Influence of Capillary Adhesion on the Sliding of a Cylinder Along the Surface of an Elastic Solid Taking Account of Wetting Hysteresis

Abstract

The contact problem of steady sliding of a rigid cylinder over an elastic half-space in the presence of liquid menisci is considered, taking into account the hysteresis of the contact angle, which leads to different adhesion conditions at the entrance to the contact and at the exit from it. The problem was considered in a flat formulation and was solved by reducing it to the Riemann–Hilbert problem. An analytical expression for the contact pressure and a system of four equations for the numerical determination of the coordinates of the ends of the contact area and the meniscus zones are obtained. The calculation was carried out in the range of input parameters corresponding to the situation when a sliding cylinder models a separate protrusion of a rough surface. The distribution of contact pressure, the size of the contact area and its displacement relative to the axis of symmetry of the cylinder, the width of the menisci at the entrance to and exit from the contact, as well as the friction force caused by capillary adhesion were studied. It has been established, in particular, that the friction force significantly depends on the value of the contact angle hysteresis, and especially on the surface tension of the liquid, but weakly depends on the capillary pressure in the menisci, which, under conditions of thermodynamic equilibrium of the meniscus with the environment, is determined by the humidity of the surrounding air.