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

TL;DR

This paper models the squeeze-out dynamics of a compressible 2D liquid monolayer between surfaces using Navier-Stokes equations, revealing the significance of compressibility effects at the edges and during initial and final stages.

Contribution

It introduces a novel analysis of compressibility effects in boundary lubrication squeeze-out dynamics using a 2D Navier-Stokes framework.

Findings

Compressibility parameter g0 determines squeeze-out behavior.

Compressibility effects are significant at the edges and during initial and final stages.

Results show deviations from incompressible models under certain conditions.

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 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.