Modeling continuous mixing of granular solids in a rotating drum

✍ Scribed by Barry A. Peratt; James A. Yorke

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 958 KB
• Volume: 118
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(98)00018-9

✦ Synopsis

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.