Stability of granular flow in converging hoppers

This paper investigates the steady state flow of an incompressible granular material in a converging hopper, in two and three dimensions. The material is modeled as a continuum which is in plastic yield throughout the bin. A.W. Jenike adopted such a model and found a similarity solution of the governing equations. In this paper, the stability of Jenike's solution to time-independent perturbations is examined, with attention given to the effect of material parameters on stability. Specifically, a linearized stability analysis is used to show that flows in three dimensions are usually stable to small perturbations, while many flows are unstable in two dimensions. It is also shown that an often used one-dimensional 'slice analysis' gives misleading stability results. Finally, the governing equations are solved numerically, thereby exploring the nonlinear behavior of solutions.