Abstract
We consider the avalanche mixing of a monodisperse collection of granular solids in a slowly rotating drum. Although not yet well understood, this process has been studied experimentally for the case where the drum rotates slowly enough that each avalanche ceases completely before a new one begins. We develop a mathematical model for the mixing in both the discrete avalanche case and in the more useful case where the drum is rotated quickly enough to induce a continuous avalanche in the material but slowly enough to avoid significant inertial effects. This continuous model in turn provides a more plausible model of the discrete avalanche case. Although avalanches are inherently a nonlinear phenomenon, the mathematical model developed here reduces to a linear integral equation. The asymptotic behavior of the solution for an arbitrary initial distribution is consistent with those obtained experimentally.
Published Version
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