Isabelle Cantat

Saltating particles in a turbulent boundary layer: experiment and theory

The work presented here focuses on the analysis of a turbulent boundary layer saturated with saltating particles. Experiments were carried out in a wind tunnel 15 m long and 0.6 m wide at the University of Aarhus in Denmark with sand grains 242 μm in size for wind speeds ranging from the threshold speed to twice its value. The saltating particles were analysed using particle image velocimetry (PIV) and particle-tracking velocimetry (PTV), and vertical profiles of particle concentration and velocity were extracted. The particle concentration was found to decrease exponentially with the height above the bed, and the characteristic decay height was independent of the wind speed. In contrast with the logarithmic profile of the wind speed, the grain velocity was found to vary linearly with the height. In addition, the measurements indicated that the grain velocity profile depended only slightly on the wind speed. These results are shown to be closely related to the features of the splash function that characterizes the impact of the saltating particles on a sandbed. A numerical simulation is developed that explicitly incorporates low-velocity moments of the splash function in a calculation of the boundary conditions that apply at the bed. The overall features of the experimental measurements are reproduced by simulation.

Lateral migration of a two-dimensional vesicle in unbounded Poiseuille flow

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles toward the center of the Poiseuille flow. This is in a marked contrast with a result [L. G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation toward its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.

Experimental growth law for bubbles in a moderately Wet 3D liquid foam

We used x-ray tomography to characterize the geometry of all bubbles in a liquid foam of average liquid fraction phi(l) approximately 17% and to follow their evolution, measuring the normalized growth rate G=V(-1/3) dV/dt for 7000 bubbles. While G does not depend only on the number of faces of a bubble, its average over f-faced bubbles scales as G(f) approximately f - f(0) for large fs at all times. We discuss the dispersion of G and the influence of V and phi(l) on G.

Viscous force exerted on a foam at a solid boundary: Influence of the liquid fraction and of the bubble size

We study experimentally the pressure drop needed to push a bubble train in a millimetric channel, as a function of the velocity. For dry liquid foams, the influence of the amount of liquid and of the bubble size is pointed out and we predict theoretically that this influence is closely related to the power law obtained for the force/velocity relation. This model is in fair agreement with our experimental data and provides a new interpretation of previous results.

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

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 nonlinear 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 such as Ca1/3 and Ca2/3, 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.

The role of surface rheology in liquid film formation

The role of surface rheology in fundamental fluid dynamical systems, such as liquid coating flows and soap film formation, is poorly understood. We investigate the role of surface viscosity in the classical film-coating problem. We propose a theoretical model that predicts film thickening based on a purely surface-viscous theory. The theory is supported by a set of new experimental data that demonstrates slight thickening even at very high surfactant concentrations for which Marangoni effects are irrelevant. The model and experiments represent a new regime that has not been identified before.

The Marangoni flow of soluble amphiphiles

Surfactant distribution heterogeneities at a fluid/fluid interface trigger the Marangoni effect, i.e. a bulk flow due to a surface tension gradient. The influence of surfactant solubility in the bulk on these flows remains incompletely characterized. Here we study Marangoni flows sustained by injection of hydrosoluble surfactants at the air/water interface. We show that the flow extent increases with a decrease of the critical micelle concentration, i.e. the concentration at which these surfactants self-assemble in water. We document the universality of the surface velocity field and predict scaling laws based on hydrodynamics and surfactant physicochemistry that capture the flow features.

Gibbs elasticity effect in foam shear flows: a non quasi-static 2D numerical simulation

The origin of the dissipation in liquid foams is not fully understood, especially in the large deformation, large velocity regime. Numerical simulations, now very accurate in the quasi static regime, are still sparse in the dissipative regime, and are all based on restrictive assumptions or very small bubble numbers. Here we present the results obtained with 2D numerical simulations involving 500 bubbles under simple shear, in a non-quasi static regime. The bubble description is kept as simple as possible and the dissipation is assumed to arise from surface tension variations induced by film area variations. This model leads to a steady state stress under simple shear that is well fitted by a Herschel–Bulkley law with an exponent 0.6. We show that small tension dynamical inhomogeneities induce foam structure modifications responsible for the largest part of the stress increase.

Stokes experiment in a liquid foam

The paper reports on the quasistatic steady flow of a dry liquid foam around a fixed spherical bead, a few times larger than the typical bubble size. The force exerted on the bead is recorded with a precision and a time resolution large enough to show the succession of elastic loading of the foam, separated by sudden force drops. The foam structure is observed by direct light transmission, synchronized with the force measurement, thus allowing us to correlate the plastic events with the force variations. Scaling laws for the force signal as a function of the bubble size are detailed and interpreted with a simple elasto-plastic model. The spatial distribution of the plasticity is strongly localized in the first bubble layers around the bead and the average size of the bubble rearrangements increases with the corresponding force jump amplitude.

Deformation of soap films pushed through tubes at high velocity

The behaviour of soap films pushed through tubes at large velocities, up to several metres per second, is investigated in this paper. 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 ( J. Fluid Mech. , vol. 10, 1961, pp. 166–188) 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 diameter. A limit of stability of the films, beyond which they burst or evolve unsteadily, is predicted, and it quantitatively captures 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.