Liquid meniscus friction on a wet plate: Bubbles, lamellae and foams

Many microfluidics devices, coating processes or diphasic flows involve the motion of a liquid meniscus on a wet wall. This motion induces a specific viscous force, that exhibits a non-linear dependency in the meniscus velocity. We propose a review of the theoretical and experimental work made on this viscous force, for simple interfacial properties. The interface is indeed assumed either perfectly compressible (mobile interface) or perfectly incompressible (rigid interface). We show that, in the second case, the viscous force exerted by the wall on the meniscus is a combination of two power laws, scaling like $Ca^{1/3}$ and $Ca^{2/3}$, with $Ca$ the capillary number. We provide a prediction for the stress exerted on a foam sliding on a wet solid and compare it with experimental data, for the incompressible case

Vesicle propulsion in haptotaxis : a local model

We study theoretically vesicle locomotion due to haptotaxis. Haptotaxis is referred to motion induced by an adhesion gradient on a substrate. The problem is solved within a local approximation where a Rayleigh-type dissipation is adopted. The dynamical model is akin to the Rousse model for polymers. A powerful gauge-field invariant formulation is used to solve a dynamical model which includes a kind of dissipation due to bond breaking/restoring with the substrate. For a stationary situation where the vesicle acquires a constant drift velocity, we formulate the propulsion problem in terms of a nonlinear eigenvalue (the a priori unknown drift velocity) one of Barenblat-Zeldovitch type. A counting argument shows that the velocity belongs to a discrete set. For a relatively tense vesicle, we provide an analytical expression for the drift velocity as a function of relevant parameters. We find good agreement with the full numerical solution. Despite the oversimplification of the model it allows the identification of a relevant quantity, namely the adhesion length, which turns out to be crucial also in the nonlocal model in the presence of hydrodynamics, a situation on which we have recently reported [I. Cantat, and C. Misbah, Phys. Rev. Lett. {\bf 83}, 235 (1999)] and which constitutes the subject of a forthcoming extensive study.Comment: 12 pages, 8 figures, submitted to Eur. Phys. J.

Liquid films with high surface modulus moving in tubes: dynamic wetting film and jumpy motion

We investigate the motion through a wet tube of transverse soap films, or lamellae, of high surface dilatationnal modulus. Combining local thickness and velocity measurements in the wetting film, we reveal a zone of several centimeters in length, the dynamic wetting film, which is significantly influenced by a moving lamella. The dependence of this influence length on lamella velocity and wetting film thickness provides a discrimination among several possible surfactant minimal models. A spectacular jumpy mode of unsteady motion of a lamella is also evidenced

Deformation of soap films pushed through tubes at high velocity

International audienceThe behaviour of soap films pushed through tubes at large velocities, up to several m/s, is investigated. The film shape deviates from its equilibrium configuration perpendicular to the walls and gets curved downstream. A simple model relates the radius of curvature of the film to the friction in the lubrication films touching the wall, and the scaling of Bretherton (1961) holds up to surprisingly high velocities, at which the capillary and Weber numbers are no longer small parameters. The tube geometry is varied and accounted for through the notion of hydraulic diametre. A limit of stability of the film, beyond which the films burst or evolve unsteadily, is predicted, and captures quantitatively the observations. The new questions raised by our results on the dissipation in soap films are discussed, especially the role of Plateau borders and inertial effects

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

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

Response of a two-dimensional liquid foam to air injection: Influence of surfactants, critical velocities and branched fracture

International audienceExperiments where air is injected into a foam confined in a Hele-Shaw cell are convenient to study the rheology of foams far from the quasistatic regime, and their limit of stability. At low overpressure, the injected air forms a ductile crack, whereas at high overpressure, it breaks the foam like a brittle material. We present new results in this configuration, complementary with previous studies. We show that air injection is slowed down for surfactants giving incompressible interfaces instead of mobile ones. The injection rate is quantitatively captured by a simple model balancing the air overpressure with known foam/wall friction laws for incompressible interfaces. We also revisit the critical velocity criteria for the injected air proposed by Arif et al. [1]. The upper bound of velocity in the ductile regime, based on the resistance of soap films against wall friction, is shown to hold much better for mobile than for incompressible interfaces. The propagation speed of shear waves is confirmed to be a good lower bound for the velocity in the brittle regime, provided the motion of all liquid within the foam is accounted for. Finally, a short description of branching in the fragile regime is given

Generation of Giant Soap Films

Artists regularly make soap bubbles several meters long. In this article we make soap films up to two meters high by pulling a horizontal fishing line driven by belts out of a soapy solution at velocities ranging from 20 cm/s to 250 cm/s. We characterize the thickness profile of the central part of the film that behaves like a rubber band under tension. We show that its thickness profile is well described by a static model in which a homogeneous elastic film is stretched by its own weight. This leads to an exponential thickness profile with a characteristic length given by a competition between gravity and surface elasticity. The prefactor is fixed by the shape and area of the film, governed by the fishing line motion but also by a continuous extraction of foam film from the lateral menisci, thicker than the central part, and that progressively invades the film from its lateral boundaries. The model we propose captures the subtle interplay between gravity, film elasticity and film extraction and leads to predictions in good agreement with our experimental data

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

Foam Drainage Control Using Thermocapillary Stress in a Two-Dimensional Microchamber

International audienceWe investigate the drainage of a 2D microfoam in a vertical Hele-Shaw cell, and show that the Marangoni stress at the air-water interface generated by a constant temperature gradient applied in situ can be tuned to control the drainage. The temperature gradient is applied in such a way that thermocapillarity and gravity have an antagonist e ect. We characterize the drainage over time by measuring the liquid volume fraction in the cell and find that thermocapillarity can overcome the e ect of gravity, e ectively draining the foam towards the top of the cell, or exactly compensate it, maintaining the liquid fraction at its initial value over at least 60 s. We quantify these results by solving the mass balance in the cell, and provide insight on the interplay between gravity, thermocapillarity and capillary pressure governing the drainage dynamics