Dilatant double shearing theory applied to granular chute flow

Summary Although the steady flow of a granular material down a plane inclined slope has been exhaustively examined from both theoretical and experimental points of view, there is still no general agreement concerning the basic flow properties such as density and velocity profiles. The majority of studies assume that the velocity component of the material perpendicular to the inclined plane is sufficiently small to assume that it is everywhere zero. However, recent dynamical modelling of granular chute flow indicates that this component of velocity, although small, is actually non-zero. In this paper, we examine a dilatant double shearing theory for chute flow assuming that the perpendicular component of velocity is non-zero. An explicit analytical form for the perpendicular velocity profile is deduced which gives rise to an integral expression for the chute stream velocity. Assuming a linear decreasing density profile, numerical integration for the chute stream velocity predicts a non-linear profile which is concave in shape and which is in agreement with recent results from computer simulation and existing experimental data in the literature.