Viscous damping force during head-on collision of two spherical particles

Abstract

Viscous damping is known to play a critical role in determining the restitution coefficient for the collision of two spherical particles at low and moderate Stokes numbers due to fluid motion in the squeeze-film between the particles. The classical expression for the viscous damping force of approaching spheres, valid prior to collision of the particles, has been used by several investigators to model the effect of viscous damping on the restitution coefficient. However, viscous damping also occurs during the particle collision due to the corner flow associated with a change in the radius of the contact region, within which the particle surfaces deform into flattened parallel surfaces due to high fluid pressure within the squeeze-film. The current paper derives a simple expression for the fluid damping force caused by the squeeze-film dynamics associated with a change in the contact region radius during collision. This expression is then used in conjunction with the damping force expression for spherical particles before and after collision to predict the variation of restitution coefficient with the particle Stokes number and elasticity parameter. The viscous damping force during collision exhibits sensitive dependence on the minimum approach distance separating the particle surfaces within the contact region, which, in turn, is controlled by factors such as microscopic particle surface roughness and pressure-dependent density and viscosity changes of the fluid.