Granular flow in partially filled slowly rotating drums

Abstract

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 fluidlike 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.

Particle-size segregation and diffusive remixing in shallow granular avalanches

“…The theory is designed to be compatible with the assumptions of shallowness, incompressibility and bulk lithostatic pressure, that are made by almost all current avalanche models (e.g. Grigorian et al 1967;Kulikovskii & Eglit 1973;Eglit 1983;Savage & Hutter 1989;Iverson 1997;Gray et al 1999Gray et al , 2003Iverson & Denlinger 2001;Gray 2001). The segregation-remixing theory can therefore be coupled to these models to compute segregation and remixing in dynamically evolving avalanches.…”

“…Grigorian, Eglit & Iakimov 1967;Kulikovskii & Eglit 1973;Eglit 1983;Savage & Hutter 1989;Iverson 1997;Gray, Wieland & Hutter 1999;Iverson & Denlinger 2001;Gray 2001;Gray et al 2003) that the bulk velocity u is incompressible and the overburden pressure p is lithostatic.…”

“…The avalanche is now in a steady state maintained by continuous erosion and deposition at its base (e.g. Gray 2001) and the diffusion is considerably stronger in this higher-energy flow. The reverse grading within the flowing avalanche is therefore weaker and this is reflected in the radial grading in the underlying rotating material.…”

A three-phase mixture theory for particle size segregation in shallow granular free-surface flows

“…Rotating drums and blenders (e.g. Metcalfe et al 1995, Shinbrot et al 1999, Hill et al 1999, Gray 2001 are often used in the pharmaceutical and food industry, while rotary kilns and inclined rotating cylinders (e.g. Davidson et al 2000, Spurling et al 2001) are favoured by chemical engineers for sintering, calcination, humidification, oxidation, drying, mixing, induration, reducing, gas-solid reaction, incineration, heating, cooling and cement production, because they allow continuous feed.…”

On impinging near‐field granular jets

“…For example, for many materials, relatively large electrostatic charges can build up for grains below the one millimeter scale. For general overviews of different granular physical phenomena, we refer the reader to work by Behringer and collaborators [1][2][3], Hutter and collaborators [4][5][6][7][8][9][10][11][12][13][14][15][16][17], and Jaeger and collaborators [18][19][20][21][22][23][24][25][26].…”