Effect of interfacial liquid bridges on contact between an elastic body and a rigid base with a periodic array of rectangular grooves

Abstract

The frictionless contact between an elastic body and a rigid base with periodically arranged
rectangular grooves is considered. There are liquid bridges in the middle parts of interface gaps,
and the edges of interface gaps contain a gas under constant pressure. It is assumed that the liquid
is incompressible and perfectly wets the surfaces of the bodies. Due to the surface tension of the
liquid, a pressure drop described by Laplace’s equation occurs in the liquid and the gas.
The contact problem for the elastic half-space is reduced to a singular integral equation (SIE)
with Hilbert kernel for a derivative of a gaps height and a transcendental equation for a length of
the liquid regions. The dependences of the liquid regions, the pressure drop, the shape of the
grooves and the contact approach of the bodies on the applied load, the volume and the surface
tension of the liquid are analyzed.