Contact Between an Elastic Body and a Rigid Base with Periodic Array of Quasielliptic Grooves Partially Filled with Liquid Wetting the Surfaces of the Bodies

Abstract

We model the frictionless contact between an elastic body and a rigid base with periodically placed quasielliptic grooves in the case where an incompressible liquid wetting the surfaces of the bodies is present near the edges of interface gaps. The middle parts of the gaps are filled with a gas under a constant pressure. Due to the surface tension of the liquid, a pressure drop described by the Laplace equation is formed in the liquid and in the gas. The posed contact problem for the elastic half space is reduced to a singular integral equation with Hilbert kernel for the derivative of the height of gaps and to a transcendental equation for the width of the area filled with gas. We analyze the dependences of the width of an area filled with gas, pressure drop, shape of the gaps, and the contact approach of the bodies on the applied load, volume of the liquid, and its surface tension.