Squeeze flow of interstitial Herschel–Bulkley fluid between two rigid spheres

Interaction between two spheres with an interstitial fluid is crucial in discrete element modeling for simulating the behaviors of ‘wet’ particulate materials. The normal viscous force of squeeze flow between two arbitrary rigid spheres with an interstitial Herschel–Bulkley fluid was studied on the basis of Reynolds’ lubrication theory, resulting in analytical integral expressions of pressure distribution and the viscous force between the two spheres. According to the variation of shear stress, the fluid was divided into yielding and unyielding regions, followed by a discussion on the thickness of the two regions. The result of this paper could be reduced to either the power-law fluid or the Bingham fluid case.