Granular segregation in circular tumblers: theoretical model and scaling laws

We 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, Λ ; the ratio of advection to diffusion, Pe ; and the dimensionless flowing layer depth, ε . The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, Λ\,Pe , and the degree of segregation increases as ΛPe increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ε and Pe when ΛPe is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.