Elastohydrodynamics of a sliding, spinning and sedimenting cylinder near a soft wall

We consider the motion of a fluid-immersed negatively buoyant particle in the vicinity of a thin compressible elastic wall, a situation that arises in a variety of technological and natural settings. We use scaling arguments to establish different regimes of sliding, and complement these estimates using thin-film lubrication dynamics to determine an asymptotic theory for the sedimentation, sliding, and spinning motions of a cylinder. The resulting theory takes the form of three coupled nonlinear singular-differential equations. Numerical integration of the resulting equations confirms our scaling relations and further yields a range of unexpected behaviours. Despite the low-Reynolds feature of the flow, we demonstrate that the particle can spontaneously oscillate when sliding, can generate lift via a Magnus-like effect, can undergo a spin-induced reversal effect, and also shows an unusual sedimentation singularity. Our description also allows us to address a sedimentation-sliding transition that can lead to the particle coasting over very long distances, similar to certain geophysical phenomena. Finally, we show that a small modification of our theory allows to generalize the results to account for additional effects such as wall poroelasticity

Viscoelastic effects and anomalous transient levelling exponents in thin films

We study theoretically the profile evolution of a thin viscoelastic film supported onto a no-slip flat substrate. Due to the nonconstant initial curvature at the free surface, there is a flow driven by Laplace pressure and mediated by viscoelasticity. In the framework of lubrication theory, we derive a thin film equation that contains local viscoelastic stress through the Maxwell model. Then, considering a sufficiently regular small perturbation of the free surface, we linearise the equation and derive its general solution. We analyse and discuss in details the behaviour of this function. We then use it to study the viscoelastic evolution of a Gaussian initial perturbation through its transient levelling exponent. For initial widths of the profile that are smaller than a characteristic length scale involving both the film thickness and the elastocapillary length, this exponent is shown to reach anomalously high values at the elastic-to-viscous transition. This prediction should in particular be observed at sufficiently short times in experiments on thin polymer films.Comment: 4 figure

Two-phase flow in a chemically active porous medium

We study the problem of the transformation of a given reactant species into an immiscible product species, as they flow through a chemically active porous medium. We derive the equation governing the evolution of the volume fraction of the species -- in a one-dimensional macroscopic description --, identify the relevant dimensionless numbers, and provide simple models for capillary pressure and relative permeabilities, which are quantities of crucial importance when tackling multiphase flows in porous media. We set the domain of validity of our models and discuss the importance of viscous coupling terms in the extended Darcy's law. We investigate numerically the steady regime and demonstrate that the spatial transformation rate of the species along the reactor is non-monotonous, as testified by the existence of an inflection point in the volume fraction profiles. We obtain the scaling of the location of this inflection point with the dimensionless lengths of the problem. Eventually, we provide key elements for optimization of the reactor.Comment: 13 pages, 10 figure

Wake and wave resistance on viscous thin films

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface - a wake - that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in details. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates in a 1D geometry, or diverges in a 2D geometry

Elastowetting of Soft Hydrogel Spheres

When a soft hydrogel sphere is placed on a rigid hydrophilic substrate, it undergoes arrested spreading by forming an axisymmetric foot near the contact line, while conserving its global spherical shape. In contrast, liquid water (that constitutes greater than 90% of the hydrogel's volume) spreads into a thin film on the same surface. We study systematically this elastowetting of gel spheres on substrates of different surface energies, and find that their contact angle increases as the work of adhesion between the gel and the substrate decreases, as one would observe for drops of pure water - albeit being larger than in the latter case. This difference in the contact angles of gel and water appears to be due to the elastic shear stresses that develop in the gel and oppose its spreading. Indeed, by increasing the elastic modulus of the gel spheres, we find that their contact angle also increases. In addition, the length of the contact foot increases with the work of adhesion and sphere size, while it decreases when the elastic modulus of the gel is increased. We discuss those experimental results in light of a minimal analysis based on energy minimization, volume conservation, and scaling arguments