Boundary Lubrication: Squeeze-out Dynamics of a Compressible 2D Liquid
U. Tartaglino, B. N. J. Persson, A. I. Volokitin, E. Tosatti
Abstract
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 characterized by the parameter g0 ~ P0/(rho c2), where P0 is the average perpendicular (squeezing) pressure, rho the liquid (3D) density and c the longitudinal sound velocity in the monolayer film. When g0 << 1 the result of the earlier incompressible treatment is recovered. Numerical results for the squeeze-out time, and for the time-dependence of the radius of the squeezed-out region, indicate that compressibility effects may be non-negligible both in time and in space. In space, they dominate at the edge of the squeeze-out region. In time, they are strongest right at the onset of the squeeze-out process, and just before its completion.
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