Film drainage, essential in droplet and bubble coalescence and surface wetting, is influenced strongly by the stress boundary condition, in particular, when interfacial stresses are present. These stresses, caused by ubiquitous surface-active components, significantly impact the dynamics of liquid films. Through dynamic thin film balance experiments, we compare the effects of Marangoni stresses, interfacial viscosity, and interfacial viscoelasticity on the drainage of free-standing thin liquid films. These data serve to demonstrate that film deformation intricately depends on the interplay between these stresses and capillarity, resulting in widely varied drainage times. Seemingly subtle changes, especially in the local stress-carrying capacity of the interface, can lead to significant differences in film dynamics. This makes it a promising area for research into interfacial-rheologically active materials for stabilizing potentially more sustainable multiphase materials.

Film drainage, a ubiquitous physical phenomenon, plays an important role in a multitude of processes, such as bubble and droplet coalescence, the longevity of antibubbles, and the wetting of solid surfaces [1–4]. These phenomena are encountered across diverse applications, from inkjet printing to stability issues in monoclonal antibody formulations [5,6], the generation of aerosols [7], the rheology of emulsions and foams [8,9], the evolution of structure in polymer blends [10,11], and the stability of multiphase food products [12]. Notably, the liquids under consideration in these applications are seldom pure, giving rise to complex interfaces between liquid/liquid or air/liquid phases that inherently carry stresses. These stresses, arising from an array of sources, can significantly prolong the time scales of film drainage and thus in many cases control the macroscopic stability of the respective multiphase materials [13]. For example, surfactants are well known to cause Marangoni stresses through surface concentration gradients [14,15], but film stability is also significantly affected by interfacial shear and dilatational viscoelasticity [13]. Regulatory and sustainability requirements are driving us away from the ideal surfactants in terms of interfacial stability. This necessitates the development of new engineered materials, with, for example, enhanced interfacial rheological activity, to counteract reduced effects on interfacial tension.

The complex interplay between interfacial stresses, capillarity, hydrodynamics, and intermolecular forces however complicates the complete understanding of thin film drainage [13]. For simple interfaces, in which bulk viscous stresses dominate, the film drainage problem has been thoroughly examined both experimentally and theoretically (see, e.g., Chatzigiannakis et al. [13] for a review of recent work). Leal and co-workers, in a series of articles involving polymer/polymer interfaces, showed that droplet coalescence can be tackled only if it is divided in an outer problem of droplet collision and an inner film drainage problem [16]. Using scaling relations and the lubrication approximation, they showed that the drainage rate of a film deformed at sufficiently high stresses, such that a dimple develops, is approximately equal to [17]
d h d t h 3 Δ P η R f 2 α ,
(1)
where h is the thickness of the film, R f is its radius, Δ P is the pressure drop that drives drainage, and η is the viscosity of the film’s phase. The “mobility factor” α is a parameter that was introduced to capture deviations from the no-slip boundary condition at the film’s interface and is thus directly connected to the stress-boundary condition [13], for example, through the Boussinesq–Scriven equation [18],
η υ r z = σ r + ( η s + η d ) r [ 1 r r υ r , s r ] ,
(2)
where υ r is the radial component of the velocity in the film’s phase, υ r , s is the radial velocity of the air/liquid interface, η s is the interfacial shear viscosity, η d is the interfacial dilatational viscosity, and σ is the surface tension, which a state variable that depends only on the (local) surface concentration ( Γ) and temperature ( T). However, the total surface stress, influenced by the extra stresses, is not a state variable. The time dependence of the overall stress can arise from various factors, such as global concentration variations causing spatial and temporal changes in tension due to transport phenomena but also due to strain or strain rate dependency of the interfaces rheological response [19].
One important aspect in the analysis of Leal and co-workers is that the film radius in Eq. (1) is a direct consequence of the deformation of the droplets and thus depends on the “outer problem” of droplet collision. Thus, upon integration of Eq. (1), the dimensionless drainage time t = t d Δ P / η is t C a n, where n is a constant with a value close to unity [17], t d is the drainage time, and C a is the capillary number that describes the ratio between the viscous and the capillary stresses, defined here as [20–22]
C a = Δ P 2 σ / R η υ R 2 σ h 2 ,
(3)
where Δ P is the pressure that drives drainage, R is the radius of the bike-wheel’s hole, or equivalently of the mimicked bubble, and υ is the characteristic velocity. Equation (3) indirectly expresses the shape of the film. A planar film is expected for C a 1 and a dimple (i.e., the thickness of the film is higher at its center region than at its rim) is expected to emerge for C a > 1.

However, another and less obvious aspect is that for deformable droplets, the initial thickness of film formation h 0, the initial thickness at which the dimple is formed, h d, and the radius of the film, R f, depend not only on the Capillary number, but also on the stress-boundary condition at the interface of the droplet [Eq. (2)]. To motivate the importance of droplet deformability, we will start with the simplest possible case in which interfaces are simple and interfacial stresses are controlled by the viscosity ratio of the two phases λ = η d r o p / η, where η d r o p is the viscosity of the droplet [23,24] and we will then extend to complex interfaces.

For simple interfaces, the dependence of droplet deformability on λ is described by a function f ( λ ) that can be determined from the mobility functions describing the hydrodynamic forces exerted on two colliding droplets [25–27]. Using scaling analysis again, it was shown that R f f ( λ ) C a 1 / 2 and h 0 f ( λ ) C a [23]. Following the analysis of Baldessari and Leal [27] and using the mobility functions calculated in [25] and [26], we calculated f ( λ ) for viscosity ratios in the range of 10 5 up to 100 (see supplementary material). The polymeric systems studied by Leal had λ O ( 10 2 10 0) [28] and thus this function exhibited a very small dependence of f ( λ ) λ 0.1 [23]. As a consequence, the overall effect of f ( λ ) on drainage was deemed negligible. However, this is not necessarily the case for systems that have larger viscosity ratios or have complex, rather than simple, interfaces (Fig. S4 in the supplementary material).

As we will show in this study, the intricate relationship between the deformation of the droplet and film drainage, which was simply expressed in Leal’s work by f ( λ ), vastly affects the drainage of films with complex interfaces (the inner problem). Compared to simple interfaces, complex ones are likely to show a more rich dynamic behavior, affected by the changing surface excess properties over time, along with local deformation rates and amplitudes. Therefore, the shape of a droplet with a Newtonian interface [18] depends not only on C a and the viscosity ratio λ as studied by Cox [29], but also on the interfacial shear and dilatational viscosities and the magnitude of Marangoni stresses [30].

Using a first order perturbation analysis, Flumerfelt [30] showed that the shape of droplets with complex interfaces depends on an “effective viscosity ratio,” defined here as λ , that encompasses the effect of bulk viscous stresses, described by λ, as well as surface stresses. For small deformations, the latter were shown to depend linearly on the surface shear and dilatational viscosities, on the evolution of Marangoni stresses, on interfacial transport phenomena, and on the capillary number. Consequently, for most systems with complex interfaces, it is expected that λ 1. Following the analysis made previously for the case of simple interfaces, it can now be estimated that for λ O ( 10 2 ), it is f ( λ ) λ (see supplementary material), which is a much stronger dependence than what was expected for the simple polymer interfaces in Leal’s work. Therefore, in droplets or bubbles with complex interfaces, f ( λ ) will depend significantly on the spatiotemporal evolution interfacial stresses and affect remarkably film drainage by controlling the shape of the films.

The effect of interfacial stresses on film drainage and thus coalescence complicates further if one considers the final stage of the process, i.e., rupture. It has been predicted that interfacial stresses can promote or hinder instabilities related to rupture [31–33]. However, it is still unclear how exactly interfacial stresses, and specifically those related to viscoelasticity, affect film rupture.

Here, we experimentally explore how predominantly Marangoni stabilized, interfacially viscous, or clearly viscoelastic interfaces and the different development of interfacial stresses impact film drainage. We examine their interaction with capillarity across a range of relevant, albeit varying Capillary numbers, focusing on the drainage and deformation of free-standing films. Our results indicate that the type of interfacial stress greatly affects its spatial and temporal evolution. This finding challenges the validity of using filmwide time-averaged surface immobilization for films with complex interfaces, as opposed to simple interfaces [34,35]. Although the interfacial “immobility” assumption, i.e., a zero interfacial velocity, can even be used for simple, surfactant-free, interfaces under certain conditions [36], this does not hold true when complex interfaces are involved, even if similar experimental conditions are employed, at least not without involving more assumptions in the theoretical models used [37,38].

We find that the timing and manner of stress activation are crucial, especially during late drainage stages when films are thinnest and most unstable due to the attractive van der Waals interactions. At these late stages of drainage, Marangoni and viscoelastic stresses are particularly effective in stabilizing the film, suppressing the instabilities that might lead to the spontaneous rupture of simple films [39].

Both model surface viscous and surface viscoelastic interfaces are created in situ and their responses compared to those for well studied systems known to give rise to Marangoni stresses. For Marangoni stress-stabilized films, we used a low molecular weight, nonionic surfactant (polyoxyethylene ester—C12E8) at a concentration of 50 μ M. The respective films were prepared using adsorption from the bulk aqueous phase, which is the typical practice in the literature [40–42]. The surface viscosity is small and can be neglected, and the adsorption isotherm can be described by a Frumkin or generalized Frumkin isotherm [43–45],
Γ Γ = C a exp [ k ( Γ / Γ ) n ] + C ,
(4)
where Γ is the surface concentration, Γ = 5.5 × 10 10 mol / c m 2 is the maximum surface concentration, C is the bulk concentration, a is a prefactor that depends on the activation energies for desorption and adsorption, and is equal to 0.23 × 10 11 mol / cm 3, and n = 0.5 [43]. The spatial and temporal dependencies of Γ ( r , t ) are representative of the propensity to develop Marangoni stresses [46].

Predominantly viscous films were formed by applying two 0.5 μ L droplets of 1 g L 1 hexadecanol dissolved in isopropanol onto a water film in the dynamic thin film balance (DTFB). Its interfacial behavior at this concentration can be described by a Boussinesq–Scriven equation [Eq. (2)] with a surface shear viscosity equal to η s = 5 × 10 4 Pa m s, a surface dilational viscosity η d = 1 Pa m s, a Gibbs modulus (compressibility) of about 200 mN/m, and small to negligible surface shear modulus [47–49].

Surface viscoelastic films were created using multilayers of poly(vinylpyrrolidone)-poly(methacrylic acid) (PVP/PMAA), prepared by a sequential adsorption protocol, following the work of Monteux and co-workers [49,50]. The preparation of the PVP/PMAA films was done using a layer-by-layer deposition protocol, similar to [51]. The solutions of PMAA (molecular weight M w = 100000 g / mol) and PVP ( M w = 30000 g / mol) were prepared by dissolving each polymer in de-ionized water (Millipore Milli-Q system, USA, resistivity 18.2 M Ω cm at 25  °C) at a concentration of 1 wt.  established by using a 1M solution of hydrochloric acid or a 1M solution of sodium hydroxide. At this pH, both hydrogen bonds and hydrophobic interactions between the two polymers are maximum [50] and the rheological response of the surfaces is expected to be the strongest. The glass transition temperature of both polymers is well above 100 ° C [52,53] and thus no plasticization is expected during our experiments [54]. Rather hydrophobic interactions and hydrogen bonding are responsible for the viscoleastic response [49,50].

The PVP/PMAA films can be characterized by a neo-Hookean model [51], with η s = 3 × 10 2 Pa m s, η d = 80 Pa m s, a compression modulus K = 170 mN / m, and a surface shear modulus G = 40 mN / m [49,51].

The rest of the surface properties of all systems have been reported in the studies mentioned above and the material parameters are hence known. Further information regarding the materials employed here can be found in the supplementary material.

Film drainage experiments were conducted with the DTFB technique [55], which is a modified version of prior-developed TFB techniques [56–58] and allows the precise control of the pressure that drives film drainage, Δ P. By controlling the pressure in the air phase Δ P, we can explore a relevant range of Capillary numbers C a [Eq. (3)]. A detailed description of the setup, including a pressure balance that describes all the contributions during film drainage, can be found in [55].

Films were initially created and then thinned under the application of a constant external pressure ranging from Δ P = 50 up to 600 Pa. Film drainage was monitored using microinterferometry [59] with an employed monochromatic wavelength of 508 nm. The general principles of the technique and the experimental protocol can be found elsewhere [55], while the detailed methodologies for the systems studied here are outlined in the supplementary material. In the following, we will mainly discuss data that correspond to experiments for C a > 1 where the interplay between capillarity and interfacial stresses is more pronounced.

Interferometric imaging reveals distinct qualitative differences in film drainage, particularly when comparing the time evolution of three archetypal interfaces at C a 2, as shown in Figs. 1(e)1(g). The hexadecanol (viscous) and polymer-multilayer (viscoelastic) films exhibit symmetrical drainage, aligning with expectations for films with uniform stress response—often described as “immobile” interfaces [6,60] [Figs. 1(f) and 1(g)]. In contrast, the drainage of the Marangoni stabilized films proceeds symmetrically only for C a 1 and asymmetrically for C a > 1 [Figs. 1(a) and 1(e)]. This asymmetry is triggered by destabilization of the dimple, in agreement with previous observations on surfactant-laden films [60–64].

FIG. 1.

(a) A draining thin liquid film (not to scale). (b)–(d) Thickness profiles, i.e., dimensionless thickness h = h / R as a function of r = r / R, of the three different films as a function of time at C a 2. The C a 2 ensures that the films are dimpled and that R f < R. Note the completely different time scales involved in the drainage of each film. (e)–(g) Interferometric images of the films at various time intervals for C a 2. The scalebar is 100 μ m.

FIG. 1.

(a) A draining thin liquid film (not to scale). (b)–(d) Thickness profiles, i.e., dimensionless thickness h = h / R as a function of r = r / R, of the three different films as a function of time at C a 2. The C a 2 ensures that the films are dimpled and that R f < R. Note the completely different time scales involved in the drainage of each film. (e)–(g) Interferometric images of the films at various time intervals for C a 2. The scalebar is 100 μ m.

Close modal

Apart from the markedly different drainage type, Figs. 1(e)1(g) show that the time evolution of the radii and thickness profiles of the films vary substantially. By imposing the pressure that drives the drainage, we allow the film to select its deformation pathway and drainage state. This approach contrasts with other experimental methods where the flow rate or the film’s area is the controlled variable [36,65]. The differences in film shape over time can be more clearly represented by the time resolved, radially averaged thickness profiles [Figs. 1(b)1(d)]. The initial noticeable difference between the three film types lies in their initial dimensionless thickness h = h / R where we observe the formation of a planar film, which we define as the start of the film dynamics process t = 0 as h 0 . From scaling analysis, it is established that the dynamic regime of thin film dynamics begins when two approaching bubbles begin to deform as they come into proximity, and the hydrodynamic pressure P H is comparable to the capillary pressure 2 σ / R [66]. However, the hydrodynamic pressure P H in the thin film is influenced by the precise nature of the deformation of the bubbles, which is determined by the magnitude and nature of the stress boundary condition. As a result, surface viscous films, like those of hexadecanol, initially exhibit higher thickness (and deform less) because surface viscous stresses are instantaneous.

In contrast, Marangoni and viscoelastic stresses require time to develop. Marangoni stresses necessitate surface concentration gradients, which are absent at equilibrium t = 0. Similarly, extra stresses from surface elasticity only manifest when sufficient deformation occurs, and when it occurs faster than the characteristic time scale of the relaxation of the adsorbed polymer molecules. Initially, the deformation rate is slow, increasing as the film thins. Thus, the initial dimensionless thickness h 0 is comparatively low for both Marangoni and viscoelastic stress cases. This observation, especially for C12E8 films, aligns with simulations that predict a gradual buildup of surface stresses [67], but is also observed to act for the viscoelastic interfaces. Our results suggest that the time needed for the full development of Marangoni stresses in foam films can be as high as O ( 0.1 s ), orders of magnitude slower than what would be expected for emulsion films with λ > 10 2 at high enough surface Péclet numbers P e s = υ R f / D s 1, where D s is the surface diffusivity [67] (see supplementary material). The different spatial and temporal evolution of Marangoni stresses explains why nonionic surfactants similar to C12E8 have been shown to exhibit different magnitude of Marangoni stresses and thus of “average interfacial mobilities” depending on the set up and the conditions employed [37,40,68].

Intuitively, it might be expected that when the films form earlier, with a higher initial thickness ( h 0), that this would result in longer drainage times; however, this is not the case. In contrast, the drainage of the films of C12E8 and of the polymer multilayers strongly decelerated as the film became thinner, as can be seen from the evolution of the thickness profiles in Figs. 1 and 2(a). Although the viscoelastic and Marangoni stresses come into play later, their local stress-carrying capacity—acting efficiently where the film is most deformed—leads to substantially extended overall drainage duration and a crossover behavior is observed [Fig. 2(a)].

FIG. 2.

(a) Evolution of the initial thickness for the three different films draining at C a 2. The dimensionless time is t = t Δ P / η. (b) The long-time evolution of the thickness of the Marangoni-C12E8 film that drains under the influence of Marangoni stresses at C a 2. (c) The long-time evolution of the thickness of the viscoelastic—PVP/PMAA film that drains under the influence of extra viscoelastic stresses drains at C a 2. In all cases, solid lines correspond to the thickness at the rim of the film ( h min ) and the dotted lines correspond to the maximum thickness ( h max ) at the center of the dimpled film.

FIG. 2.

(a) Evolution of the initial thickness for the three different films draining at C a 2. The dimensionless time is t = t Δ P / η. (b) The long-time evolution of the thickness of the Marangoni-C12E8 film that drains under the influence of Marangoni stresses at C a 2. (c) The long-time evolution of the thickness of the viscoelastic—PVP/PMAA film that drains under the influence of extra viscoelastic stresses drains at C a 2. In all cases, solid lines correspond to the thickness at the rim of the film ( h min ) and the dotted lines correspond to the maximum thickness ( h max ) at the center of the dimpled film.

Close modal

The long-term thinning of the C12E8 film at C a 2 at the rim and in its thickest part is shown in Fig. 2(b). This process undergoes a transition from symmetric to asymmetric drainage, marked by a sudden decrease in the maximum thickness h max caused by the wash-out of the dimple. This leads to significant surfactant surface concentration gradients, causing recirculation of bulk liquid within the film and resulting in thickness corrugations [see also Movie S1 (supplementary material)]. These dynamics create strong Marangoni flows that notably slow down the drainage at thicknesses below 60 nm, in line with previous observations [68,69].

For the surface viscoelastic polymer multilayers, the drainage patterns and dynamics differ. Here, the dimple remains stable and drains slowly, while the thickness at the rim is almost unchanged over extended periods [Fig. 2(c)]. The almost constant minimum thickness is indicative of highly stress-carrying interfaces and hints toward an augmented contribution by extra viscoelastic stresses that arise when film thickness is small and thus the interfacial deformation rates fast.

In addition to the thickness profile, examining the evolution of the radius of the thin film region provides valuable insights [Fig. 3(b)]. The radius of the film is also controlled by the interplay between the local hydrodynamic pressure inside the film, capillarity, and interfacial stresses and is crucial for the overall drainage time, given that t d R f 2 [Eq. (1)]. At early times, the expansion of the three different films is similar as can be seen from the time evolution of R in Fig. 3(b). For t > 10 4, the evolution differs, in contrast to films with stress-free interfaces [70]. The C12E8 films gradually expand in size until they reach a constant value of R = R f / R 0.75. This value tends toward the value expected for mechanical equilibrium R e q = [ 1 1 / ( 1 + C a ) ] [71].

FIG. 3.

(a) Film expansion over time for C a 2. For the PVP/PMAA films, expansion is halted at a t that corresponds to D e s 1. (b) The deformation parameter D f as a function of applied C a for all three types of films.

FIG. 3.

(a) Film expansion over time for C a 2. For the PVP/PMAA films, expansion is halted at a t that corresponds to D e s 1. (b) The deformation parameter D f as a function of applied C a for all three types of films.

Close modal
In contrast, the PVP/PMAA films reach a much smaller constant radius of R 0.3. To affirm that the halting of film expansion originates from surface viscoelasticity, we introduce a surface Deborah number,
D e s = d h d t τ h ,
(5)
where d h / d t is the local thinning rate, h is the measured thickness at the rim, and τ = 35 s is the characteristic relaxation time of the PVP/PMAA multilayers as obtained by interfacial shear rheometry [51]. For all PVP/PMAA films at C a 1, film expansion halted when D e s 1, indicating that surface viscoelastic effects come into play when the deformation rate of the interface is faster than the characteristic relaxation time of the adsorbed polymer chains.

The thinning velocity at the rim of the film, which is crucial in determining the overall drainage time, is governed by the interplay of interfacial stresses with the film’s radius and thickness. Hexadecanol films drain faster, despite having interfaces with high average stress carrying capacity. This can be caused by the fact that the film’s dimple is relatively small both in height and in area [Figs. 1(c) and 2(a)] and the fact that the film does not expand a lot, leading to a facile drainage of the bulk liquid from the thin film region. Thus, the relatively high h 0 of these files does not considerably prolong their drainage time.

In contrast, the C12E8 films drain slowly when their thickness is small and the film keeps expanding in radius. Moreover, the Marangoni stresses act where the film is strongly deformed [67,72,73]. As a result, the overall drainage time is longer, despite the rather small initial h 0. Specific mention must be given to the PVP/PMAA films. As mentioned above, the extra viscoelastic stresses cause the expansion of the film to halt, which is different from the Marangoni stress case. However, the TFB experiments are conducted at constant applied pressure (or C a) rather than a constant flow rate [74] or film radius [65], which means that the film is allowed to attain freely the preferred deformation state. The halting of the film expansion results thus in a pronounced dimple [Fig. 1(d) and specifically t = 1.99 s]

In addition to analyzing the evolution of the film’s radius, it is equally important to characterize the film’s deformation. As mentioned earlier, deformation plays a pivotal role in film drainage. It can be described by a Taylor-like [75] deformation parameter,
D f = h max h min R R f ,
(6)
where the geometrical characteristics of the film are shown in Fig. 1(a). The higher the D f, the stronger the deformation of the film (i.e., the film is more dimpled). The maximum D f during drainage for the various C a is shown in Fig. 3(b). Two distinct regimes are observed based on the capillary number. At low C a, the maximum deformation of the C12E8 films is smaller than both the hexadecanol and the PVP/PMAA films. At low C a, the surface Péclet number P e s = υ R f / D s is also low. This indicates that Marangoni stresses are not sufficiently strong to generate high hydrodynamic pressure inside the film to counterbalance capillary forces [14,76]. The situation is quite different at higher C a. Here, Marangoni stresses are more influential, leading to greater film deformation. The larger film radii significantly affect the deformation factor D f. In contrast, surface-viscous films, like those with hexadecanol, show considerably less deformation, aligning with existing reports [77,78]. The PVP/PMAA films exhibit strain-hardening, resulting in smaller film radii but significantly higher dimple heights, thus leading to a high D f across the examined C a range.

This interplay results in significant differences in the dimensionless drainage time ( t = t d Δ P / η) (Fig. 4). The t C a scaling is observed, in agreement with the past studies [23,79,80]. According to the existing literature results [14,81], large deviations in the observed t C a scaling are only expected when catastrophic changes in the stress-boundary condition take place, i.e., when a transition from no-slip to full-slip occurs. In the thin film balance experiments, all systems presented here were chosen to specifically avoid such effects [51,60,68] at least within the range of C a numbers that we examined.

FIG. 4.

The dimensionless drainage time t as a function of C a for the three film types. Solid lines correspond to t C a.

FIG. 4.

The dimensionless drainage time t as a function of C a for the three film types. Solid lines correspond to t C a.

Close modal

Despite the similar t C a scaling observed for all systems, the actual drainage time for the PVP/PMAA films is markedly higher. The spatial and temporal evolution of interfacial stresses impacts the film shape and, consequently, the local drainage rate, which determines the film’s lifespan. The Marangoni stresses and viscoelastic stresses get to work where the interfaces are being mostly deformed, leading to an efficient drainage rate decrease.

As discussed in Sec. I, differences in t at a constant C a and the same stress-boundary condition are also expected in films with simple interfaces (i.e., with stress continuity being valid across the interface). In such cases, the overall drainage has been modeled by coupling the “inner” drainage problem to the “outer” droplet deformation [27,80], the latter being described by mobility functions [25,26]. The influence of this coupling was rather small in Leal’s seminal work given that the surface stresses were exclusively related to the somewhat similar viscosities of the two phases. However, for bubbles or droplets with stress-carrying interfaces, like those in our study, the interplay between film deformation and drainage is more complex and pronounced, in line with ideas coming from numerical simulations [30,82].

This interplay, however, also means that theoretical models of film drainage that neglect the effect of interfacial stresses on droplet deformation and thus on the hydrodynamic forces between interacting droplets or bubbles should be used with extreme care when the experiments involve complex interfaces. One notable such example is the Derjaguin approximation, i.e., the expression that connects the force exerted between two colloidal objects with the interaction free energy per unit area [83,84], which has been traditionally used in studies with atomic force microscopy mostly on droplets or bubbles with simple interfaces [3,36,85]. Extending this technique to droplets with complex interfaces might require revalidating this main approximation, as also pointed out by Chan et al. [86,87], and partially done by Danov et al. [88].

Finally, interfacial stresses are expected to affect significantly the critical thickness at which rupture occurs due to the attractive van der Waals interactions [33]. Due to the system-specific heterogeneities in film thickness, our results cannot provide more insight regarding the rupture of films with surface stresses. Yet, it is clear that the spatial and temporal evolution of both Marangoni and extra viscoelastic stresses will impact rupture too, further complicating processes like bubble and droplet coalescence [89–92].

Experiments on thin film drainage with interfaces exhibiting different interfacial stresses, including those from viscoelasticity, show that these stresses subtly, but significantly, affect film deformation. This dynamic interplay critically determines film stability and leads to significant variations in drainage time, sometimes by orders of magnitude and this will influence the macroscopic stability of multiphase products. Of course, the view presented in this perspective is still rather coarse grained, and the classification of the films as viscous, viscoelastic and Marangoni stabilized leaves much room for further studies, for example, to investigate the role of strain hardening, rate dependent thinning, or the role of the relative values of dilational and shear properties, due to the presence of specific structures or anisotropy. Although our study provides clear insights into the subtle role of interfacial stresses on film drainage and bubble coalescence, a quantitative analysis of the exact mechanism by which interfacial stress act is most likely only possible by experiments coupled to numerical simulations that include appropriate constitutive models for the rheologically complex interfaces and span toward long drainage times. Yet, our results already suggest that when designing surface active agents aimed at slowing down film drainage, it is most efficient to engineer mechanical responses that robustly resist localized deformations, either by a strong reaction to concentration gradients or by having a strain hardening response. These mechanical responses are controlled by the characteristic times for the evolution of Marangoni stresses and the viscoelastic relaxation, respectively, and can thus be tuned by optimizing the structure of the interfacially active species. This is an exciting area for efficient design of interfacial-rheologically active materials (interfacial rheological-actants) in stabilizing potentially sustainable multiphase materials: think local and act global!

The authors have no conflicts to disclose.

See the supplementary material online for additional experimental results, a detailed description of the methods and materials used, a comparison with past studies, and the movies of the film drainage experiments.

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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