The coefficient of normal restitution for the Hertzian contact of two rough spheres colliding in a viscous fluid
Abstract We use previous theoretical results for the added mass, history and lubrication forces between two spheres colliding in a fluid with viscosity n 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 t and that the minimum approach distance between particles is approximately equal to the height s of surface micro asperities. A non dimensionalization of the equation of motion indicates that the contact dynamics is governed by two parameters the ratio of the surface roughness s and the sphere radius a, and a contact Stokes number defined as Stc s2/nt. An asymptotic solution of the equation of motion in the limit of small /Stc 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.