It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for description of the film drainage and classifies all the known results from the literature. The obtained general expression for the thinning rate is a heuristic one and predicts variety of drainage models, which are even difficult to simulate in practice. It is a typical example of a scaling law, which explains the origin of the complicate dependence of the thinning rate on the film radius.
A brief review of the classical theory of foam film drainage is presented as well as a new theory accounting for the effect of thickness non-homogeneities in the film developed by the film drainage.
The present work is trying to explain a discrepancy between experimental observations of the drainage of foam films from aqueous solutions of sodium dodecyl sulfate (SDS) and the theoretical DLVO-accomplished Reynolds model. It is shown that, due to overlap of the film adsorption layers, an adsorption component of the disjoining pressure is important for this system. The pre-exponential factor of the adsorption component was obtained by fitting the experimental drainage curves. It corresponds to a slight repulsion, which reduces not only the thinning velocity as observed experimentally but cor…
Gravitational drainage of vertical films supported on a wire frame of superspreader SILWET L-77 and its cousin non-superspreader SILWET L-7607 revealed drastic differences. The superspreader films showed complicated dynamic turbulent-like interferometric patterns in distinction from the ordered color bands of the cousin non-superspreader which reminded those of the ordinary surfactants. Nevertheless the superspreader films stabilized themselves at the thickness below 50 nm and revealed an order of magnitude longer life time before bursting compared to the cousin non-superspreader. Notably, the…
Soap bubbles are by essence fragile and ephemeral. Depending on their composition and environment, bubble bursting can be triggered by gravity-induced drainage and/or the evaporation of the liquid and/or the presence of nuclei. They can also shrink due to the diffusion of the inner gas in the outside atmosphere induced by Laplace overpressure. In this paper, we design bubbles made of a composite liquid film able to neutralize all these effects and keep their integrity for more than one year in a standard atmosphere. The unique properties of this composite film are rationalized with a nonlinear…
The prediction of the lifetime of surface bubbles necessitates a better understanding of the thinning dynamics of the bubble cap. In 1959, Mysel \textit{et al.} \cite{mysels1959soap}, proposed that \textit{marginal regeneration} i.e. the rise of patches, thinner than the film should be taken into account to describe the film drainage. Nevertheless, an accurate description of these buoyant patches and of their dynamics as well as a quantification of their contribution to the thinning dynamics is still lacking. In this paper, we visualize the patches, and show that their rising velocities and si…
Coalescence of micrometer-scale droplets is impacted by several parameters, including droplet size, viscosities of the two phases, droplet velocity and angle of approach, as well as interfacial tension and surfactant coverage. The dynamics and thinning of films between coalescing droplets can be particularly complex in the presence of surfactants, due to the generation of Marangoni stresses and reduced film mobility. In this work, a microfluidic hydrodynamic Stokes trap is used to gently steer and trap surfactant-laden micrometer-sized droplets at the center of a cross-slot. Incoming droplets …
The thin-liquid film drainage between two curved surfaces is a fundamental process for many hydrodynamic measurements, for which Vinogradova's formula has played a central role when flow slip occurs at fluid-solid interfaces. By performing a rigorous order-of-magnitude analysis, we reveal the importance of the curvature contribution to boundary flow, neglected sofar. Vinogradova's result is found to considerably underestimate the slip-induced reduction of the hydrodynamic drainage force. Our theory can play a crucial role in distinguishing finite-slip from no-slip and quantifying the degree of…
We investigate the effect of loading rate on drainage in molecularly thin films of a simple fluid made of quasi-spherical molecules (octamethylcyclotetrasiloxane, OMCTS). We find that (i) rapidly confined OMCTS retains its tendency to organize into layers parallel to the confining surfaces, and (ii) flow resistance in such layered films can be described by bulklike viscous forces if one accounts for the existence of one monolayer immobilized on each surfaces. The latter result is fully consistent with the recent work of Becker and Mugele, who reached a similar conclusion by analyzing the dynam…
We present a theoretical and experimental investigation of drainage in porous media. The study is limited to stabilized fluid fronts at moderate injection rates, but it takes into account capillary, viscous, and gravitational forces. In this theory the work applied on the system, the energy dissipation, the final saturation and the width of the stabilized fluid front can all be calculated if we know the dimensionless fluctuation number, the wetting properties, the surface tension between the fluids, the fractal dimensions of the invasion front and the invading structure, and the exponent descr…
Surfactants in aqueous solutions self-assemble in the presence of salt, to form long, flexible worm-like micelles (WLM). WLM solutions exhibit viscoelastic properties and are used in many applications, such as for cosmetic products, drag reduction and hydraulic fracturing. The dynamics of bubbles in WLM solutions are important considerations for the stability of many of these products. In this manuscript, we investigate the thin film drainage dynamics leading up to the coalescence of bubbles in WLM solutions. The salts and surfactant type and concentrations were chosen so as to have the viscoe…
Flowing menisci: coupled dynamics and liquid exchange with soap films
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；INPHYNI（物理化学与界面研究所）；Université de Rennes（雷恩大学）；IPR (Institut de Physique de Rennes)（雷恩物理研究所）；Institut Universitaire de France (IUF)（法兰西学院）
Here, we report experimental results on the rupture of flat colloidal films over a large range of volume fractions, 0.00 $\le ϕ\le$ 0.47. The films are formed using a constant fluid volume, ruptured with a needle, and recorded using a high-speed camera. We show that colloidal films rupture in a manner quantitatively similar to Newtonian fluids, even well into the shear thinning regime. These results are consistent with the well-known mechanism of the rupture of Newtonian films, where the rupture rim rolls outward collecting more fluid and thus film rupture is a shear-free process. However, in …
The growth mechanism of pentacene film formation on SiO2 substrate was investigated with a combination of atomic force microscopy measurements and numerical modeling. In addition to the diffusion-limited aggregation (DLA) that has already been shown to govern the growth of the ordered pentacene thin films, it is shown here for the first time that the Schwoebel barrier effect steps in and disrupts the desired epitaxial growth for the subsequent layers, leading to mound growth. The terraces of the growing mounds have a fractal dimension of 1.6, indicating a lateral DLA shape. This novel growth m…
Thin liquid films are central to everyday life. They are ubiquitous in modern technology (pharmaceuticals, coatings), consumer products (foams, emulsions) and also serve vital biological functions (tear film of the eye, pulmonary surfactants in the lung). A common feature in all these examples is the presence of surface-active molecules at the air-liquid interface. Though they form only molecularly-thin layers, these surfactants produce complex surface stresses on the free surface, which have important consequences for the dynamics and stability of the underlying thin liquid film. Here we cond…
Although soap films are prone to evaporate due to their large surface to volume ratio, the effect of evaporation on macroscopic film features has often been disregarded in the literature. In this work, we investigate experimentally the influence of environmental humidity on soap film stability. An original experiment allows to measure both the maximum length of a film pulled at constant velocity and its thinning dynamics in a controlled atmosphere for various values of the relative humidity $\RH$. At first order, the environmental humidity seems to have almost no impact on most of the film thi…
The stability of floating drops on the liquid surface of the same liquid is considered in terms of viscous drainage theory. We have expressed the minimal thickness of the air film, separating the drop from the liquid surface, and the lifetime of the drop through the Hamaker constant, characterizing the intensity of van-der-Waals forces which make the air film unstable. It is shown that a horizontally moving or just rotating drop can have an infinite lifetime when the drop surface velocity exceeds some critical value. A spectacular example of a long-living rotating paraffin droplet on a burning…
Thin polymer films have attracted attention because of both their broad range of applications and of the fundamental questions they raise regarding the dynamic response of confined polymers. These films are unstable if the temperature is above their glass transition temperature Tg. Here, we describe freestanding thin films of centimetric dimensions made of a comb copolymer melt far from its glass transition that are stable for more than a day. These long lifetimes allowed us to characterize the drainage dynamics and the thickness profile of the films. Stratified regions appear as the film drai…
Surface bubbles have attracted much interest in the past decades. In this article, we propose to explore the lifetime and thinning dynamics of centimetric surface bubbles. We study the impact of the bubbles size as well as that of the atmospheric humidity through a careful control and systematic variation of the relative humidity in the measuring chamber. We first adress the question of the drainage under saturated water vapor conditions and show that a model including both capillary and gravity driven drainage provides the best prediction for this process. Additionally, unprecedented statisti…
We perform drainage experiments of a linear alkane fluid (n-hexadecane) down to molecular thicknesses, and focus on the role played by the confinement rate. We show that molecular layering is strongly influenced by the velocity at which the confining walls are approached: under high enough shear rates, the confined medium behaves as a structureless liquid of enhanced viscosity for film thickness below $\sim$10 nm. Our results also lead us to conclude that a rapidly confined film can be quenched in a metastable disordered state, which might be related with recent intriguing results on the shear…
We probe the rheology of the model liquid octamethylcyclotetrasiloxane (OMCTS) confined into molecularly thin films, using a unique Surface Forces Apparatus allowing to explore a large range of shear rates and confinement. We thus show that OMCTS under increasing confinement exhibits the viscosity enhancement and the non-linear flow properties characteristic of a sheared supercooled liquid approaching its glass transition. Besides, we study the drainage of confined OMCTS via the propagation of "squeeze-out" fronts. The hydrodynamic model proposed by Becker and Mugele [Phys. Rev. Lett. {\bf 91}…
The foaming properties, foaming capacity and foam stability, of soluble complexes of pectin and a globular protein, napin, have been investigated with a "Foamscan" apparatus. Complementary, we also used SANS with a recent method consisting in an analogy between the SANS by foams and the neutron reflectivity of films to measure in situ film thickness of foams. The effect of ionic strength, of protein concentration and of charge density of the pectin has been analysed. Whereas the foam stability is improved for samples containing soluble complexes, no effect has been noticed on the foam film thi…
We use field emission scanning electron microscope (FE-SEM) to investigate the growth of palladium colloids over the surface of thin films of WO3/glass. The film is prepared by Pulsed Laser Deposition (PLD) at different temperatures. A PdCl2 (aq) droplet is injected on the surface and in the presence of steam hydrogen the droplet is dried through a reduction reaction process. Two distinct aggregation regimes of palladium colloids are observed over the substrates. We argue that the change in aggregation dynamics emerges when the measured water drop Contact Angel (CA) for the WO3/glass thin film…
In this paper, we investigate the thinning dynamics of evaporating surfactant-stabilised surface bubbles by considering the role of the physical-chemistry of solutions used in the liquid bath. We study the impact of the surfactant concentration below and above the cmc (critical micelle concentration) and the role of ambient humidity. First, in a humidity-saturated atmosphere, we show that if the initial thickness depends on the surfactant concentration and is limited by the surface elasticity, the drainage dynamics are very well described from the capillary and gravity contributions. These dyn…
The film thickness dependence of crystal growth is investigated for isotactic polystyrene (it-PS) in thin films, the thickness of which is from 20nm down to 4nm. The single crystals of it-PS grown at 180 in the ultrathin films show the morphology typical in the diffusion-controlled growth: dense branching morphology (DBM), fractal seeweed (FS). The characteristic length of the morphology, i.e. the width of the branch, increases with decreasing film thickness. The thickness dependence of the growth rate of crystals shows a crossover around the lamellar thickness of the crystal, 8 nm. The thickn…
The merging of two soap bubbles is a fundamental fluid mechanical process in foam formation. In the present experimental study the liquid films from two soap bubbles are brought together. Once the liquid layers initially separated by a gas sheet are bridged on a single spot the rapid merging of the two liquid films proceed. Thereby the connecting rim is rapidly accelerated into the separating gas layer. We show that due to the dimple formation the velocity is not uniform and the high acceleration causes initially a Rayleigh-Taylor instability of the liquid rim. At later times, the rim takes he…
We investigate a gas of wet granular particles, covered by a thin liquid film. The dynamic evolution is governed by two-particle interactions, which are mainly due to interfacial forces in contrast to dry granular gases. When two wet grains collide, a capillary bridge is formed and stays intact up to a certain distance of withdrawal when the bridge ruptures, dissipating a fixed amount of energy. A freely cooling system is shown to undergo a nonequillibrium dynamic phase transition from a state with mainly single particles and fast cooling to a state with growing aggregates, such that bridge ru…
