Boundary Lubrication: Squeeze-out Dynamics of a Compressible 2D Liquid

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 c^2), 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.