;k t t’ ms ðt t’Þ ¼ ¼ exp (38) dt’ λk λk k¼1 The damping function can be represented either by a single (Eq. (39)) or double (Eq. (40)) exponential functions, by means of the Wagner and Laun models, respectively, that provide an exact solution for the Wagner equation. The Soskey-Winter model can also be used (Eq. (41)), but the integral has to be solved numerically for each case. hs ðγ s Þ ¼ f ⋅expð

n1 γs Þ

hs ðγ s Þ ¼ f ⋅expð

n1 γs Þ þ ð1

� � hs ðγ s Þ ¼ 1 1 þ aγbs

Fig. 9. Cryo-scanning electron microscopy (cryo-SEM) image of an emulsion stabilized by chitosan (CH) and potato protein.

(39) f Þ⋅expð

n2 γs Þ

3.3. Case study 3: rheology of crayfish protein/chitosan mixed films

(40)

Finally, some results obtained for the rheology of crayfish protein (CFPI)/chitosan (CH) mixed films are discussed both DWR geometry fitted to a rheometer and using a magnetic rod interfacial stress rheometer (Romero, Verwijlen, Guerrero, & Vermant, 2013b; 2013a). Fig. 8 shows a good agreement between the results obtained by the two shear techniques (double wall ring and interfacial stress rheometer), provided that the surface pressure values are similar. It can be noticed that addition of CH may duplicate the viscoelastic response of the protein-adsorbed layer. In addition, it is worth pointing out that there is a critical chitosan/surface ratio above which the elastic properties cannot be further improved. This may be related to some migration to the subphase. Particular attention has to be paid to control the conditions at the interface. At this point, it is interesting to remark the role of chitosan in mixed systems. On one hand, CFPI shows lower interfacial tension values than CH. However, on the other hand, CH gives rise to higher elastic interfaces. This behaviour is illustrated by a cryo-SEM image of an emulsion containing CH and protein (Fig. 9). As may be inferred from this image, protein is preferentially adsorbed on the oil droplet surface, whereas CH form a fine strands-like 3D network at the bulk. These strands can even extend to the interface reinforcing the elastic properties of mixed interfacial layers. This can be modulated by the presence of protein-chitosan interactions.

(41)

This equation (Eq. (38)) can be applied to reproduce any nonlinear rheological property for the O/W interface, such as the state flow properties. Fig. 7 shows the flow curves obtained for O/W interfaces stabilized by chickpea protein at different pH values. These experi­ mental values are compared to predictions from the Wagner equation using the Laun model for the damping function. As may be observed, this constitutive equation agrees well with the experimental results. The agreement is less accurate at pH 5.0, but this may be related to some inconsistency between the experimental and calculated values for the linear relaxation modulus. The evaluation fails at high shear rate, but in this case the response of the interface is affected by the adjoining phases as predicted by the low values of the Boussinesq number. Values of the interfacial complex viscosity (η*s ) obtained from iSAOS measurements are also included, in order to make a comparison with the interfacial apparent viscosity, revealing that the Cox-Merz rule cannot be applied, although the slope for both functions is quite similar. These results, together with the high values of the slopes for both curves, suggest that the O/W interface is very sensitive to shear forces under­ going a progressive disruption of physical interactions between protein segments.

9

Food Hydrocolloids 104 (2020) 105719

M. F�elix et al.

In spite of the promising results shown in these three case studies, further studies should be carried out in order to make progress in the interfacial rheological analysis of protein-adsorbed layers, alone or in combination with a polysaccharide.

Baumgaertel, M., Schausberger, A., & Winter, H. H. (1990). The relaxation of polymers with linear flexible chains of uniform length. Rheologica Acta, 29(5), 400–408. https://doi.org/10.1007/BF01376790. Bengoechea, C., Cordob� es, F., & Guerrero, A. (2006). Rheology and microstructure of gluten and soya-based o/w emulsions. Rheologica Acta, 46(1), 13–21. https://doi. org/10.1007/s00397-006-0102-6. Bengoechea, C., Puppo, M. C., Romero, A., Cordob�es, F., & Guerrero, A. (2008). Linear and non-linear viscoelasticity of emulsions containing carob protein as emulsifier. Journal of Food Engineering, 87(1). https://doi.org/10.1016/j.jfoodeng.2007.11.024. Benjamins, J., & Lucassen-Reynders, E. H. (1998). Surface dilational rheology of proteins adsorbed at air/water and oil/water interfaces. Proteins at Liquid Interfaces, 7, 341. Calero, N., Mu~ noz, J., Cox, P. W., Heuer, A., & Guerrero, A. (2013). Influence of chitosan concentration on the stability, microstructure and rheological properties of O/W emulsions formulated with high-oleic sunflower oil and potato protein. Food Hydrocolloids, 30(1), 152–162. https://doi.org/10.1016/j.foodhyd.2012.05.004. Danov, K. D., Kralchevsky, P. A., & Stoyanov, S. D. (2010). Elastic Langmuir layers and membranes subjected to unidirectional compression: Wrinkling and collapse. Langmuir, 26(1), 143–155. https://doi.org/10.1021/la904117e. Derkach, S. R. (2009). Rheology of emulsions. Advances in Colloid and Interface Science, 151(1–2), 1–23. Dickinson, E. (1998). Rheology of emulsions—the relationship to structure and stability. In Modern aspects of emulsion science (pp. 145–174). Dickinson, E. (2019). Strategies to control and inhibit the flocculation of proteinstabilized oil-in-water emulsions. Food Hydrocolloids. https://doi.org/10.1016/j. foodhyd.2019.05.021. Erni, P., Fischer, P., Windhab, E. J., Kusnezov, V., Stettin, H., & Lauger, J. (2003). Stressand strain-controlled measurements of interfacial shear viscosity and viscoelasticity at liquid/liquid and gas/liquid interfaces. Review of Scientific Instruments, 74(11), 4916–4924. https://doi.org/10.1063/1.1614433. Felix, M., Romero, A., Carrera-Sanchez, C., & Guerrero, A. (2019a). Assessment of interfacial viscoelastic properties of Faba bean (Vicia faba) protein-adsorbed O/W layers as a function of pH. Food Hydrocolloids, 90, 353–359. https://doi.org/ 10.1016/j.foodhyd.2018.12.036. Felix, M., Romero, A., Carrera-Sanchez, C., & Guerrero, A. (2019b). Modelling the nonlinear interfacial shear rheology behaviour of chickpea protein-adsorbed complex oil/water layers. Applied Surface Science, 469, 792–803. https://doi.org/10.1016/j. apsusc.2018.11.074. Gallegos, C., & Franco, J. M. (1999). Rheology of food, cosmetics and pharmaceuticals. Current Opinion in Colloid & Interface Science, 4(4), 288–293. Hermans, E., Saad Bhamla, M., Kao, P., Fuller, G. G., & Vermant, J. (2015). Lung surfactants and different contributions to thin film stability. Soft Matter, 11(41), 8048–8057. https://doi.org/10.1039/C5SM01603G. Huang, X., Kakuda, Y., & Cui, W. (2001). Hydrocolloids in emulsions: Particle size distribution and interfacial activity. Food Hydrocolloids, 15(4–6), 533–542. https:// doi.org/10.1016/s0268-005x(01)00091-1. Jaensson, N., & Vermant, J. (2018). Tensiometry and rheology of complex interfaces. Current Opinion in Colloid & Interface Science, 37, 136–150. https://doi.org/10.1016/ j.cocis.2018.09.005. Li, X., Murray, B. S., Yang, Y., & Sarkar, A. (2020). Egg white protein microgels as aqueous Pickering foam stabilizers: Bubble stability and interfacial properties. Food Hydrocolloids, 98, 105292. https://doi.org/10.1016/j.foodhyd.2019.105292. Lucassen, J., & Van Den Tempel, M. (1972). Dynamic measurements of dilational properties of a liquid interface. Chemical Engineering Science, 27(6), 1283–1291. https://doi.org/10.1016/0009-2509(72)80104-0. Mason, T. G., Lacasse, M. D., Grest, G. S., Levine, D., Bibette, J., & Weitz, D. A. (1997). Osmotic pressure and viscoelastic shear moduli of concentrated emulsions. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 56 (3), 3150–3166. https://doi.org/10.1103/PhysRevE.56.3150. McClements, D. J. (2015). Food emulsions: Principles, practices, and techniques. USA: CRC Press. Boca Raton. Pepicelli, M., Verwijlen, T., Tervoort, T. A., & Vermant, J. (2017). Characterization and modelling of Langmuir interfaces with finite elasticity. Soft Matter, 13(35), 5977–5990. https://doi.org/10.1039/C7SM01100H. Princen, H. M., & Kiss, A. D. (1986). Rheology of foams and highly concentrated emulsions: III. Static shear modulus. Journal of Colloid and Interface Science, 112(2), 427–437. https://doi.org/10.1016/0021-9797(86)90111-6. Raikos, V. (2010). Effect of heat treatment on milk protein functionality at emulsion interfaces. A review. Food Hydrocolloids, 24(4), 259–265. https://doi.org/10.1016/j. foodhyd.2009.10.014. Reynaert, S., Brooks, C. F., Moldenaers, P., Vermant, J., & Fuller, G. G. (2008). Analysis of the magnetic rod interfacial stress rheometer. Journal of Rheology, 52(1), 261–285. https://doi.org/10.1122/1.2798238. Romero, A., Verwijlen, T., Guerrero, A., & Vermant, J. (2013a). Interfacial behaviour of crayfish protein isolate. Food Hydrocolloids, 30(1), 470–476. https://doi.org/ 10.1016/j.foodhyd.2012.07.009. Romero, A., Verwijlen, T., Guerrero, A., & Vermant, J. (2013b). Interfacial properties of crayfish protein isolate/chitosan mixed films. Food Hydrocolloids, 32(2), 395–401. https://doi.org/10.1016/j.foodhyd.2013.02.002. Sagis, L. M. C. (2013). Dynamic surface tension of complex fluid-fluid interfaces: A useful concept, or not? The European Physical Journal - Special Topics, 222(1), 39–46. https://doi.org/10.1140/epjst/e2013-01824-1. Sagis, L., & Fischer, P. (2014). Nonlinear rheology of complex fluid–fluid interfaces. Current Opinion in Colloid & Interface Science, 19(6), 520–529. https://doi.org/ 10.1016/j.cocis.2014.09.003.

4. Conclusions This work evidences the importance of macroscopical rheological properties on the characterization of disperse systems, and how this technique can be used to predict the stabilization of protein-stabilized emulsions. Thus, the first case study shows how the Mason model can correlate viscoelastic properties (i.e. G’), microstructural parameters (i. e. d32), composition (i.e. φ) and interfacial tension, giving an adequate correlation. Furthermore, in a micro or nanoscale context, there has been recent substantial progress in the technology for the rheological characterisa­ tion of complex fluid-fluid interfaces. The case study 2 puts forward that this progress has led to improve the understanding of the different fac­ tors which contribute to the dynamics of rheologically complex fluidfluid interfaces, although careful separation and quantification of these factors are required in order to deliver the right material charac­ teristics. However, more efforts are still required in modelling the behaviour of complex interfaces, particularly the nonlinear interfacial behaviour which evidences a strong connection with interfacial micro­ structure. An extrapolation from the constitutive modelling at the bulk seems to be a good strategy, although taking into account the physi­ ochemical singularities of the interface and giving more attention to structural models. Moreover, the case study 3 indicates that poly­ saccharides (such as chitosan) can be used to the stabilization of disperse systems. In fact, chitosan contributes not only to develop a continuous network responsible for the stabilization of this type of disperse systems, but also to the properties of protein-adsorbed complex fluid-fluid interfaces. However, the challenges are still considerable, and there is a sub­ stantial need for further research and development, but the benefits are also relevant with a clear target for tailoring the interface for the development of optimal emulsion microstructure and stability. This could be helpful not only in food product development but also to tackle suitable strategies for encapsulation of bioactive compounds with adequate delivery along the gastrointestinal tract. CRediT authorship contribution statement �lix: Formal analysis, Investigation, Data curation, Visu­ Manuel Fe alization. Cecilio Carrera: Methodology, Formal analysis, Resources, Supervision. Alberto Romero: Conceptualization, Validation, Writing original draft, Project administration. Carlos Bengoechea: Software, Resources, Writing - original draft, Project administration. Antonio Guerrero: Conceptualization, Data curation, Writing - review & editing, Supervision, Funding acquisition. Acknowledgements The authors acknowledge the grant awarded to Manuel Felix by the "Universidad de Sevilla", Spain (VPPI-US, Ref.-II.5). References Araiza-Calahorra, A., Akhtar, M., & Sarkar, A. (2018). Recent advances in emulsionbased delivery approaches for curcumin: From encapsulation to bioaccessibility. Trends in Food Science & Technology, 71(September 2017), 155–169. https://doi.org/ 10.1016/j.tifs.2017.11.009. Araiza-Calahorra, A., & Sarkar, A. (2019). Designing biopolymer-coated pickering emulsions to modulate in vitro gastric digestion: A static model study. Food and Function, 10(9), 5498–5509. https://doi.org/10.1039/C9FO01080G. Barnes, H. A. (1994). Rheology of emulsions — a review. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 91, 89–95. https://doi.org/10.1016/09277757(93)02719-U.

10

M. F�elix et al.

Food Hydrocolloids 104 (2020) 105719 Tadros, T. (2013). Emulsion formation and stability. Wiley. Vandebril, S., Franck, A., Fuller, G. G., Moldenaers, P., & Vermant, J. (2010). A double wall-ring geometry for interfacial shear rheometry. Rheologica Acta, 49(2), 131–144. https://doi.org/10.1007/s00397-009-0407-3. Verwijlen, T., Imperiali, L., & Vermant, J. (2014). Separating viscoelastic and compressibility contributions in pressure-area isotherm measurements. Advances in Colloid and Interface Science, 206, 428–436. https://doi.org/10.1016/j. cis.2013.09.005. Wagner, M. H. (1976). Analysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-density branched polyethylene melt. Rheologica Acta, 15(2), 136–142. https://doi.org/10.1007/BF01517505. Yunker, P. J., Gratale, M., Lohr, M. A., Still, T., Lubensky, T. C., & Yodh, A. G. (2012). Influence of particle shape on bending rigidity of colloidal monolayer membranes and particle deposition during droplet evaporation in confined geometries. Physical Review Letters, 108(22), 228303. https://doi.org/10.1103/PhysRevLett.108.228303. Zembyla, M., Lazidis, A., Murray, B. S., & Sarkar, A. (2019). Water-in-Oil pickering emulsions stabilized by synergistic particle–particle interactions. Langmuir, 35(40), 13078–13089. https://doi.org/10.1021/acs.langmuir.9b02026.

Sagis, L. M. C., & Scholten, E. (2014). Complex interfaces in food: Structure and mechanical properties. Trends in Food Science & Technology, 37(1), 59–71. https:// doi.org/10.1016/j.tifs.2014.02.009. Sarkar, A., Zhang, S., Murray, B., Russell, J. A., & Boxal, S. (2017). Modulating in vitro gastric digestion of emulsions using composite whey protein-cellulose nanocrystal interfaces. Colloids and Surfaces B: Biointerfaces, 158, 137–146. https://doi.org/ 10.1016/j.colsurfb.2017.06.037. Scholten, E., Sagis, L. M. C., & van der Linden, E. (2004). Bending rigidity of interfaces in aqueous phase-separated biopolymer mixtures. The Journal of Physical Chemistry B, 108(32), 12164–12169. https://doi.org/10.1021/jp048439r. Smeulders, J. B. A. F., Mellema, J., & Blom, C. (1992). Changing mechanical properties of lipid vesicle bilayers investigated by linear viscoelastic measurements. Physical Review A, 46(12), 7708–7722. https://doi.org/10.1103/PhysRevA.46.7708. Soskey, P. R., & Winter, H. H. (1984). Large step shear strain experiments with paralleldisk rotational rheometers. Journal of Rheology, 28(5), 625–645. https://doi.org/ 10.1122/1.549770. Tadros, T. (2004). Application of rheology for assessment and prediction of the long-term physical stability of emulsions. Advances in Colloid and Interface Science, 108, 227–258. https://doi.org/10.1016/j.cis.2003.10.025.

11