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