Influence of interstitial liquid bridges on contact interaction between bodies with wavy relief

Abstract

The frictional contact between two semi-infinite elastic bodies, one of which has a wavy surface, is
considered for the case when there are an incompressible liquid wetting the surfaces of the bodies
at the edges of the intersurface gaps and a gas under constant pressure in the central parts of the
gaps. Due to the surface tension of the liquid, a pressure drop occurs in the liquid and the gas,
which is described by the Laplace formula. The formulated contact problem is reduced to a
singular integral equation (SIE) with the Hilbert kernel, which is transformed into a SIE with the
Cauchy kernel for a derivative of a heigth of the gaps. A system of transcendental equations for
widths of gaps and regions with the gas is obtained from the condition of boundedness of the SIE
solution at the integration interval ends and the condition of liquid’s amount conservation, and
then it is solved numerically. The dependences of the width and shape of the gaps, the width of the
regions with the gas, the contact approach of the bodies on the applied load and the surface
tension of the liquid are analyzed.