Granular flow in partially filled slowly rotating drums

In many industrial processes granular materials are mixed together in parti ally filled slowly rotating drums. In this paper a general theoretical fram ework is developed for the quasi-two-dimensional motion of granular materia l in a rotating drum. The key assumption is that the body can be divided in to a fluid-like and a solid-like region, that are separated by a non-materi al singular surface at which discontinuities occur. Experiments show that c lose to the free surface there is a thin rapidly moving fluidlike avalanche that flows downslope, and beneath it there is a large region of slowly rot ating solid-like material. The solid region provides a net transport of mat erial upslope and there is strong mass transfer between the two regions. In the theory the avalanche is treated as a shallow incompressible Mohr-Coulo mb or inviscid material sliding on a moving bed at which there is erosion a nd deposition. The solid is treated as a rigid rotating body, and the two r egions are coupled together using a mass jump condition. The theory has the potential to model time-dependent intermittent flow with shock waves, as w ell as steady-state continuous flow. An exact solution for the case of stea dy continuous flow is presented. This demonstrates that when the base of th e avalanche lies above the axis of revolution a solid core develops in the centre of the drum. Experiments are presented to show how a mono-disperse g ranular material mixes in the drum. and the results are compared with the p redictions using the exact solution.