Effective boundary conditions for dense granular flows.

We derive an effective boundary condition for dense granular flow taking into account the effect of the heterogeneity of the force network on sliding friction dynamics. This yields an intermediate boundary condition which lies in the limit between no slip and Coulomb friction; two simple functions relating wall stress, velocity, and velocity variance are found from numerical simulations. Moreover, we show that this effective boundary condition corresponds to Navier slip condition when the model of G. D. R. Midi [Eur. Phys. J. E 14, 341 (2004)] is assumed to be valid, and that the slip length depends on the length scale that characterizes the system, viz. the particle diameter.