Boundary conditions for high-shear grain flows

Boundary conditions are developed for rapid granular flows in which the rheology is dominated by grain–grain collisions. These conditions are at the wall and to adopt the no-slip condition. Exceptions occur where d/h is not very small, when the wall is not rough, and when the grain–wall collisions are very elastic. Similar insight into other flows can be obtained qualitatively by a dimensional analysis treatment of the boundary conditions. Finally, the more difficult problem of self-bounding fluids is discussed qualitatively.