Non-steady state boundary conditions for collisional granular flows at flat frictional moving walls

This paper derives new boundary conditions for the solids stresses and the flux of fluctuation energy for collisional granular flows of spheres at flat frictional moving walls. In contrast to state-of-the-art boundary conditions, we propose a theory connecting non-sliding and sliding collisions in one expression. The new expression for the boundary traction is further augmented by including non-steady state effects, i.e. compression and expansion of the granular flow, as it is observed at walls moving perpendicular to the granular flow. For the steady state the theory delivers the same results as the calculations of Jenkins [J. Appl. Mech. 59 (1992)] for the ratio of tangential and normal stresses, S/N, for the “large friction/no sliding” and the “low friction/all sliding” limits. Comparing the theory to literature data shows that it provides a good prediction of S/N as well as of the flux of fluctuation energy for nearly elastic particles and physically reasonable coefficients of friction. The theory also predicts a considerable dependence of the boundary traction and the flux of fluctuation energy on the compression and expansion of the granular flow.