The coefficient of normal restitution for the Hertzian contact of two rough spheres colliding in a viscous fluid

摘要

We use previous theoretical results for the added mass, history and lubrication forces between two spheres colliding in a fluid with viscosity v to investigate the effect of viscous dissipation on the coefficient of restitution during contact. We assume that the mechanical interaction is governed by Hertzian mechanical contact of small duration tau and that the minimum approach distance between particles is approximately equal to the height sigma of surface micro-asperities. A non-dimensionalization of the equation of motion indicates that the contact dynamics is governed by two parameters - the ratio epsilon of the surface roughness sigma and the sphere radius a, and, a contact Stokes number defined as St(c) = sigma(2)/v tau. An asymptotic solution of the equation of motion in the limit of small epsilon/St(c) is used to obtain an explicit expression for the coefficient of restitution during contact and the latter is compared with estimates based on numerical solutions of the non-linear equation of motion. Published by Elsevier Ltd.