Dynamics of driven particle systems with drag

Abstract

We consider the motion of a large number of particles that experience a linear drag force from the interstitial fluid excited by a vibrating boundary. The dissipation in such systems arises from two main sources: inelasticity in particle collisions and the effects of interstitial fluid on the particles. In many applications, order of magnitude estimates suggest that the dissipation due to interstitial fluid effects may greatly exceed that due to inelasticity and one may be led to neglect inelastic effects. We show that if the vibration speed of the boundary is below a critical value then one may safely neglect inelastic effects. However, if the vibration speed of the boundary exceeds the critical value then the kinetic energy of the particles grows without bound if inelastic effects are neglected. One is therefore forced to include inelastic effects for vibration speeds above the critical value even if order of magnitude estimates suggest they are negligible.