The influence of pressure-dependent density and viscosity on the elastohydrodynamic collision and rebound of two spheres

Abstract

A theoretical description of the low-Reynolds-number collision and rebound of two rigid or elastic spheres separated by a thin layer of viscous fluid with pressure-dependent physical properties is presented. It has previously been shown by Davis et al. (1986) that the hydrodynamic pressure which builds up in the thin fluid layer must become large enough to elastically deform the spheres near the axis of symmetry, if they are to rebound subsequent to colliding. Under these extreme pressures, however, it is expected that the fluid may also compress and that its viscosity may increase by several orders of magnitude. It is shown that these pressure-dependent effects may significantly alter the minimum separation reached during approach of the spheres, as well as the maximum separation and relative velocity attained during rebound of the spheres. In particular, the pressure buildup during the collision process is predicted to become sufficiently large under some conditions so that the corresponding viscosity increase causes the fluid in the gap between the colliding spheres to behave nearly as a solid and to limit the close approach of the opposing surfaces. Also, the storage of energy via the compression of the fluid in the gap allows rigid spheres to bounce as this energy is released subsequent to their collision. However, it is found that this rebound is very weak relative to that which is predicted for elastic spheres.