Axial dispersion of granular material in inclined rotating cylinders with bulk flow: Geometric model for 50% fill

• Analytic models for the mean squared deviation of axial position in rotating cylinders are developed.
• The models give sustained oscillations in the mean squared deviation.
• The results help to clarify the complex dynamics in inclined rotating cylinders.

Monte Carlo particle tracking methods used to model particle motion in inclined rotating cylinders with bulk flow have been reported in the literature. This paper reports some analytic results for the mean squared deviation of axial position in the following special case: the particles are in the rolling mode; the bed surface is flat, with no axial variation of bed depth; the avalanche is instantaneous and of negligible thickness; collisional axial dispersion is ignored; fill = 0.5. Fill = 0.5 means that in every half-rotation of the cylinder every particle will have participated in one and only one avalanche; this simplification allows analytic results to be obtained. The calculations are carried out by relating the number densities of tracer particles in successive cycles of avalanching. In the case of well-mixed avalanches, the model is also developed using a random walk approach. The results confirm predictions obtained from discrete element modelling and Monte Carlo particle tracking simulations, which indicate that the mean squared deviation of axial position can oscillate with time for short enough times.

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