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We present a simple mechanism of cell motility in a confined geometry, inspired by recent
motility assays in microfabricated channels. This mechanism relies mainly on the coupling
of actin polymerisation at the cell membrane to geometric confinement. We first show
analytically using a minimal model of polymerising viscoelastic gel confined in a narrow
channel that spontaneous motion occurs due to polymerisation alone. Interestingly, this
mechanism...
Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinear surface tension terms. Finally, in the case of a thin film flow driven by a surface active agent (surfactant),...
We propose here a model and a numerical scheme to compute the motion of rigid particles interacting through the lubrication force. In the case of a particle approaching a plane, we propose an algorithm and prove its convergence towards the solutions to the gluey particle model described in [B. Maury, ESAIM: Proceedings 18 (2007) 133–142]. We propose a multi-particle version of this gluey model which is based on the projection of the velocities onto a set of admissible velocities. Then, we describe...
We propose here a model and a numerical scheme to compute the motion
of rigid particles interacting through the lubrication force. In the
case of a particle approaching a plane, we propose an algorithm and
prove its convergence towards the solutions to the gluey particle model
described in [B. Maury, ESAIM: Proceedings18 (2007)
133–142]. We propose a multi-particle version of
this gluey model which is based on the projection of the velocities
onto a set of admissible velocities. Then, we describe...
In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic
problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a
rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and
hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a...
We consider a two-dimensional Navier-Stokes shear flow with time dependent boundary driving and subject to Tresca law. We establish the existence of a unique global in time solution and then, using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set, we prove the existence of the pullback attractor for the associated cocycle. This research is motivated by a problem from lubrication theory.
We consider an optimal control problem for a class of non-linear elliptic equations. A result of existence and uniqueness of the state equation is proven under weaker hypotheses than in the literature. We also prove the existence of an optimal control. Applications to some lubrication problems and numerical results are given.
We consider an optimal control problem for a class of non-linear
elliptic equations. A result of existence and uniqueness
of the state equation is proven under weaker hypotheses than in the
literature. We also prove the existence of an optimal
control. Applications to some lubrication problems and numerical
results are given.
The hydrodynamic lubrication of a cylindrical bearing is governed by the Reynolds equation that must be satisfied by the pressure of lubricating oil. When cavitation occurrs we are carried to an elliptic free-boundary problem where the free-boundary separates the lubricated region from the cavited region.Some qualitative properties are obtained about the shape of the free-boundary as well as the localization of the cavited region.
We analyze the problem of shear-induced electrokinetic lift on a particle freely suspended near a solid wall, subject to a homogeneous (simple) shear. To this end, we apply the large-Péclet-number generic scheme recently developed by Yariv et al. (J. Fluid Mech., Vol. 685, 2011, p. 306). For a force- and torque-free particle, the driving flow comprises three components, respectively describing (i) a particle translating parallel to the wall; (ii) a particle rotating with an angular velocity vector...
The stability and evolution of very thin, single component, metallic-melt films is
studied by analysis of coupled strongly nonlinear equations for gas-melt (GM) and crystal-melt (CM) interfaces, derived using the lubrication approximation. The crystal-melt interface is deformable by freezing and melting, and there is a thermal gradient applied across the
film. Linear analysis reveals that there is a maximum applied far-field temperature in the
gas, beyond which there is no film instability. Instabilities...
We study pressure-driven, two-layer flow in inclined channels with high density and
viscosity contrasts. We use a combination of asymptotic reduction, boundary-layer theory and the
Karman-Polhausen approximation to derive evolution equations that describe the interfacial dynamics.
Two distinguished limits are considered: where the viscosity ratio is small with density
ratios of order unity, and where both density and viscosity ratios are small. The evolution equations
account for the presence of...
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