Generation of soap films with instantaneously adsorbed surfactants: concentration-dependent film thinning

International audienceIn this theoretical work, we predict the steady state thickness of soap films pulled from a bath of surfactants. Assuming simplified thermodynamical properties for the surfactants, we compute the interfacial stresses by taking explicitly into account surfactant convection along the film. We make no assumption on interfacial rheology: the rigidification of the interfaces results entirely from confinement and depletion effects. Two main approximations are used: the concentration of surfactants is supposed homogeneous within the thickness of the film, and at equilibrium with the adsorbed layer. With these hypotheses, we show that the thickness of the film follows Frankel's law at low capillary numbers, and that deviations occur at higher pulling velocities. We study the dependence of the film thickness with the characteristics of the surfactant used and especially with its initial concentration, and we show that our predictions are compatible with available data by Saulnier and coworkers

Coupled vibrations of a meniscus and liquid films

International audienceWe investigate the vibration properties of a circular horizontal film, that is bounded by a meniscus (or Plateau border) and suspended to two catenary films. The suspending films act as capillary springs, and the system is thus free to oscillate around its equilibrium position. We study successively its free and forced oscillations. In our experiments, we track simultaneously the positions of the Plateau border and of the film. The model that we present predicts the eigenfrequency of the system, and its resonance characteristics (in forced oscillations). In particular, we show that the dynamics of both the Plateau border and the film have to be taken into account, in order to provide an accurate prediction of the oscillation frequency

Coating of a textured solid

International audienceWe discuss how a solid textured with well-defined micropillars entrains a film when extracted out of a bath of wetting liquid. At low withdrawal velocity V, it is shown experimentally that the film exactly fills the gap between the pillars; its thickness hd is independent of V and corresponds to the pillar height hp. At larger velocity, hd slowly increases with V and tends towards the Landau-Levich-Derjaguin (LLD) thickness h LLD observed on a flat solid. We model the entrainment by adapting the LLD theory to a double layer consisting of liquid trapped inside the texture and covered by a free film. This model allows us to understand quantitatively our different observations and to predict the transition between hp and hLLD. © 2011 Cambridge University Press

Flexible scraping of viscous fluids

International audienceWe study the thickness h(d) of the liquid film left on a wet surface after scraping it with an elastic wiper (length L, rigidity B) moved at a velocity V. The scraper is clamped vertically at a given distance above the substrate, and h(d) is maximal when the tip of the scraper is just tangent to the surface. We show experimentally and theoretically that this maximum thickness is hmax similar or equal to 0.33L (eta VL2/B)(3/4) where eta is the liquid viscosity. The deposition law is found to be sensitive to the shape of the wiper: the film thickness can also be tuned by using wipers with a permanent curvature, and varying this curvature

Theoretical study of the generation of soap films: role of interfacial visco-elasticity

International audienceIn this work, we study theoretically the thickness of a liquid film (typically made of a surfactant solution) pulled out of a bath at constant speed in the absence of gravity, when it features a viscous or an elastic interfacial rheology. We show that a purely viscous rheology does not lead to the extraction of a steady state film of constant thickness. In contrast, the thickness of the film is well defined in the elastic case, which allows us to compute it. This thickness depends on the capillary number of the experiment, and on the elasticity of the interface. It is always lower than or equal to that obtained for an incompressible interface predicted by Frankel (Mysels, Shinoda and Frankel, Soap Films: Studies of their Thinning and a Bibliography, 1959), which is recovered in the limit of an arbitrary large elasticity

Extension of a suspended soap film: A homogeneous dilatation followed by new film extraction

Liquid foams are widely used in industry for their high effective viscosity, whose local origin is still unclear. This Letter presents new results on the extension of a suspended soap film, in a configuration mimicking the elementary deformation occurring during foam shearing. We evidence a surprising two-step evolution: the film first extends homogeneously, then its extension stops, and a new thicker film is extracted from the meniscus. The second step is independent of the nature of the surfactant solution, whereas the initial extension is only observed for surfactant solutions with negligible dilatational moduli. We predict this complex behavior using a model based on Frankel's theory and on interface rigidification induced by confinement

Entraînements visqueux

We study experimentally different configuration of Newtonian viscous entrainment and drainage. We show that surface roughness drastically affects the coating laws of the dip- coating experiment : the entrained thickness is equal to the texture height below a critical capillary number, then increases and tends towards the smooth limit when it becomes much larger than the roughness. Th drainage is also affected, and features a sharp decrease. A two layer model is able to quantitatively reproduce all these observations. We then study the coating by an elastic sheet. When the scraper is just tangent to the deposition surface, a model reproduces the experimental results within a prefactor, which is part due to finite width effetcs. We then show that the deposition is very different when using a rigid scraper, and arrises from the stress divergence at scraper's tip. This study features the crucial role of the shape of the scraper. Lastly, we consider the filament withdrawn from a bath of viscous oil with a cylinder, and show the its size comes from a balance between viscous and gravity forces. The observed drainage law strongly depends on the size of the thread. This characteristic is also found when considering a horizontal viscous thread in the gravity field. We explain why "thick" filaments keep a catenary-like shape throughout their fall, whereas "small" ones evolve toward a "U" shape.Nous étudions expérimentalement diverses configurations d'entraînement et de drai- nage visqueux. Dans un premier temps, nous montrons que la rugosité modifie les lois de l'enduction par trempage : l'épaisseur est égale à la taille de la texture jusqu' à un nombre capillaire critique, à partir duquel elle augmente pour rejoindre la loi obtenue sur surface lisse lorsque'elle devient largement supérieure à la rugosité. Le drainage gravitaire est également modifié, et présente en particulier une marche d'épaisseur. Un modèle à deux couches permet de rendre quantitativement compte de toutes ces observations. Nous étudions ensuite le dépôt à l'aide d'une membrane flexible. Dans le cas où le racloir est juste tangent à la surface de dépôt, un modèle décrit les expériences à un facteur près. Cette déviation est en partie due à des effets de bords. Nous montrons ensuite que la loi de dépôt est très différente avec un racloir rigide, et peut être comprise en considérant l'écoulement dans un coin. Cette étude nous permet d'insister sur l'importance de la forme de la membrane dans détermination de la loi d'entraînement. Enfin, nous nous intéressons à l'entraînement vertical par un cylindre d'un filament visqueux, dont la taille résulte alors d'un équilibre entre viscosité et gravité. Le drainage de ces objets est très différent selon les dimensions du cylindre. Cette différence de com- portement en fonction de la géométrie se retrouve dans l'évolution d'un filament horizontal soumis à la gravité. Nous expliquons pourquoi un "gros" filament conserve une forme de chaînette tout au long de sa chute, tandis qu'un "petit" évolue sous l'effet de la capillarité vers une forme de "U"

Instability of a fluctuating membrane driven by an ac electric field.

International audienceShape fluctuations of a planar lipid membrane in an ac electric field are investigated using a zero-thickness electromechanical model, which accounts for membrane conductivity and capacitance, and asymmetry in the properties of the fluids separated by the membrane. A linear stability analysis shows that unlike in the case of a dc electric field, a purely capacitive membrane can be destabilized in an ac electric field. The theory highlights that the instability originates from electric pressure exerted on the membrane

Extension of a suspended soap film: a two-step process.

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Velocity measurements in draining foam films

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