Granular segregation in circular tumblers: theoretical model and scaling laws. (28th January 2015) - Schlick, Conor P.; Fan, Yi; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
Abstract: 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, ${\itΛ}$ ; the ratio of advection to diffusion, $Pe$ ; and the dimensionless flowing layer depth, ${\itε}$ . The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, ${\itΛ}\, Pe$, and the degree of segregation increases as ${\itΛ}Pe$ increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ${\itε}$ and $Pe$ when ${\itΛ}Pe$ is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.