An average lubrication equation for thin film grain flow with surface roughness effects

A closed-form average lubrication equation for thin film grain flow with the effects of surface roughness is derived. This equation is based on Haff's grain flow theory and also the flow factors proposed by Patir and Cheng. The flow factors, derived by the perturbation approach and coordinate transformation, are expressed in terms of surface characteristics (three characteristics for each surface: roughness orientation, Peklenik number and standard derivation) and particle size. Finally, the flow factors under different surface characteristics and particle size are discussed.