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In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…
A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the…
We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to…
A Stokes experiment for foams is proposed. It consists in a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the…
The viscosity of liquids under nanoconfinement remains controversial. Reports range from spontaneous solidification to no change in the viscosity at all. Here, we present thorough measurements with a small-amplitude linear atomic force…
We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…
In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid…
We perform drainage experiments of a linear alkane fluid (n-hexadecane) down to molecular thicknesses, and focus on the role played by the confinement rate. We show that molecular layering is strongly influenced by the velocity at which the…
In this paper we present the molecular theory of viscosity of confined fluids in small or nano systems. This theory is also applicable to the interfacial viscosity. The basis of this research work is the Enskog kinetic theory and the…
Ionic liquids have generated interest in applications as lubricants and as additives to conventional lubricants due to their unique physical properties. In these applications, the liquid thin film can be subjected simultaneously to…
Motivated by the dynamics of microbubbles near catalytic surfaces in bubble-powered microrockets, we consider theoretically the growth of a free spherical bubble near a flat no-slip surface in a Stokes flow. The flow at the bubble surface…
A water monolayer squeezed between two solid planes experiences strong out-of-plane confinement effects while expanding freely within the plane. As a consequence, the transport of such two-dimensional water combines hydrodynamic and…
We investigate the effect of loading rate on drainage in molecularly thin films of a simple fluid made of quasi-spherical molecules (octamethylcyclotetrasiloxane, OMCTS). We find that (i) rapidly confined OMCTS retains its tendency to…
Hydrocarbon films confined between smooth mica surfaces have long provided an experimental playground for model studies of structure and dynamics of confined liquids. However fundamental questions regarding the phase behavior and shear…
The ice surface is known for presenting a very small kinetic friction coefficient, but the origin of this property remains highly controversial to date. In this work, we revisit recent computer simulations of ice sliding on atomically…
Free boundaries of biofilms advancing on surfaces evolve according to conservation laws coupled with systems of partial differential equations for velocities, pressures and chemicals affecting cell behavior. Thin film approximations lead to…
Using molecular dynamics simulations we investigate the relaxation dynamics of a supercooled liquid close to a rough as well as close to a smooth wall. For the former situation the relaxation times increase strongly with decreasing distance…
The expulsion dynamics of the last liquid monolayer of molecules confined between two surfaces has been analyzed by solving the two-dimensional (2D) Navier-Stokes equation for a compressible liquid. We find that the squeeze-out is…
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is…