Measurement Techniques for Interfacial Rheology of Surfactant, Asphaltene, and Protein-Stabilized Interfaces in Emulsions and Foams

Abstract

This work provides a comprehensive review of experimental methods used to measure rheological properties of interfacial layers stabilized by surfactants, asphaltenes, and proteins that are relevant to systems with large interfacial areas, such as emulsions and foams. Among the shear methods presented, the deep channel viscometer, bicone rheometer, and double-wall ring rheometers are the most utilized. On the other hand, the main dilational rheology techniques discussed are surface waves, capillary pressure, oscillating Langmuir trough, oscillating pendant drop, and oscillating spinning drop. Recent developments—including machine learning and artificial intelligence (AI) models, such as artificial neural networks (ANN) and convolutional neural networks (CNN)—to calculate interfacial tension from drop shape analysis in shorter times and with higher precision are critically analyzed. Additionally, configurations involving an Atomic Force Microscopy (AFM) cantilever contacting bubble, a microtensiometer platform, rectangular and radial Langmuir troughs, and high-frequency oscillation drop setups are presented. The significance of Gibbs–Marangoni effects and interfacial rheological parameters on the (de)stabilization of emulsions is also discussed. Finally, a critical review of the recent literature on the measurement of interfacial rheology is presented.

1. Introduction

Interfacial rheology studies the deformation and flow behavior of the zone between two immiscible substances—typically two phases such as two liquid fluids [1,2]. The zone, which can be called interphase—or more usually interface—may be just a bidimensional frontier or a thin film of one, two, or more layers. This is fundamental to understanding the properties, particularly the stability, of complex systems presenting an interface limit as in liquid/liquid emulsions, or a surface boundary as in gas/liquid foams. In real cases, including at least a third substance with amphiphilic tendencies, it may also include more complex structures occurring in the suspension of colloidal particles with bi- or three-dimensional aggregates, liquid crystals and bilayer or multilayer membranes often produced by microorganisms in biological systems [3].

The mechanical properties of fluid interfaces profoundly influence the dynamics and functionality of systems with large interfacial area, such as emulsions and foams stabilized by surfactants and/or polymers [4,5,6,7], in fields such as food [8], energy [9], biointerfaces [10,11] and biofuel industries [12]. Applications include dispersions and particle-stabilized emulsions, electrospinning [13], biofilms [3], hydrate formation [14], enhanced oil recovery (EOR) [15], and crude oil dewatering and processing, where the stability and dynamics of emulsions [16,17] and foams are critical [12,18,19,20]. In dispersed systems these properties not only govern interfacial behavior but also influence the hydrodynamic phenomenology within the dispersed phases [7,21,22,23,24]. When interfaces exhibit complex structures, they may significantly affect also the overall rheology of the bulk phases [9,25,26,27].

Accurately characterizing the rheology of interfacial layers is challenging due to the complex interplay of two deformation modes, i.e., interface shear and its compression/dilatation. Traditional models often consider these deformation modes independently, which may not accurately represent systems where both modes are often intrinsically coupled [28]. Shear rheology involves tangential deformation without changes in interfacial area. Shear modulus (G in the following) can reach values of several mN/m for particle or microgel-laden interfaces [29,30,31,32]. On the other hand, compression/dilatation interfacial rheology (also called dilational rheology) refers to changes in the interfacial area without tangential flow. It is characterized by the dilational modulus (E in the following), which quantifies the interface resistance to area changes. Typical values for E can range from 10 to 100 mN/m for protein or polymer-laden interfaces [9,33,34,35,36].

1.1. Historical Account of Interfacial Rheology Measurements

The study of interfacial rheology can be traced back to the early 20th century, beginning with the work of Hadamard and Rybczynski in 1911. They applied Stokes’ law to predict that fluid droplets, owing to slip and friction at the interface, experience less drag and therefore sediment faster than solid spheres of the same size and density difference. However, later experimental work by Silvey and Levich in 1916 demonstrated that very small droplets sediment in a manner similar to solid spheres, in accordance with Stokes’ law, thereby challenging Hadamard and Rybczynski’s theoretical predictions [25].

In 1913, Boussinesq, in an attempt to resolve the discrepancy between Hadamard and Rybczynski theoretical reasoning, with Silvey and Levich’s experimental data, postulated the existence of a “surface/interface viscosity”, conceived as a two-dimensional equivalent to the three-dimensional viscosity present within fluid phases. Due to the resistance to deformation caused by surface viscosity-induced friction, a more deformation-resistant interface is formed, reducing its mobility, which was observed in systems with very small droplets. Boussinesq derived an analytical expression for the sedimentation velocity of a deformable spherical droplet, showing in agreement with some experiments, that the interface becomes “hardened” as the radius decreases, such that they behave like solid spheres. For many years, Boussinesq’s solution, based on his postulate of surface viscosity, was accepted as an explanation for the variation in droplet sedimentation velocity relative to its size, driving the development of various instruments to measure surface/interface viscosity [25,37].

However, it should be remembered that the original Boussinesq’s theory is assuming that the densities of the two fluids on both sides of the interface are very close, e.g., with less than a 5–10% difference, which is not the case between a gas and a liquid, as well as often in an oil/water system. Boussinesq’s theory actually assumes a single phase model with a variation of the density in the direction perpendicular to the boundary which is not necessarily flat. This is probably why there are some experimental discrepancies in some cases, and why an extended theory is required to explain instabilities close to the interface [38].

In 1947, Frumkin and Levich [39] postulated that the experimental results showing that small droplets sedimenting like solid spheres was due to the presence of surfactants, which were displaced to the rear of the drop as it settled. These concentration gradients at the interface were then assumed to be responsible for the variation in sedimentation velocity and the delay when the droplet size increased. The process by which a tension gradient is generated at the interface was linked to the Gibbs–Marangoni effect, which refers to variations in interfacial tension caused by surfactant concentration gradients along an interface or surface. For example, in emulsions, both the interfacial viscosity and the Gibbs–Marangoni effects result in a synergy that slows down the drainage of the liquid film between two approaching interfaces. This film is produced by a droplet getting close to another droplet, or to another shaped interface such as a flat boundary. Interfacial viscosity specifically describes how this tension gradient relaxation occurs [40].

Levich’s theory, a generalization of Boussinesq’s theory to interfaces of different curvatures, along with Scriven’s improvements on the interfacial turbulence [41,42] as well of his later introduction of the bicontinuity concept, are of great importance for the understanding of “modern” interfacial rheology issues [43,44].

It is remarkable to note that Scriven eliminated in the title of these outstanding publications the confusing term “microemulsion”, which is actually not an emulsion nor of micrometer drop size dispersion. This is why we present the following paragraph dedicated to improving the understanding of the interfacial zone occurrence, not always as a monolayer film but sometimes as a middle phase between oil and water in the three phase separation case, well described by Winsor in his historical work.

Such a middle phase—occurring at a specific formulation defined by Winsor as having a unit affinity ratio between the surfactant and both oil and water—is different from the single-phase colloidal dispersion of common swollen micelles or even inverse micelles, called “oleophatic hydro-micelle” by Hoar & Schulman in 1943 [45].

Actually, it seems that the term “microemulsion” was partially used in the late 1940s, but that it was finally proposed by Schulman only in 1959 [46].

It was certainly an attractive word because a swollen micelle dispersion picture looked like an emulsion with extremely small droplets. It was also a novel terminology, often suggested to be in article or book titles by the referees or publishers. In fact, this dual naming was misused by hundreds of authors, causing confusion by wrong equivalences, in particular because a micellar solution is a colloidal single phase, while an emulsion has two separated phases and an interface in between. Researchers such as Winsor stayed intransigent and never used this term in their publications, while others used it as fashionable, sometimes mentioning the possibility of misunderstanding, even from L. M. Prince, co-author of Schulman in the original paper definition [47,48,49].

The microemulsion concept was curiously called “crazy mixed-up stuff” by Scriven in his outstanding tutorial chapter [44]. This humorous terminology is noted here because it clearly indicates the misinterpretation of the microemulsion uniform meaning, in particular in the so-called Winsor’s three-phase system.

1.2. The Modern Age of Interfacial Rheology

Interfacial rheology fundamentals were significantly advanced by Scriven over the course of two decades [41,42,50]. His work provided a mathematical framework for analyzing how fluid interfaces respond to mechanical stresses. Building on Scriven’s foundation, researchers recognized the significant role of Marangoni stresses arising from surface tension gradients due to variations in adsorbed amphiphile concentration at the interface [51]. These gradients induce tangential flows, known as Marangoni flows, which can stabilize or destabilize interfaces [52]. Levich [53] as well as Sterling & Scriven [41] later incorporated what are now called Marangoni effects into the analysis of interfacial phenomena. Further research has investigated the interfacial rheology of interfaces, such as those stabilized by nanoparticles or anisotropic particles, although incorporating Marangoni effects within the moduli has been problematic. In studies involving particle-laden interfaces, the assumption that Marangoni effects are negligible may not hold true, especially when surfactant impurities are present [30]. Even trace amounts of surfactants can create significant surface tension gradients, influencing the measured interfacial rheological properties [20,54].

In the case of soluble surfactants, surface motion involves mainly Marangoni effects because the response to shear is usually negligible. Upon compression, surfaces frequently behave like more rigid surfaces even without added surfactants due to the presence of residual impurities. On top of this, Levich [53] further developed a new theoretical framework by introducing the concept of surface dilational elasticity (E) accounting for the adsorption and desorption kinetics of surfactants at the interface, which is crucial to understanding emulsion and foam interface behavior. It was shown that damping of surface waves is significantly affected by the elastic compression modulus. The required surface tension gradients to immobilize the surface of bubbles are also small [55]. When surfactant concentration in the bulk is low, the surfaces could behave as if the surfactant molecules were insoluble. It is only when the surfactant concentration is large enough, and when exchanges between the surface and bulk phases become much faster, that the compression viscoelastic coefficients vanish and the response to shear is important [55]. For insoluble surface layers in an oil or in a gas phase, or for layers that adsorb irreversibly, the surface response is generally a combination of Marangoni and shear effects, thus making the interpretation difficult.

1.3. The Gibbs–Marangoni Effect

Marangoni stresses arise from gradients in surface tension along an interface, leading to tangential forces that drive fluid motion. These gradients result from variations in concentration of surface-active species [56,57]. The Marangoni effect plays a crucial role in various interfacial phenomena, such as the “tears of wine”, thermocapillary flows, and the stabilization or destabilization of liquid films in high internal phase ratio emulsions and foams [42]. Marangoni stresses induce interfacial flows from regions of low surface tension to high surface tension, affecting the distribution of surfactants and the dynamics of the interface [20,58]. This flow opposes the deformation generating the surface tension gradient, acting as a restoring force that influences the interfacial rheological response [20,59].

Another explanation is that liquid flow within the thin film between two approaching drops—caused by drainage—creates surfactant concentration gradients at the interface, thereby producing the Gibbs–Marangoni effect [59]. This flow removes a part of the surfactant from the interface, creating a non-uniform concentration across it, resulting in a non-uniform interfacial film thickness—creating thinner local regions and others of greater thickness. This implies an increase in the interfacial area in the thinner zones and hence a decrease in surfactant concentration. The formation of interfacial tension gradients causes a net force to restore the interface area, which slows down the drainage of the interfacial liquid film [25].

In terms of interfacial rheology, the Gibbs–Marangoni effect can also occur if the interface expands or contracts. In such a case, the interfacial tension in this zone will change with respect to its equilibrium value, thus generating interfacial tension gradients [60]. This will cause the interface to behave elastically. These interfacial tension gradients are quantified with a dimensionless number, the Marangoni number, M = E/γ, where E is the dilational modulus and γ is the interfacial tension [59,61]. Accurate modeling requires coupling the interfacial rheology with surfactant transport equations, such as the convection–diffusion equation for surface concentration (Γ) [62]. Neglecting the coupling between Marangoni stresses and surfactant dynamics can result in models that fail to predict experimental observations accurately, particularly under dynamic conditions where surfactant redistribution is significant. To address these challenges, Levich (1962) provided expressions for the complex dilational modulus (E* = E’ + i E″) as a function of cyclic frequency (ω) [20]. Recognizing the contributions of Marangoni stresses helps in distinguishing between elastic and viscous responses, particularly in complex systems such as with protein or polymer-covered interfacial structures [34,63,64,65,66]. In surfactant solutions such as sodium dodecyl sulfate (SDS) near the critical micelle concentration (CMC), Marangoni stresses can be measured with interfacial rheology [67]. Experimental studies below the CMC have shown that at low frequencies (<0.01 Hz), the dilational modulus real part (E′) can be as low as 5 mN/m due to surfactant redistribution facilitating surface tension equilibration. At higher frequencies (>1 Hz), E′ increases to approximately 20 mN/m as the interface behaves more elastically, and surfactant molecules cannot redistribute quickly enough to relieve surface tension gradients. In the case of protein loaded surfaces with β-casein at the air–water interface, the dilational modulus exhibits significant frequency dependence due to exchanges with the bulk [35]. At low frequencies (<0.01 Hz), E′ is around 20–30 mN/m, indicating a predominantly viscous behavior as proteins have time to adsorb/desorb and equilibrate surface tension gradients. At higher frequencies (>0.1 Hz), E′ increases to over 100 mN/m, indicating an elastic response where protein molecules cannot be redistributed rapidly.

A recurring source of confusion in interfacial rheology stems from mixing purely rheological, stress–strain-based concepts (e.g., shear and dilational moduli) with other parameters (e.g., Gibbs or “surface elasticity”, which depends on equilibrium interfacial tension variations). Gibbs elasticity arises from changes in surface tension due to variations in surface concentration of amphiphiles at or near equilibrium. Essentially, Gibbs elasticity reflects how the interfacial tension responds to alterations in the chemical potential of surfactants or other surface-active agents at the interface. Conversely, elasticity modulus captures the dynamic response of an interface to deformation. The shear modulus G and dilational modulus E measure resistance to deformation under imposed strain. These properties can be strongly frequency-dependent and are related to surface “viscosities” that dissipate energy. Further, the stress tensor at an interface includes both hydrostatic components (surface pressure) and dynamic components (Marangoni stresses, viscous stresses). In many methods, Marangoni contributions can amplify or mask purely viscous responses, especially under high-frequency oscillations [20].

1.4. Frequency and Concentration Dependence of Rheology of Interfacial Layers

In classical bulk fluids, the relaxation frequencies are much higher, but monolayers are locally very viscous; therefore, the relaxation frequencies in monolayers are quite low. Furthermore, nonlinear responses are frequent [20,59]. In many practical systems, compression and shear deformations are coupled, and their interplay significantly affects interfacial rheology measurements [68]. Moreover, Marangoni stresses introduce additional complexity [52]. For instance, in surfactant-laden interfaces, concentration gradients caused by deformation can lead to Marangoni flows that counteract the applied deformation, thus affecting the measured properties [69].

The total interfacial dilational modulus (E) equals the intrinsic modulus multiplied by a factor that account for exchanges with the bulk—that vanishes at low frequency. It is only at very small surfactant concentrations, when diffusion is slow enough that the surface compression elasticity and viscosity are equal to their intrinsic values [59]. When a pure shear stress is generated, there is no compression (i.e., change in surface concentration) and Marangoni forces are not present. These variations make it complex to compare data across different experimental techniques to measure interfacial rheology for specific deformation modes and stresses involved. Given the complexities, there is a gap in the literature in describing the coupling between compression/dilation and shear deformations and properly incorporating Marangoni effects and surfactant dynamics.

The present work reviews advanced methodologies for measuring interfacial rheology in interfacial layers happening in dispersed biphasic systems—such as emulsions and foams. It aims to evaluate existing methods to measure shear and dilational interfacial rheology, identifying advantages and limitations. Measurement techniques are compared, with a discussion on how deformation modes inherent to each method affect the results and their interpretation. Section 2 examines interfacial rheology measurement methods, contrasting shear and dilational modes, with an emphasis on their roles in affecting interfacial stability. Section 3 provides a detailed exploration of the specific methods used to measure interfacial rheology, including shear and dilational techniques, with particular attention to dilational methods such as oscillating pendant drop, oscillating spinning drop and their practical applications. Section 4 presents recent advances in interfacial rheology measuring techniques. Finally, Section 5 shows applications of interfacial rheology measurements for processes involving emulsions, in particular, cases such as crude oil emulsion breaking, where the interfacial behavior of asphaltenes becomes critical.

2. Measurement Techniques for Interfacial Rheology

The equipment used for interfacial rheology measurement is classified into shear and dilational methods. The most frequently used shear methods include the disk and ring rheometers; among these, the bicone rheometer and the double-wall ring are the most used. Within dilational methods, surface waves and capillary pressure techniques are mainly used to assess the surface rheology of air/water and oil/water systems. Cyclic deformation events of bubbles or droplets are measured using oscillating pendant drop or oscillatory spinning drop or bubble techniques [16,17].

2.1. The Two Deformation Cases: Interfacial Shear and Dilational Rheology

As mentioned above, interfacial rheology measurements are divided into shear and dilatation deformations (Figure 1). In shear interfacial rheology the perturbation is created either by stationary rotation of a solid in contact with the surface or by its periodic oscillations. The processing of measured torque dependence on the interfacial deformation is based on the analysis of dynamic equations that result in the values of shear parameters, such as shear viscosity and elastic shear modulus [20]. The interfacial shear viscosity may further depend on the deformation rate and fluid bulk and may exhibit a non-Newtonian behavior. In dilational rheology, the perturbation is created through the oscillatory expansion or compression of the drop interface where the interfacial area is subject to changes that generate gradients in the interfacial tension. The relationship between stress and interfacial area changes makes possible the calculation of interfacial rheological parameters [20].

As previously introduced, the existence of interfacial tension gradients that generate dilational elasticity at interfaces with adsorbed surfactants is a phenomenon related to the Gibbs–Marangoni effect. In addition, interfacial rheological stresses of a viscous nature—related to shear and dilational interfacial viscosities—may be present and generally occur at interfaces with adsorbed surface-active substances having intra- and intermolecular interactions, as well as interactions with the bulk of the fluid producing some resistance to deformation.

These interfacial viscosities create a dissipation effect, similar to viscosity in the bulk of the fluids, in the three-dimensional zone near the fluid interface [2]. Most authors and commercially available measuring devices use the nomenclature for interfacial shear moduli as follows (Equation (1)) [70,71]:

G* = G′ + i G″

(1)

where G* is the complex shear modulus, G′ is the elastic shear modulus, and G″ is the viscous shear modulus.

Similarly, for dilational moduli (Equation (2)) [20,72]:

E* = E′ + i E″

(2)

where E* is the complex dilational modulus, E′ is the elastic dilational modulus, and E″ is the viscous dilational modulus. The moduli G*, G′, G″, E*, E′, and E″ all have the same units [mN/m]. The elastic components G′ or E′ are related to the behavior of the interface as an elastic solid, following Hooke’s law if the deformation is small (linear response), while the viscous components G″ or E″ are associated with viscous behavior. These moduli can be physically described as the interface’s ability to recover potential energy (elastic modulus) and the dissipation of lost energy due to permanent deformation (viscous modulus).

Since Scriven’s work [42,51], theoretical analyses of existing measurement instruments have been conducted to enable reproducible quantitative measurements of interfacial rheological properties. These include deep channel interfacial rheometers [73], spinning drop rheometers [74], ring rheometers [75], oscillating pendant drop rheometers [35], bicone rheometers [76], and, more recently, double-wall ring rheometers [77]. These devices allow for the measurement of properties such as interfacial viscosity and elasticity, which are related to Boussinesq’s proposed surface viscosity and interfacial tension gradients, respectively.

In recent years, the study of the interfacial rheological behavior of water–crude oil systems has been based on the use of bicone shear rheometers [78,79,80] and oscillating pendant drop rheometers [18,81,82,83,84,85,86,87]. However, these methods have an instability drawback, i.e., they cannot be used in systems with low or ultra-low interfacial tensions, typically below 1 mN/m. Fortunately, the spinning drop interfacial rheometer with rotational gravity action could result in stable systems even with ultra-low interfacial tensions [88,89,90].

Pure shear or pure dilational modes rarely exist in real multiphase devices. For instance, the oscillatory spinning drop imposes radial compression from rotation, generating tangential flow around the droplet; thus, the measured response is effectively a combination of dilational (E) and shear (G) moduli. Pendant-drop analyses can also exhibit mixed modes if the drop shape changes are large enough or if contact-line forces introduce tangential stresses [20].

Another illustrative example comes from dynamic bubble-shape analyses where the Young–Laplace equation alone, which assumes equilibrium between gravitational and surface tension forces, neglects Marangoni or viscoelastic contributions. Hegemann et al. [85] and Nagel et al. [86] pointed out that interpreting measured moduli in such mixed-deformation fields requires more advanced numerical shape-fitting procedures. Guzmán et al. [54] further reviewed how partial shape changes can combine shear, dilational, and even bulk stresses in one measurement. Moreover, the standard Young–Laplace assumption is purely hydrostatic. When additional tangential stresses arise, either from surfactant transport or solid-like films at the interface, recent machine learning (ML)-based shape analyses would need to incorporate these effects to avoid systematic under- or over-estimation of E* and G*.

2.2. Shear Interfacial Rheology

The shear interfacial rheological parameters are obtained by applying an oscillatory shear strain σ to the interface, while the interfacial area remains constant [27,91]. The surface changes over time t through a sinusoidal oscillation at a constant frequency ω, which can be expressed with Equation (3):

$$\sigma ={\sigma }_0 sin \left(\omega t\right)$$

(3)

and a response is obtained that is recorded through the appearance of harmonic shear stresses τ phase-shifted with a phase angle δ relative to the generated deformation (Equation (4)):

$$\tau ={\tau }_{0}sin \left(\omega t+\delta \right)$$

(4)

where σ₀ and τ₀ are the deformation and stress amplitudes, respectively, ω is the oscillation frequency, and δ is the phase angle that is presented due to the viscous dissipation of the interface. The shear strain σ and the response τ and δ for an oscillatory test are shown schematically in Figure 2.

The main parameter of a measure of shear interfacial rheology is the complex shear interfacial modulus $G_S^{*}$, which is defined as (Equation (5)):

$$G_S^{*}={\displaystyle \frac{{\tau }_0}{{\sigma }_0}}$$

(5)

The complex module $G_S^{*}$ can be expressed as the sum of the real and imaginary components (Equation (6)):

$$G_S^{*}=G_S^{\prime }+{iG}_S^{″}=G_S^{\prime }+i \omega {\eta }_S$$

(6)

where $G_S^{\prime }$ and $G_S^{″}$ are the elastic modulus and the loss modulus, respectively, which are a function of the oscillation frequency ω, where η_S is the shear interfacial viscosity. $G_S^{\prime }$ and $G_S^{″}$ are related to the complex module $G_S^{*}$ and phase angle δ through the following equations (Equation (7)):

$$G_S^{\prime }=\left|G_S^{*}\right| cos\delta , { G}_S^{″}=\left|G_S^{*}\right| sin\delta$$

(7)

The elastic contributions (real component) and dissipation losses (imaginary component) make up the complex module.

The interfacial viscosity is defined as (Equation (8)):

$${\eta }_S={\displaystyle \frac{G_S^{″}}{\omega }}$$

(8)

and by analogy with bulk rheology, the complex viscosity η*_S is calculated as (Equation (9)):

$${\eta }_S^{*}={\displaystyle \frac{G^{*}}{\omega }}$$

(9)

Another useful parameter for the analysis of interfacial viscoelastic properties is the phase angle tangent, defined as (Equation (10)):

$$tan \delta ={\displaystyle \frac{G_S^{″}}{G_S^{\prime }}}={\displaystyle \frac{\omega {\eta }_S}{G_S^{\prime }}}$$

(10)

This parameter makes it possible to relate the dissipative losses with respect to the elastic contribution of the interface.

2.3. Dilational Interfacial Rheology

In interfacial rheology measurements, the dilational modulus is calculated as (Equation (11)):

$$E=A \partial \Pi /\partial A$$

(11)

where A is the superficial area and Π is the surface pressure, which is Π = γ₀ − γ, i.e., the interfacial tension difference between a clean interface and an interface in the presence of a surfactant. This shows that E arises from surface tension gradients and describes the Marangoni stress whatever the frequency.

For an insoluble monolayer, the surface surfactant concentration can be expressed as Γ~1/A (Equation (12)):

$$E=\Gamma \partial \Pi /\partial \Gamma$$

(12)

The modulus E is also called compression modulus in the literature.

When the droplet in the spinning drop equipment is subjected to an oscillatory expansion and contraction of area (A), a response of the interfacial tension (γ) can be measured. Thus, the interfacial dilational modulus E can be calculated with Equation (13):

$$E=A_0 {\displaystyle \frac{\mathsf{\Delta }\gamma }{\mathsf{\Delta }A}}$$

(13)

where Δγ (= γ_max − γ_min) is the change in the amplitude of the interfacial tension. ΔA (= A_max − A_min) is the amplitude of variation of the area, and A₀ is the initial interfacial area of the drop.

The dilational modulus can also be expressed as the complex number shown in Equation (14) that includes both the elastic (or storage modulus E′) and viscous (or loss modulus E″) contributions (Equation (14)):

$$E=E^{\prime }+i{ E}^{″}$$

(14)

In viscoelastic interfaces, γ and A variations measured at a frequency ω, result in an occurring time shift, represented by the phase angle $\phi$. E′ and E″ account for the energy stored and the energy dissipated through relaxation processes, respectively. They can be obtained from the phase angle through Equation (15):

$$E^{\prime }=E cos\phi , { E}^{″}=E sin\phi$$

(15)

The interfacial viscosity η_E can be calculated as (Equation (16)):

$${\eta }_E={\displaystyle \frac{E^{″}}{\omega }}$$

(16)

where ω is the frequency of oscillation.

Figure 3 depicts a measurement with dilational interfacial rheology, including the variation of the interfacial tension, interfacial area and phase shift.

3. Methods to Measure Interfacial Rheology

The interfacial rheological properties can be measured under different deformation modes, which can significantly influence the behavior of emulsions, foams, and other dispersed systems [20]. Dilational methods are highly sensitive to surfactant adsorption/desorption kinetics, which can dominate the response, especially at certain frequencies. Methods using pure shear deformations are not influenced by Marangoni effects due to the constant interfacial area during shear deformation. However, interfacial shear properties can still be affected by the presence and dynamics of surface-active species.

Table 1. Types of equipment for the measurement of shear and dilational interfacial rheology effects, operating ranges, advantages and limitations. Operating ranges vary according to the type of sample (e.g., surfactant, protein, asphaltenes); therefore, values are only for reference.

Method	Geometry	Frequency Range	Interfacial Tension Thresholds	Moduli Range	Advantages	Limitations	Ref
Shear Methods
Deep channel viscometer		~0–1 Hz	>5 mN/m	G′ ~1–50 mN/m	- Non-invasive - Good for soluble surfactants	- Narrow measurement range - Lower sensitivity - Challenging to measure small interfaces	[73]
Bicone rheometer		0.001–10 Hz	>1 mN/m	G′ ~1–100 mN/m	- Effective for shear moduli - Broad measurement range - Rotational rheometers are available in many labs.	- Potential for bulk contributions - Complex setup	[76,92]
Ring viscometer		0.01–10 Hz	>1 mN/m	G′ up to ~100 mN/m	- Simple setup - Direct measurement of interfacial shear viscosity	- Limited frequency range - Low sensitivity - Bulk contributions from submerged portions can affect results	[75,77,93]
Magnetic rod interfacial rheometer		0.1–10 rad/s	>5 mN/m	G′ up to ~100 mN/m	- Precise Measurement - Controlled Shear - Minimal Invasiveness	- Limited frequency range - Complex Alignment and Calibration	[94,95]
Dilational methods
Oscillating Langmuir trough		0.001–1 Hz	>10 mN/m	E′ up to ~200 mN/m	- Precise control over surface concentration - Effective for insoluble monolayers - Useful for phase behavior studies	- Narrow measurement and frequency ranges - Not ideal for systems with soluble surfactants	[96,97]
Capillary and longitudinal waves		10–500 Hz	>15 mN/m	E′ up to ~200 mN/m	- High sensitivity - Wide frequency range - Suitable for small interfacial changes	- Complex setup - Limited applicability to certain interfacial systems	[20,98,99]
Oscillating pendant drop		0.001–1 Hz	~1–100 mN/m	E′ ~1–100 mN/m	- Broad measurement range - High applicability - Easy setup	- Limited sensitivity in ultralow interfacial tension systems	[1,27,35]
Oscillating spinning drop		0.001–1 Hz	~1–100 mN/m	E′ up to ~100 mN/m	- Excellent for ultralow interfacial tensions - Broad measurement range	- Complex setup - Lower frequency range - Limited applicability to high-tension interfaces	[74,88,89,90]
Capillary pressure		0.01–0.25 Hz	10−4–10 mN/m	E + G up to ~10–50	- Direct measurement of small-scale interfaces - Simple setup	- Limited frequency range - Less sensitive than other methods - Difficulty in controlling surface concentration	[100]

presents a summary of the equipment and geometry that has been most widely used for the measurement of interfacial shear and dilational rheology. Sensitivity and operating windows vary significantly among devices (Table 1). For instance, Renggli et al. [91] have discussed how channel depth in a deep channel viscometer can strongly influence bulk-interfacial coupling, with insufficient depth causing shear fields in the subphase to dominate. Insufficient channel depth can result in dominant shear fields within the subphase, thereby skewing the measurement of interfacial properties. Similarly, Sánchez-Puga et al. [92] showed that the geometry of bicone or ring rheometers can partly submerge into the fluid bulk, thus blending the intended interfacial shear flow with undesirable 3D flow components.

3.1. Shear Interfacial Rheology Methods

Shear interfacial rheology measurement methods can be classified into channel viscometers, disk interfacial rheometers, and ring viscometers [9,101,102].

3.1.1. Deep Channel Viscometers

The deep channel viscometer allows the measurement of interfacial shear viscosity by observing the flow of a liquid in a deep, narrow channel with an interface at the top [19,101] (Figure 4). The presence of an interfacial layer with finite shear viscosity alters the velocity profile near the interface. This device has been used for a variety of applications, including the measurement of interfacial shear rheology in water/crude systems in the presence of surfactants [73]. The outer and inner cylinders are fixed, and the base rotates at an angular velocity so that the flow occurs in a small circular space. The monolayer of an insoluble surfactant to be studied is placed at the interface in this space. The evaluation of the interfacial properties is based on the direct measurement of the distribution velocity on the surface, placing tracers on the surface [27]. The main disadvantage of this equipment is that it requires a small tracer particle to be placed and to remain at interface to follow its velocity. The black opacity of a crude oil—generally the upper phase unless it is a heavy crude denser than water—may be a problem to follow the position of the tracer particle. Additionally, this may be particularly complex in heavy crude systems for which the particle may require several hours to complete a revolution, as well as with systems in which placing the particle at the interface may be complex [25]. The velocity profile in the channel is influenced by the interfacial shear stress. The interfacial shear viscosity can be determined by measuring the flow rate and the velocity gradient near the interface. This technique has certain advantages such as it is a non-invasive method for measuring interfacial shear viscosity and it is suitable for studying steady shear properties. It can be applied to a variety of interfaces, including those with soluble surfactants. On the other hand, limitations include the requirement of precise control of flow conditions and measurement of velocity profiles. Complex data analysis due to coupling between bulk and interfacial flows, and sensitivity to channel dimensions and surface conditions have been reported [25].

3.1.2. Interfacial Disk Rheometers

Among the disk rheometers, the bicone is the most frequently used instrument (Figure 5). In this technique, the disk rotates while the cell remains fixed. These measurements are made so that the disk only touches the liquid surface, and the space between the disk and the cell is small compared to the disk radius. Therefore, the bicone rheometer is the most widely used instrument for the measurement of interfacial shear rheology. The data analysis is similar to conventional rheology calculations, using the Maxwell complex G*, elastic G′ and viscous G″ modules and obtaining a phase shift angle δ [103,104]. Soo-Gun and Slattery carried out the theoretical analysis of this equipment in 1978 [76]. Among the main features of the technique are the direct measurement of interfacial shear properties without dilational contributions. It is suitable for studying viscoelastic, solid-like interfaces, and capable of steady and oscillatory shear measurements over a range of frequencies. It requires precise alignment to ensure deformation is confined to the interface, with potential bulk contributions if the flow penetrates into the subphase.

Disk viscometers are generally less sensitive for the measurement of interfacial shear viscosity than channel viscometers, and they exhibit a more complex flow field. The main advantage of disc techniques is their ability to measure torque directly; however, placing the disc at the interface and avoiding contact angle anomalies is problematic. This is why these devices are more helpful in measuring systems with high viscosity interfaces [9,27].

3.1.3. Interfacial Ring Viscometers

The ring viscometer measures interfacial shear viscosity by moving a thin, ring-shaped probe horizontally along the interface and measuring the force or torque required. The ring is partially submerged to interact with the interface. The first of these types of equipment, the oscillating ring viscometer, is based on the use of a Lecomte du Noüy ring-like configuration with controlled oscillating stress (Figure 6) [9,75]; the measurements are performed by placing the ring plane at the liquid interface, sinusoidally oscillating at a resonance frequency. Several systems have been studied including systems with cationic and anionic surfactant complexes [105]

The second of these devices, the double-wall ring rheometer (DWR) (Figure 7), consists of a double-wall ring geometry that sits precisely at the interface, minimizing disturbances to the bulk phases and reducing inertia effects [77,106,107,108]. The DWR rheometer applies shear deformation through the ring, and the resulting torque is measured to determine interfacial shear viscosity and elasticity. The interfacial shear viscosity (η_s) is calculated using the measured torque and angular velocity, providing highly sensitive data on the interfacial rheological properties. Again, geometry has the advantage that it can be adapted to a modern rotational rheometer [77]. Among the advantages can be mentioned a simple experimental setup with direct measurement of interfacial shear viscosity. Also, it is applicable to both gas–liquid and liquid–liquid interfaces. Limitations include potential bulk contributions due to submersion of the ring and its sensitivity to immersion depth and alignment. Vermant et al. [77,106] developed the DWR geometry to address limitations in existing rheometers, such as bulk phase disturbances and low sensitivity to interfacial properties. It is nowadays one of the most used methods for shear interfacial rheology measurements.

3.1.4. Magnetic Rod Interfacial Stress Rheometer

Fuller et al. [94,95] developed the magnetic rod interfacial stress rheometer (ISR). The principle of this equipment involves placing a small, magnetized rod floating on the surface, which is moved by the force generated from a magnetic field gradient produced by Helmholtz coils (Figure 8). This configuration allows an oscillatory shear flow to be produced, with the capability to vary the frequency between 0.1 and 10 rad/s. The rod is induced to rotate or oscillate by applying a controlled magnetic field, causing shear deformation in the interfacial layer. The resistance of the interface to this deformation is measured in terms of torque versus angular displacement, providing quantitative data on interfacial shear viscosity and elasticity. An inverted microscope is focused on one end of the rod, and the rod’s displacement is projected onto a linear photodiode array, allowing real-time tracking of the rod’s position. The device is designed to apply time-dependent forces (surface stress) and monitor the corresponding time-dependent strain. The rheometer has been utilized to investigate rheological transitions of Langmuir monolayers at the air–water interface [95]. The rheometer was explored to study complex amphiphilic systems including the formation of physical networks in polymers, examining the kinetics of polymer cross-linking, measuring relaxation times with flexible polymers, and analyzing the adsorption kinetics of proteins at the air–water interface [94].

3.2. Dilational Interfacial Rheology Methods

The most widely used methods for measuring dilational interfacial rheology are surface waves and droplet deformation methods [110,111]. Surface wave methods were addressed by Levich [53], who validated the possibility of measurements of interfacial elasticity and viscosity, including transverse capillary wave methods [98], and longitudinal waves [112], followed by theoretical analyses of the methods of the oscillating spinning drop [74] and oscillating pendant drop [35]. The latter has been widely used to measure interfacial rheological properties of systems with interfaces containing surfactants, proteins, or asphaltenes [27,64,81].

Noskov [4] presented a detailed review on the frequency ranges of different experimental methods of dilational surface rheology for polymer and polymer/surfactant solutions (Figure 9). Each dilational interfacial rheology technique presents a frequency range according to the limitations of the physical characteristics of the system:

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At high frequencies (>500 Hz), methods such as capillary wave techniques dominate. In this range, polymer films adsorbed at the interface behave like insoluble monolayers, and their dynamic elasticity is mainly influenced by interactions between adsorbed macromolecules. Although capillary wave methods have been widely used since the 1980s, their popularity has declined due to difficulties in interpreting results.

-

Low-frequency methods (f < 1 Hz), including oscillating barrier techniques, have gained attention due to their simplicity and relevance in studying slow relaxation processes in polymer surface layers. These methods focus on resolving long-term, slow relaxation dynamics, which are important for understanding the behavior of polymer films at the interface.

3.2.1. Surface Wave Methods

The development of measurement equipment for studying capillary and longitudinal waves [99,101,113], led to advances in the study of interfacial and surface behavior in the presence of surfactants, revealing that an interfacial (or surface) viscosity effect would influence wave damping similarly to the Gibbs–Marangoni effect. Surface wave methods are generally employed to measure the dilational rheological behavior of surfaces at high-frequency. These usually require an adequate theoretical description of surfactant transport and the Gibbs–Marangoni effect. The most commonly used wave techniques are transverse and longitudinal capillary waves [59].

Capillary waves are produced under the action of small perturbations in liquid surfaces. These generally have low amplitudes and lengths. The measurement is made through the expansion and compression of the surface film, presenting surface tension gradients due to wave growth and depression (Figure 10). Transverse and longitudinal waves can be produced [98,99], allowing reliable measurement of the wave amplitude and damping coefficient. The advantage of these methods is that they allow the measurements of dilational interfacial rheology at high oscillation frequencies of up to hundreds of Hz (surface light scattering methods could reach even larger frequencies [114]). This method has been used to study the dilational interfacial rheology of surfaces and interfaces in contact with air or oil and for applications in systems mainly used for foam formation [25,27,101,115].

The propagation of capillary waves is influenced by the interfacial tension and dilational rheology. It is a non-invasive method to measure interfacial rheology, capable of probing high-frequency responses. On the other hand, it is a complex technique due to damping and dispersion effects, and it requires precise instrumentation for wave generation and detection. Lucassen and van den Tempel [112] used capillary wave damping measurements to determine the interfacial dilational viscosity of various surfactant solutions. They found that the presence of surfactants significantly increased the damping of capillary waves due to the added dilational modulus and interfacial viscosity. Noskov et al. [116] investigated the dynamic surface tension and elasticity properties of polyethylene oxide (PEO) and polyethylene glycols (PEG) solutions with longitudinal (at frequencies from 0.1 to 3 Hz) and transversal (at frequencies from 100 to 300 Hz) surface waves. They observed how molecular weight and concentration influence the adsorption kinetics and viscoelastic properties of the interfacial layers, where the main relaxation processes are connected with the monomer exchange between different regions of the surface layer.

3.2.2. Oscillating Barrier Method Using Langmuir Troughs

The oscillating barrier method employs a Langmuir trough to measure the dilational rheology of insoluble monolayers spread at the air–water interface [96,97]. A monolayer is formed by spreading an insoluble surfactant on the water surface. Movable barriers periodically compress and expand the monolayer, changing the surface area. This method imposes dilational deformation by varying the surface area. For oscillatory deformations, the complex dilational modulus E* = E′ + iE″ can be determined by measuring the in-phase and out-of-phase components of the surface pressure response.

Among the main aspects of the technique can be mentioned the measurement of the effective modulus for insoluble monolayers rather than the intrinsic one. Precise control are required over surface concentration and packing density. It is useful for studying phase behavior and transitions in monolayers. It is limited to insoluble or very weakly soluble surfactants. Edge effects and non-uniform compression can affect measurements. Using this method, He et al. [97] studied the dilational rheology of fatty acid monolayers. They observed that the dilational modulus increased significantly upon monolayer condensation, indicating a transition from a liquid-expanded to a liquid-condensed phase. Noskov et al. [117] studied the dynamic surface elasticity of sodium poly(styrenesulfonate) solutions by using the oscillating barrier method in the Langmuir trough. They measured and analyzed the impact of molecular weight and concentration on the interfacial behavior at frequencies from 0.01 up to 500 Hz. They found significant distinctions between the dilational surface elasticity of anionic and nonionic polymer solutions. Nonionic polymer dynamic surface elasticity changed faster in comparison to the sodium poly(styrenesulfonate), which is determined mainly by lateral electrostatic interactions between the ionized sulfonate groups and the formation of aggregates.

3.3. Oscillating Droplet Deformation Methods

There are several methods for measuring dilational interfacial rheology through rotational or translational deformations of bubbles or drops. These methods involve an interfacial flow that is accompanied by interfacial tension gradients. This is why these methods have a useful, practical application for measuring dilational interfacial elasticities and viscosities. Droplet deformation is the principle of pendant drop, capillary pressure, and spinning drop tensiometers. Both methods can be adapted to perform deformations of the interfacial area in an oscillatory way [27].

3.3.1. Oscillating Pendant Drop Method

This method has been the most widely used in oil–water systems in the last 15 years due to the availability of measuring equipment and the development of cameras and drop profile analysis programs at greater speed [118,119]. It consists of a bubble of gas or a drop of liquid placed inside another liquid phase volume under natural gravity conditions (Figure 11), where the interface takes the shape that minimizes the total energy of the system. In this technique a liquid drop is formed at the tip of a capillary and hangs in an immiscible fluid (usually air or another liquid). Dilational rheological properties can be determined by controlling the drop volume oscillations and analyzing the dynamic response of the interfacial tension [35,120,121,122]. The shape is determined by a combination of the interfacial/superficial tension and the gravitational effects. The interfacial tension tends to make the drop spherical, while gravity produces its vertical elongation. An analysis of the drop profile is performed, and the interfacial tension and interfacial area value are obtained through the Laplace equation, applying an oscillatory expansion and contraction of the drop. With the values of interfacial tension and the area dilational elasticity, the phase angle and dilational interfacial viscosity of the system are calculated. The maximum oscillation frequency limit is close to 1 Hz [35]. This equipment has, however, a serious limitation which is that in order to avoid the drop or bubble detachment, it can only be used when interfacial tension is greater than 1 mN/m.

It is important to note that in the oscillating pendant drop method, the deformation is primarily dilational, and shear deformation is negligible (shear occurs only at the connection with the syringe). Therefore, the modulus measured is predominantly the dilational modulus E. Among the main aspects of the technique, it can be mentioned that the equipment is capable of measuring frequency-dependent dilational moduli over a range of frequencies (typically 0.01–10 Hz). It is suitable for studying soluble surfactants, proteins, and polymers. It has a relatively simple setup with accessible equipment. Among the limitations, it is sensitive to surfactant adsorption/desorption kinetics and Marangoni effects, requiring careful data interpretation. Additionally, it utilizes an axisymmetric drop shape; therefore, deviations due to instabilities can introduce errors.

3.3.2. Capillary Pressure Method

The capillary pressure method involves measuring the pressure difference across a curved interface, such as in a capillary tube or between two approaching droplets. The dilational modulus is calculated by inducing controlled deformations of the interface and measuring the corresponding pressure changes [14]. The capillary pressure method uses the Laplace equation directly to determine the pressure difference across a drop or bubble interface close to a sphere. The measurement equipment consists of two chambers connected by a capillary tube. A piezoelectric system is used to control the volume of the drop or bubble formed at the tip of the glass capillary, which is continuously monitored with a video camera (Figure 12). An essential feature of this technique is that it does not require a drop deformed by the force of gravity because it preferably works with perfectly spherical shapes. This makes it useful for both liquid–liquid and liquid–gas systems using (very) small drops or bubbles [100]. The interfacial rheology measurements are made by recording the response of the interfacial tension to small perturbations of the amplitude of the interfacial area. Using sinusoidal oscillations, the dilational elasticity and viscosity can be measured at frequencies up to 1 Hz. A disadvantage of this method is that it has an interfacial tension limit of about 1 mN/m to avoid detachment of the drop. Among the advantages of the method are the direct measurement of pressure changes due to interfacial deformation and its applicability to small-scale spherical drop emulsions. Disadvantages include challenges inducing controlled and measurable deformations, and it is sensitive to experimental errors in pressure and curvature measurements.

3.4. Use of Machine Learning (ML) and Artificial Intelligence (AI) for Drop Shape Analysis in Complex Systems

ML and AI approaches have been integrated recently into the field of interfacial rheology, specifically in techniques such as pendant drop tensiometry and dynamic surface rheology [125,126,127]. These approaches offer the potential to improve both the accuracy and speed of measurements, particularly under dynamic conditions, where real-time analysis in complex systems is crucial. In this section, we examine recent studies showing the application of ML, artificial (ANN), and convolutional (CNN) neural networks in this area.

Kratz and Kierfeld [126] trained an ANN using a large set of numerically generated drop shapes based on non-dimensional quantities such as the Bond (Bo) number. These dimensionless parameters allowed the neural network to generalize across different experimental conditions, magnifications, and constraints. The trained model was used to analyze drop shapes and infer the surface tension in dynamic scenarios, such as those encountered in dilational surface rheology. The architecture of the ANN used for pendant drop tensiometry is shown in Figure 13. The network is trained to solve the inverse problem of determining surface tension from the shape of a pendant drop. The input consists of 226 sample points along the contour of the drop, transformed into a vector of 2D elements (with r- and z-values). Each layer gradually reduces the number of outputs from 512 in the first hidden layer, to 1024, 256, 16, and finally 2 output parameters: $\widetilde{p_L}, ∆\tilde{\rho }$. These output parameters correspond to the fitting parameters used in the calculation of surface tension and density difference [126].

Soori et al. [127] utilized ML for estimating the surface tension of water–alcohol mixtures from pendant drop images. The performance of the ML model was particularly notable in its ability to predict surface tension in cases where the mechanical equilibrium of axisymmetric drops was not fully maintained or when the composition of the mixture was unknown. Figure 14 shows the architecture of the CNN used for predicting surface tension values from pendant drop images. The input image is processed through a series of convolutional layers with 3 × 3 filters, ReLU activation, and maxpooling layers for down-sampling. Dropout layers are used to prevent overfitting. The convolutional layers extract features from the image, which are passed through two fully connected dense layers. The first dense layer has 512 nodes with ReLU activation, while the second dense layer has 5 nodes with Softmax activation to predict surface tension values. The training process involved augmenting the dataset using Keras image data generators to improve model generalization by introducing variations such as rotations, shifts, flips, and shearing of the images. Multiple models were trained using different combinations of known and unknown surface tension datasets to evaluate the CNN’s ability to extrapolate surface tension values from previously unseen drop shapes [127].

Hyer et al. [125] implemented a convolutional neural network (CNN) to analyze pendant drop images in real-time. The steps of the model architecture are depicted in Figure 15 as follows:

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(a) The Young–Laplace equation is employed to generate drop profiles. The drop profiles are influenced by two critical parameters, denoted as $\Delta \tilde{\rho }$ (dimensionless density difference) and $\widetilde{p_L}$ (pressure parameter), which govern the shape and volume of the drop. The drop volume is determined by varying these parameters within a pre-defined range. The generated drop profiles serve as the foundational data for the subsequent stages of model training.

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(b) Representative drop profile generated from the solution of the Young–Laplace equation. Small variations in parameters Bond number (Bo) and Worthington number (Wo) affect the drop shape and volume.

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(c) Generated images used for training the CNN models. These images correspond to different surface tension values and exhibit variations in image quality and focus to simulate complex experimental conditions, such as the presence of particles.

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(d) Experimental pendant drop images, which are used as inputs to the CNN model. These images were pre-processed to standardize them and enhance model accuracy.

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(f) and (g) The trained CNN models predict Bo and γ.

Their deep learning approach was able to process images within 1.5 milliseconds, providing surface tension values with absolute errors as low as 0.15 mN/m (Figure 15h). One of the key innovations of this work was the robustness of the model under challenging conditions, such as poor image quality, blurring, or misalignment. Even under such suboptimal conditions, the model maintained accuracy, keeping errors below 0.3 mN/m.

3.5. The Oscillatory Spinning Drop Technique

The oscillatory spinning drop interfacial rheology technique (OSDIR) is particularly interesting because it can measure the rheology of interfacial layers at low interfacial tensions (<1 mN/m), which cannot be performed in the simple Du Noüy ring or Wilhelmy plate methods. In sophisticated pendant drop equipment, often used in laboratories, the droplet detaches from the needle at interfacial tensions lower than 1 mN/m, thus excluding such apparatus for oscillating methods [20,128]. The method was recently revisited, indicating the accuracy and flexibility that is still achievable [129].

The oscillatory spinning drop method recently presented in detail [88] can be used to perform interfacial rheology measurements of both low and ultralow interfacial tensions (as low as 10⁻⁴ mN/m). This is critical when the formulation of a SOW system is at or close to the so-called optimum as was shown 50 years ago in enhanced oil recovery or crude dehydration applications [130,131,132,133,134].

Such oscillatory spinning drop apparatus was developed at the University of the Andes about 14 years ago and recently divulgated with some explanations [91,135]. A few years ago, Dataphysics made available similar oscillating spinning drop equipment, but with no reports on its use with low or ultralow interfacial tensions.

The principle of the oscillatory spinning drop method involves the uniaxial compression of a droplet induced by rotation, generating both shear and dilational deformations on the interface. Consequently, the modulus measured is a combination of the dilational modulus E and the shear modulus G, effectively representing E + G [88,90]. This combined modulus is related to the interface overall resistance to deformation, incorporating both area changes and shear effects.

The equipment shown in Figure 16 features a spinning capillary with a 4 mm internal diameter, coupled to a motor and a transducer. The rotational speed is precisely controlled via a PID unit, and the droplet area is modulated by varying the rotational speed sinusoidally at frequencies ranging from 0.015 to 0.25 Hz. High-resolution images are captured at specified time intervals (as short as 0.05 s), allowing for the accurate determination of the elongated droplet diameter and rotational velocity. The interfacial tension is then calculated using the simplified Vonnegut equation [88].

Accurate measurements using the oscillatory spinning drop technique require careful control of experimental conditions, including droplet volume, rotational speed, and oscillation amplitude. Selecting an appropriate droplet volume is critical and depends on the interfacial tension and density difference between the fluids (

Table 2. Typical values of interfacial (or surface) tension, droplet volume, recommended rotational speed, and equilibration time for operation with the oscillatory spinning drop apparatus.

System	Tension (mN/m)	Droplet Volume (µL)	Recommended Rotational Speed Interval (rpm) 1	Approximate Equilibration Time
Surfactant–air–water	10–40	20–25	7000–10,000	30 min to a few hours
Oil–water (with asphaltenes)	10–40	20–25	7000–10,000	1 h to several hours
SOW with high interfacial tension	2–10	10–20	6000–10,000	20 min to 2 h
SOW system with low interfacial tension	0.1–2	5–10	4000–6000	20 min to 2 h
SOW system with ultralow interfacial tension	10−4–0.1	0.5–5	3000–4000	1 min to 1 h

¹ The recommended rotational speed varies with interfacial tension. To maintain a linear rheological response, the interfacial area change during oscillation should remain below 10% [88].

).

The oscillation frequency (ω) is adjusted based on the specific measurement objectives. For studies related to emulsion stability, an oscillation frequency of 0.1 Hz may be used to align with the characteristic timescale of coalescence phenomena [90], or a broader analysis of system response to frequency changes, with a typical sweep ranging from 0.015 to 0.25 Hz.

When conducting a frequency sweep with the oscillatory spinning drop rheometer, two frequency regimes are of particular interest [59,88]:

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Low-Frequency Regime (≤0.025 Hz): At very low frequencies, the oscillation period is sufficiently long to allow surfactant molecules to exchange between the bulk and the interface. This results in minimal surface concentration gradients and thus negligible Gibbs–Marangoni effects, leading to low dilational modulus values.

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Medium-Frequency Regime (≥0.25 Hz): At higher frequencies, the oscillation period is short, limiting the time available for surfactant adsorption during droplet elongation. This causes the interface to behave more elastically, with the dilational modulus approaching a plateau corresponding to an “insoluble” monolayer.

3.6. Comment on Practical Tips to Measure Interfacial Properties in Some Systems

Each type of interfacial rheology equipment has unique characteristics that must be taken into account to perform a correct and precise measurement. Among them, sample purity is key; even trace impurities drastically alter moduli. For instance, impurities in water can indicate a dilational response at the air/water surface, although the response should be negligible in pure water and controlled laboratory settings [20]. In bicone or ring rheometers, ensuring the probe just touches the interface is critical. Some ring designs submerge their arms too deeply into the fluid. Over-submersion generates bulk effects. The double-wallring was invented to reduce this [54].

The drop volume for pendant drops must be large enough for stable shape but not so large as to detach (especially when tension < 5 mN/m) [12]. In the oscillating spinning drop, the droplet length must be carefully elongated at a rotational speed to comply with Vonnegut equation [135]. At very low frequencies, temperature drift or slow surfactant partitioning can overshadow small moduli changes [20]. At high frequencies, inertial or wave effects appear [20]. Increasing salinity often increases asphaltene film rigidity, raising E′ or G′ [18].

On the other hand, pH controls ionizable groups in proteins or asphaltenes, generating a shift in the modulus [20,40]. Typically, lower interfacial tension or modulus speeds up surfactant diffusion, and can irreversibly reorganize some polymer or protein monolayers. Further details can be found in extensive reviews and books on the subject [1,7,20,21,27,70].

4. Recent Advances in Methods to Measure Rheology of Interfacial Layers

Table 3. Recent advances in interfacial rheology measurement methods.

System	Measurement Method	Equations	Frequency Range	Novelty	Reference
Review on Adsorption Layers at Liquid Interfaces	- Drop and Bubble Profile Tensiometry - Langmuir Isotherm Fitting	- $\mathrm{Langmuir} \mathrm{Isotherm}: \sigma ={\sigma }_0-{\displaystyle \frac{RT{\mathsf{\Gamma }}_m}{\ln \left(1+KC\right)}}$ - Gibbs Adsorption Equation: $\mathsf{\Gamma }=-{\displaystyle \frac{1}{RT}}{\displaystyle \frac{d\sigma }{d\ln C}}$ - Elastic Modulus: $E_{\mathrm{Young}}=E+G$	- Dilational: 0.1 Hz - Shear: 1 Hz	- Quantitative modeling of dynamic dilational surface viscoelasticity - Application of models to surfactant mixtures	Kovalchuk et al. [21]
Tween 80 Surfactant at Crude Oil–Water Interfaces	- Dilational Rheology (pendant drop) - Shear Rheology (Double-wallRing)	- $\mathrm{Gibbs} \mathrm{Modulus}: E_G={\displaystyle \frac{d\gamma }{d\ln \mathsf{\Gamma }}}$ - Equation of State: $\mathsf{\Gamma }\sim {\displaystyle \frac{d\gamma }{d\ln C}}$	- Dilational: 0.1 Hz - Shear: 1 Hz	- Customization of DWR cell for long-duration experiments - Correlation of dilational and shear rheology	Saad et al. [136]
Triton X30 Surfactant at Air/Water Interfaces	- Atomic Force Microscopy (AFM) - Drop and Bubble Profile Tensiometry	- $\mathrm{Levich}’\mathrm{s} \mathrm{Model} \mathrm{for} \mathrm{Capillary} \mathrm{Wave} \mathrm{Damping}: {\omega }_n^2={\displaystyle \frac{\sigma k_n^3}{\rho }}$ - Modified Damping Equations: ${\beta }_{vn}={\displaystyle \frac{2\eta k_n^2}{\rho }}$ - Dispersion Relation: ${\omega }_n=\sqrt{{\displaystyle \frac{\sigma k_n^3}{\rho }}}$	- Thermal Fluctuations: Resonance Modes	- Utilization of AFM cantilever to detect thermal oscillations without external excitation	Zhang et al. [137]
Crude Oil–Water Interface with Asphaltenes	- Interfacial Dilational Rheology (Microtensiometer) - Interfacial Shear Rheology (Microbutton Device, Double-wallRing)	- Dilational Modulus: $E^{*}={\displaystyle \frac{d{P}_S}{d\ln A}}$ - Shear Modulus: $G^{*}={\displaystyle \frac{m{B}_0{e}^{i\delta }\omega \mathsf{\Delta }\theta }{4\pi a^2}}$ - Boussinesq Number: $Bo={\displaystyle \frac{{\eta }^{*}s{P}_c}{\eta A_c}}$	- Dilational: 0.5 < ω < 5 rad/s - Shear: 6.3 rad/s	- Development of microtensiometer and microbutton devices for simultaneous dilational and shear measurements	Ma et al. [138]
Insoluble Asphaltene Layers at Oil–Water Interfaces	- Langmuir Trough Compression–Expansion Experiments - Radial Trough for Dilational Rheology - Double-wallRing (DWR) for Shear Rheology	$E_{\mathrm{app}}\approx -{\displaystyle \frac{{\mathsf{\Pi }}_1-{\mathsf{\Pi }}_2}{\ln \left(A_1\right)-\ln \left(A_2\right)}}$	- Frequency Sweeps: Various (e.g., 0.1 Hz, 1 Hz)	- Comprehensive characterization combining Langmuir trough compression rheology - Investigation of different asphaltene subfractions - Evidence supporting Pickering-like stabilization mechanisms	Alicke et al. [139]
Interfacial Dynamics and Rheology of a Crude Oil Droplet Oscillating in Water at a High Frequency	- Oscillating Drop Tensiometry	$E_d\left(\mathsf{\omega }\right)=E^{\prime \mathrm{extra}}\left(\mathsf{\omega }\right)\propto {\mathsf{\omega }}^{0.25}$ ${\mathsf{\eta }}_d\left(\mathsf{\omega }\right)={\displaystyle \frac{E^{\prime \mathrm{extra}}\left(\mathsf{\omega }\right)}{\mathsf{\omega }}}\propto {\mathsf{\omega }}^{-0.75}$	- Low Frequency: 0.05 to 1 Hz - High Frequency: 10 to 200 Hz	- Integration of low-frequency dilational rheology with high-frequency droplet oscillation dynamics - Exploration of aging effects on interfacial rheology across a broad frequency range	Chebel et al. [140]

shows a review of recent advancements in interfacial rheology at oil–water interfaces. Studies have focused on the relationship between interfacial rheology moduli, emulsion stability, and in some cases droplet dynamics. These investigations employ a range of experimental techniques including sessile drop/bubble [21], customized double-wallring cell [136], AFM cantilever contacting bubble to study thermal capillary fluctuations [137], microtensiometer platform and microbutton device capable of simultaneous dilational and shear rheology measurements [138], rectangular and radial Langmuir troughs [139], pendant drop [23] and bubble profile, high-frequency oscillation drop setup [140].

Zhang et al. [137] employed Atomic Force Microscopy (AFM) to investigate thermal capillary fluctuations at air–water interfaces. Utilizing AFM to study thermal capillary fluctuations, they performed Power Spectral Density (PSD) analysis of bubble vibrations and applied the Langmuir adsorption isotherm using the Wilhelmy plate method. Their findings demonstrated that AFM effectively probes interfacial rheology by detecting thermal capillary wave modes (Figure 17). Specifically, the measured damping coefficients aligned well with Levich’s model for higher modes, and surfactant concentration was found to influence damping, that is, increasing at higher concentrations. This study showed AFM as a powerful tool for interfacial rheology and emphasizes the role of mode number in damping behaviors, showcasing how surfactant concentration directly alters interfacial viscosity and stability.

Alicke et al. [139] utilized Langmuir troughs for compression–expansion experiments, radial troughs for dilational rheology, and double-wallring (DWR) setups for shear rheology, along with insoluble asphaltene layers at oil–water interfaces (Figure 18). Their findings revealed that both dilational and shear moduli monotonically increase with surface coverage, particularly below mean molecular areas (MMA) of approximately 50 Ų, indicating a transition from fluid-like to solid-like interfacial behavior dominated by dense packing of nanoaggregates. Additionally, asphaltene subfractions exhibited similar rheological behavior, suggesting that packing density is the primary factor influencing interfacial rheology rather than chemical interactions. High surface moduli are correlated with increased emulsion stability, leading the authors to suggest treating asphaltene-stabilized emulsions similar to Pickering emulsions, where mechanical properties are crucial for long lifetimes.

Chebel et al. [140] explored the high-frequency interfacial dynamics and rheology of crude oil droplets oscillating in water. Utilizing oscillating drop tensiometry combined with high-speed video imaging and spherical harmonics decomposition, the study measured resonance frequencies and damping rates for shape oscillation modes. The deviations found from theoretical calculations indicated substantial viscoelastic properties of the interface. Two distinct aging regimes are observed: initial slow increase of E′ and E″, followed by accelerated E′ increase and E″ decrease. At low frequencies, E′ and E″ scale as ω^0.25, consistent with low-frequency rheology. High-frequency eigen mode analysis confirms that interfaces behave as a bidimensional viscoelastic material. The study extended low-frequency rheology to high-frequency dynamics, validating the consistency of viscoelastic models across different frequency ranges.

Ma et al. [138] introduced a microtensiometer platform and a microbutton device capable of simultaneous dilational and shear rheology measurements (Figure 19). Their experiments revealed that asphaltene compression in radial troughs required higher surface pressures to induce buckling compared to rectangular troughs, highlighting the isotropic nature of compression in radial geometries. Maximum surface pressures reached approximately 72 mN/m for air/water surfaces and 50 mN/m for oil/water interfaces. Furthermore, the study showed that at high coverages, asphaltene layers exhibited viscoelastic behavior with relaxation times on the order of 10² to 10³ s, suggesting that there is a high elasticity during droplet coalescence processes occurring on much shorter timescales.

Saad et al. [136] examined polar surfactants at crude oil–water interfaces using an optical tensiometer with an oscillating drop module and a customized double-wall ring (DWR) cell. Their experiments allowed long-duration measurements, correlating dilational and shear rheology effects under varying salt and oil concentrations. They found that increasing salt concentration led to a reduction in both dilational and shear moduli. Figure 20 shows results of dilational and shear moduli for a water–crude oil interfacial layer, indicating their increase with varying salt nature (0.1 M salt concentration and 3% crude oil).

Kovalchuk et al. [21] focused on surfactant adsorption layers at liquid interfaces using drop and bubble profile tensiometry combined with Langmuir isotherm fitting. Their quantitative modeling of dynamic dilational surface viscoelasticity provided insights into how surface coverage influences the elastic modulus. The study incorporated surfactant mixtures for accurate modeling, addressing limitations of traditional adsorption models and providing a more nuanced understanding of how varying surfactant concentrations and interactions impact interfacial rheological properties.

5. Applications of Interfacial Rheology in Dispersed Biphasic Systems

Interfacial rheology is used for analyzing the behavior of systems with a large interfacial or surface area, primarily in emulsion and foam applications. Surfactants, polymers, proteins, and asphaltenes modify the interfacial rheological behavior, promoting the formation of interfacial films in emulsions, which exhibit high stability [20,61]. Among the most important applications of interfacial rheology is its relationship with emulsion destabilization [88,135,141], as in the breaking of water-in-crude oil emulsions [84,91,142,143], and in enhanced oil recovery various displacement phenomena [81,144,145]. It is involving the film drainage and rupture processes, not only in emulsion but also in foam cases [20,146]

Interfacial shear and dilational rheological parameters have different applications in the field of emulsion stability: interfacial shear rheology is important for describing the film drainage process, while dilational elasticity is crucial in both the film drainage and rupture processes [25].

5.1. Interfacial Rheology and Film Thinning in Biphasic Emulsions and Foams, as Well as in Bicontinuous Microemulsions

Emulsions and foams are stabilized by surfactants, which provide persistence to the interfacial film separating the drops or the bubbles [61,147,148,149]. This stability is due to different effects such as electrostatic and steric repulsion between the droplets (or bubbles) and the rigidity of the interfacial layer, which can be determined through measurements of interfacial elasticity and viscosity [59,90,91,142].

The stability of emulsions is critically influenced by the thinning behavior of the liquid films that separate dispersed drops. Interfacial rheological properties, particularly the dilational modulus and interfacial tension gradients influence the rate of film thinning and, consequently, the emulsion stability. This section examines the experimental aspects of film thinning dynamics, the influence of interfacial rheology, and the role of surfactant partitioning between phases. Specific cases such as double emulsions formed from Winsor III systems with ultralow interfacial tensions are also discussed.

The dynamics of film thinning are governed by many phenomena, including hydrodynamic forces, disjoining pressure, and interfacial rheological properties [1,20]. It can be said that the literature has reported that the stability of emulsions is specifically influenced by several factors and properties. This includes the physicochemical formulation expressed through many variables describing the system components, as well as the temperature and pressure. It is also related to some system properties such as the viscosity of the external phase, the drop size, the electrostatic and steric repulsion between droplet interfacial layers, physicochemical formulation, interfacial elasticity, and viscosity of the drop boundary.

However, since the crude oil price explosion in the 1970s and the resulting EOR crisis and research expansion, the phase behavior of surfactant–oil–water systems and their emulsion properties have been associated with the physicochemical formulation defined as a numerical balance of affinity. Starting with the Winsor R concept, R = Aco/Acw [150,151,152] a numerical expression of the surfactant affinity difference SAD = Aco-Acw [153] was proposed as a first order Taylor series expansion [154,155,156] which was then normalized and called the Hydrophilic Lipophilic Difference (or Deviation from optimum) HLD = SAD/RT [157,158]. The typical most simple HLD expression for nonionic surfactant systems is a linear function of the surfactant molecular characteristics (head and tail sizes), the water salinity, the oil alkane carbon number ACN or its equivalent EACN, as well as the temperature [153,159,160,161]. Because of the definition of the formulation Hydrophilic–Lipophilic Difference, the equal affinity of the surfactant for the oil and water results in three-phase behavior called WIII case in Figure 21.

Systems with low interfacial tensions, near the optimum formulation (hydrophilic lipophilic deviation, HLD = 0), exhibit small droplet sizes and, as schematically summed up in Figure 21 [162], the emulsion stability is always minimum at optimum formulation and the maximum stability is found at some distance from HLD = 0 on both sides. The emulsion type is inverted at HLD = 0 in a very unstable zone. This is the reason why the drop size seems to increase quickly when approaching HLD = 0, because the drops begin to coalesce almost instantly into larger ones, even within the few seconds required for size measurement, regardless of the method used. Additionally, second-order effects, such as the Gibbs–Marangoni effect and the viscoelastic behavior of the interfacial film, significantly influence emulsion stability [163]. It is seen in Figure 21 that the low interfacial tension is associated with a minimum in emulsion stability at the optimum formulation, even if the interfacial viscosity is large [25].

It can be said that the interfacial rheology seems to indirectly influence the coalescence phenomena [89,90]. The flow and rheology of emulsified systems are important for various applications in formulation engineering, such as food flow systems, pharmaceutical and cosmetic products, paints, oil recovery, etc. The macroscopic rheological properties of an emulsion, which determine whether it exhibits Newtonian or non-Newtonian behavior, are related to the interfacial rheological properties where the surfactant is adsorbed, but the relationships are not simple nor obvious. An emulsion with high viscosity within the phase exhibits greater stability because sedimentation, flocculation, and coalescence phenomena are delayed. High values of the phase angle indicate that the interface has a high interfacial viscosity, and, therefore, a large amount of energy is required to deform it, which is important for the stabilization of emulsions and foams [164]. On the other hand, low interfacial or surface viscosities imply that the interface or surface can be easily deformed, a critical factor to favor the breaking of emulsions and foams [20,92,165].

It was only recently that the dilational interfacial rheology of surfactant–oil–water systems was systematically found to be minimum at the optimum formulations [89,90]. It was shown that at the optimum formulation, during a formulation sweep with an anionic surfactant (e.g., salinity scan) and a nonionic surfactant (e.g., EON scan), there is a minimum in both interfacial elasticity and viscosity in SOW systems, coinciding with the minimum stability of emulsions, as schematically seen in Figure 21. This allowed a new explanation, based on dilational interfacial rheology in ultra-low interfacial tension systems, for understanding the very low stability of emulsions at the optimum formulation [90,162,166]. This is based on the fact that at the optimum formulation, the effective dilational modulus is very low due to the rapid diffusion exchange of the surfactant between the phases and the interface, and to the equal interaction of surfactant with the oil and water phases (unity partitioning) corresponding with very low tensions (Figure 22). This causes the tension gradients to become practically zero, and the dilational elasticity is thus very low at the optimum point, so coalescence occurs almost instantly, as if no surfactant were available to stabilize the emulsions. The distribution of surfactant between the continuous and dispersed phases significantly affects film thinning dynamics. It is essentially the same to say that surfactants that are more soluble in an external continuous phase, i.e., in emulsions O/W or W/O out of optimum formulation, contribute to more stable emulsions due to stronger Marangoni effects [166].

Bancroft’s Rule stated about 100 years ago that the phase in which the surfactant is more soluble tends to become the continuous phase of the emulsion [167]. Hildebrand provided a rationale for this observation, emphasizing the importance of surfactant availability in the continuous phase for stabilizing thin films [168], stating the following:

“Why does the film resist rupture better when the soap in the interfaces comes from the film solution than when it comes from the larger reserve in the droplet? The answer I suggest is that there is very little soap available in a thin film to migrate to the new surface and weaken it, while there is an ample supply if it is soluble in the liquid outside of the film” [168].

Ivanov and co-workers developed a theoretical framework for interdrop film thinning, considering the role of surfactant transport and Marangoni effects [169]. They proposed two cases: (Case 1) A surfactant in the continuous phase leads to slow film thinning due to sustained surface tension gradients and strong Marangoni forces opposing thinning. (Case 2) A surfactant in the dispersed phase results in rapid film thinning because the surfactant quickly replenishes the interface, eliminating surface tension gradients and reducing Marangoni stresses [169].

Sonin et al. [115] found that there are no surface bulk exchanges in thin films, with E presenting its intrinsic value. Traykov et al. [170] conducted experiments on emulsion films and found that films thinned more slowly and were more stable when the surfactant was present in the continuous phase. This confirmed the theoretical predictions of Ivanov’s model. Despite high surfactant concentrations, in emulsions formed from Winsor III systems, phases separate rapidly [171,172,173]. In SOW systems the very low interfacial tension close to optimum essentially eliminates the formation of tension gradient and thus excludes the Marangoni effect because of the very fast surfactant exchanges between the bulk and the interface [59].

Surfactant-polymer enhanced oil recovery processes are used to increase recovery factors in wells where natural lift, artificial lift, and steam injection methods are insufficient to displace crude oil trapped by capillary forces in reservoir pores. When surfactant is injected, and an ultra-low interfacial tension situation is achieved, the interface deforms due to this low tension, leading to oil displacement through reservoir pores because of higher capillary numbers [101,174,175]. This is also due to the nature of the contact angle between the oil and the rock surface [81], i.e., problems of wettability not only of the solid but at the three-liquid interface that was found to depend on HLD.

Since the 1970s it has been stated that in addition to ultra-low tension, low interfacial elasticities and viscosities also favor oil displacement [147,176,177,178]. Freer et al. [81] related interfacial rheology and the formation of “rigid skins” with reservoir mixed wettability. Additionally, some authors have recently indicated that interfacial rheology is an important property for analyzing “smart waterflooding” applications [179,180,181].

Botti et al. [23] recently investigated the impact of interfacial rheology on drop coalescence in water-in-oil emulsions. Utilizing oscillating drop methods and rheological tests, they varied the concentration of Span 80 surfactant from 0.5 wt.% to 2 wt.% and monitored interfacial tension alongside dilational and shear moduli. The study identified three distinct time regimes in the evolution of the elastic modulus: an initial plateau, an increase in elasticity, and a subsequent loss of elasticity. At high surfactant concentrations (>>CMC), the formation of a solid-like interfacial film prevents the coalescence between approaching drops or bubbles. The elastic modulus increases with surfactant concentration, thus enhancing emulsion and foam stability. For instance, in the reference article [23], at 2 wt.% Span 80, the elastic modulus reached up to 4.80 mN/m after approximately 410 s, while the loss modulus decreased to near zero at longer times. These findings demonstrated that higher surfactant concentrations accelerate the formation of solid-like interfacial films, effectively preventing droplet coalescence by enhancing interfacial elasticity.

Foam stability is also mainly influenced by the resistance to film deformation due to the presence of tension gradients and the Gibbs–Marangoni effect. In these phenomena, the formation of plateau borders, areas where the surfactant migrates due to film thinning, creates surfactant concentration gradients [146,182]. Additionally, the use of polymers with interfacial activity contributes to forming interfaces with higher surface shear viscosity, thus increasing foam stability. For this reason, both surface viscosity and elasticity play a significant role in foam stabilization [54,59]. An increase in dilational elasticity is directly related to increased foamability (amount of foam formed), foam stability (from breaking time), and longer film drainage time. Foam breakage is related to the thinning and destabilization of the liquid film between adjacent bubbles, a phenomenon that occurs more easily when surface elasticity is low [121]. For readers seeking a more comprehensive understanding of these phenomena, recent works by Langevin et al. on the subject have extensively examined the influence of interfacial rheology on the stability of foams [20,70,183,184,185,186,187].

The lifetime of foams is also influenced by the resistance to film deformation due to the presence Gibbs–Marangoni effects. The foam structure does not exhibit the liquid–liquid symmetry as emulsions, and thus an HLD concept cannot be used [188,189]. However, it seems that the same effects are found on the water side, i.e., when the surfactant has preferred interactions with water, as in the HLD negative case. In such an analogy there is a formulation at which the foam stability tends to zero, as it does with emulsions when HLD tends to zero. Nobody has yet proposed an equivalence of the EACN for a gas phase, but it is likely to happen in the future, because it would be useful to make more comparisons between emulsions and foams, particularly in the case of CO₂ foams which are used in EOR.

In high-pressure systems involving water, surfactants, and CO₂, foam stability has been recently studied for EOR applications. Benali et al. [190], studied the dense phase of CO₂ under high-pressure conditions (100 bar and 23 °C) and how it influences aqueous foam stability when nonionic surfactants were used. At elevated pressures, CO₂ exhibits properties such as increased density and viscosity, which significantly alter interfacial dynamics and foam behavior (Figure 23). Johns et al. have included a pressure parameter in the HLD equation [191,192]. Foam destabilization mechanisms, such as lamella rupture (coalescence), are exacerbated in dense-phase CO₂ systems. Langevin et al. [193] have explained similar mechanisms and the impact of interfacial properties on foam stability, particularly the thinning and rupture of lamellae under stress. Interestingly, this behavior mirrors trends observed in systems where the continuous phase resembles an oil-like phase: as the CO₂ phase becomes denser, the foam stability diminishes, likely due to reduced surface tension gradients and altered capillary forces. The consistent destabilization pattern of dense-phase CO₂ foams indicates the importance of understanding interfacial rheology and phase behavior in such complex systems.

5.2. Interfacial Rheological Properties to Study Asphaltene Behavior at Interfaces for Water in Crude Oil Emulsion Breaking

Extensive research has been conducted to elucidate the factors influencing the interfacial rheology of asphaltene-stabilized emulsions. Asphaltenes are slightly amphiphilic species that tend to aggregate at the oil–water interface, forming viscoelastic films with high mechanical resistance that have been shown to resemble protein gel-like networks [20,142,143]. Studies typically involve diluting crude oil in solvents such as toluene or cyclohexane or dissolving extracted asphaltenes in these solvents to simplify the complex mixture. Among the properties that have been measured are shear elasticity and dilational elasticity. However, discrepancies and inconsistencies in literature often arise due to variations in experimental methodologies, measurement techniques, and the inherent complexity of asphaltene molecules and their aggregation structures. Dilational and shear interfacial moduli increase over time due to the progressive formation and restructuring of asphaltene aggregate films at the interface. This aging process leads to more rigid interfacial films, significantly impacting emulsion stability by enhancing resistance to droplet coalescence and inhibiting film drainage [79,81,84]. Studies have demonstrated that dilational elasticity (E) can increase continuously over extended periods, sometimes exceeding 20 h, due to ongoing asphaltene adsorption and reorganization [84,85]. The formation of viscoelastic interfacial films results in highly dissipative interfaces, accurately described by models such as the Boussinesq–Scriven framework [194]. Dilational elasticity increases with asphaltene concentration, with a maximum typically between 1000 and 10,000 ppm. Beyond this concentration, further increases may lead to a decline in elasticity due to aggregation and the formation of a 3D gel-like network [195]. At low concentrations, asphaltenes adsorb as monomers or small flattened aggregates, which can form a monolayer that enhances elasticity. Higher concentrations lead to the formation of larger micellar aggregates or multilayer thick structures, reducing film flexibility and elasticity due to steric hindrance and decreased molecular mobility at the interface [196,197]. The presence of rigid, 3D interfacial films is often due to the formation of clusters by flocculation of the first asphaltene aggregates [198,199,200,201], and contributes significantly to the high stability of water-in-crude oil emulsions.

Higher molecular weight asphaltenes tend to increase shear and dilational elasticity due to stronger intermolecular interactions at the interface. Larger molecules have extensive aromatic ring systems and functional groups that facilitate π–π stacking and hydrogen bonding, leading to more rigid interfacial films [78,202]. The polarity of the oil phase significantly affects asphaltene behavior. In less polar solvents (e.g., cyclohexane, heptane), asphaltenes are less soluble, promoting their adsorption at the interface and increasing interfacial elasticity and emulsion stability [141,203,204]. Conversely, in more polar aromatic solvents like toluene, asphaltenes remain dissolved in the bulk, resulting in lower interfacial activity. Resins act as peptizing agents, stabilizing asphaltenes in the bulk and reducing their adsorption at the interface. Increasing the R/A ratio leads to decreased shear or dilational elasticity and potentially reduced emulsion stability [195,202,205]. Increasing aqueous phase salinity increases shear and dilational elasticity by screening electrostatic repulsions between asphaltene molecules at the interface. Thus, higher electrolyte concentrations facilitate closer packing and stronger intermolecular interactions [206,207,208]. Variations in pH affect the ionization of acidic and basic functional groups in asphaltenes, influencing their interfacial activity and film properties. At pH levels significantly below or above neutral (pH < 7 or pH > 7), increased ionization enhances asphaltene adsorption at the interface, leading to higher elastic modulus E′ and increased emulsion stability because of electrical repulsions of approaching interfaces [155]. Recent measurements [140] show how the dilational modulus at a crude oil–water interface increases from ~5 mN/m to over 30 mN/m upon aging, correlating with stable water-in-oil emulsions. Alicke et al. [139] found that asphaltene subfractions can yield G′ values of 10–60 mN/m, forming viscoelastic “skins” that greatly impede coalescence. When adding surfactants for crude oil dewatering, the phenomena are more complex. At the optimum formulation the lifetime of emulsions has been found to be minimum, which has been related with a minimum of the dilational moduli measured recently with the oscillating spinning drop interfacial rheometer [91,135,143]. A review on the subject was published recently [209].

6. Conclusions and Perspectives

The present work provides a critical review of experimental methods to measure interfacial rheology, specifically in dispersed systems stabilized by surfactants such as emulsions and foams. Deep channel viscometers can measure interfacial shear viscosities in water–crude oil systems with viscosities ranging from 10⁻¹ to 10² mN/m⋅s, while bicone rheometers provide accurate results for viscosity and elasticity, typically in the range of G′ (elastic modulus) = 1 to 100 mN/m. Oscillating pendant drop methods can measure dilational moduli (E′) in the range of 1 to 100 mN/m for oil–water systems. On the other hand, the oscillatory spinning drop rheometer allows measuring dilational moduli as low as 10⁻² mN/m, with rotational speeds between 3000 to 10,000 rpm, making it the only technique capable of handling ultra-low tension systems. These methods have shown interfacial tension values as low as 10⁻⁴ mN/m, for applications such as enhanced oil recovery (EOR) or crude oil dehydration, where systems near the optimum formulation (HLD = 0) can present interfacial tension reduction of around three orders of magnitude. In applications such as cosmetics, pharmaceuticals, and petroleum, dilational elasticity values greater than 10 mN/m significantly delay film rupture in foam systems, while interfacial viscosities (η_S) exceeding 100 mN/m⋅s in emulsions result in higher resistance to droplet coalescence. In EOR processes such as smart waterflooding techniques, particularly in low interfacial tension systems, small dilational moduli (E′ ≈ 10⁻² to 5 mN/m) could favor oil displacement. Nowadays, research is focusing on developing more sensitive interfacial rheometers and extending current techniques to complex multi-phase systems such as particle stabilized ones [30], including nanocellulose and lignin nanoparticles for formulation optimization in diverse industries, including cosmetics, fuels, pharmaceuticals, and many other applications [7,12,24,210,211,212,213]. Also, machine learning and interfacial intelligence models have been recently used to calculate faster and with higher precision dynamic interfacial tension from drop-shape analysis [125], which may indicate the probability of exploration of more sensitive methods for complex fluids such as when oxidized molten metals or particles are present, disturbing the surface shape evaluation [214].

Future studies could benefit from a comparative analysis of interfacial rheological properties measured using different techniques. For example, directly measuring the shear modulus G with a bicone rheometer and the dilational modulus E with a pendant drop method would allow for the calculation of the combined modulus E + G obtained from the oscillatory spinning drop technique. Such an approach could verify the consistency of the moduli across different methods and provide deeper insights on the behavior of the phase angle in novel methods. Also, the measurement of the rheology of interfacial layers with the oscillatory spinning drop in polymer/surfactant/crude oil (SP) systems for enhanced oil recovery (including low salinity water [15,215]) may shed light on better correlations to predict oil recovery in SP flooding.