Grain Flow for Rough Surfaces Considering Grain/Grain Collision Elasticity

Abstract

Previous work by this group on an average lubrication equation for grain flow with roughness effects is extended to include grain-grain collision elasticity ranging from perfectly elastic to perfectly inelastic. The average lubrication equation is based on Haff’s grain flow theory, with flow factors from Patir and Cheng and Tripp’s use of perturbation. The derived flow factors are obtained as functions of rough surface characteristics, grain size, and collision pattern. As collision energy loss approaches zero, the inelastic results approach those for perfectly elastic grain collision. The mathematical formulas for flow factors, grain/grain collision elasticity, grain size, and roughness are presented and discussed. Predicitons for the elastic and inelastic cases are graphically demonstrated and compared. The derived average lubrication equation for grain flow shows good agreement with the theoretical and experimental data of Yu, Craig, and Tichy [J. Rheol., 38(4), 921 (1994)].