Granular segregation in circular tumblers: theoretical model and scaling laws

Abstract

AbstractWe model bidisperse size segregation of granular material in quasi-two-dimensional circular tumbler flow using the advection–diffusion transport equation with an additional term to account for segregation due to percolation. Segregation depends on three dimensionless parameters: the ratio of segregation to advection, ${\it\Lambda}$; the ratio of advection to diffusion, $\mathit{Pe}$; and the dimensionless flowing layer depth, ${\it\epsilon}$. The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, ${\it\Lambda}\,\mathit{Pe}$, and the degree of segregation increases as ${\it\Lambda}\mathit{Pe}$ increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ${\it\epsilon}$ and $\mathit{Pe}$ when ${\it\Lambda}\mathit{Pe}$ is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.