Contact of Elastic Bodies in the Presence of Gas and Incompressible Liquid in Periodic Interface Gaps

摘要

We study the contact of two elastic semiinfinite bodies in the presence of an incompressible liquid (that does not wet the surfaces of the bodies) and a gas in the interface gaps caused by a periodic array of grooves on the surface of one of the bodies. The drop of pressure in the liquid and in the gas is described by the Laplace equation. The problem is reduced to a singular integral equation with Hilbert kernel. This equation is then transformed into a singular integral equation with Cauchy kernel for the height of interface gaps. A system of transcendental equations for the lengths of the gaps and the regions filled with liquid is obtained from the condition of boundedness of the solution at the ends of the interval of integration and the condition of conservation of the amount of liquid. This system is solved numerically. We also analyze the dependences of the lengths and shapes of the gaps and the contact compliances of the bodies on the applied load, volume, and surface tension of the liquid.