Granular segregation in circular tumblers: theoretical model and scaling laws. (28th January 2015)

• Record Type: Journal Article
• Authors: Schlick, Conor P.; Fan, Yi; Umbanhowar, Paul B.; Ottino, Julio M.; Lueptow, Richard M.
• Is Part Of: Journal of fluid mechanics. Volume 765(2015:Feb.)
• Page Start: 632
• Page End: 652
• Publication Date: 2015-01-28
• Subjects: complex fluids, -- granular media, -- granular mixing; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2015.4
• Languages: English
• ISSNs: 0022-1120

Abstract

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, ${\it\Lambda}$ ; 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.