Granular flow in partially filled slowly rotating drums

In many industrial processes granular materials are mixed together in partially filled slowly rotating drums. In this paper a general theoretical framework is developed for the quasi-two-dimensional motion of granular material in a rotating drum. The key assumption is that the body can be divided into a fluid-like and a solid-like region, that are separated by a non-material singular surface at which discontinuities occur. Experiments show that close to the free surface there is a thin rapidly moving fluid-like avalanche that flows downslope, and beneath it there is a large region of slowly rotating solid-like material. The solid region provides a net transport of material upslope and there is strong mass transfer between the two regions. In the theory the avalanche is treated as a shallow incompressible Mohr–Coulomb or inviscid material sliding on a moving bed at which there is erosion and deposition. The solid is treated as a rigid rotating body, and the two regions are coupled together using a mass jump condition. The theory has the potential to model time-dependent intermittent flow with shock waves, as well as steady-state continuous flow. An exact solution for the case of steady continuous flow is presented. This demonstrates that when the base of the 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 granular material mixes in the drum, and the results are compared with the predictions using the exact solution. 1. Introduction 1.1. Intermittent and continuous flow In many food manufacturing and industrial processes granular materials are often placed into a drum, pivoted so that its axis of rotational symmetry lies horizontally, and slowly rotated to try to mix the grains into a consistent blend (e. In all these flows the motion is characterized by a thin rapidly moving fluid-like avalanche of grains close to the free surface and a large solid-like region, beneath it, which slowly rotates about the axis of revolution. At slow rotation speeds there are essentially two flow regimes: intermittent flow and continuous flow (Rajchenbach 1990). In the intermittent flow regime, which is sometimes called avalanching flow, there are discrete avalanche events that come to rest before the next event starts, whereas in the continuous regime granular material is continually flowing downslope in a quasi-steady state. In this paper the term avalanche will be used to refer to both the …