TY - JOUR
T1 - Modelling size segregation of granular materials
T2 - The roles of segregation, advection and diffusion
AU - Fan, Yi
AU - Schlick, Conor P.
AU - Umbanhowar, Paul B.
AU - Ottino, Julio M.
AU - Lueptow, Richard M.
PY - 2014/2
Y1 - 2014/2
N2 - Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation and diffusion in size bidisperse granular materials. The fluxes associated with these three driving factors depend on the underlying kinematics, whose characteristics play key roles in determining particle segregation configurations. Unlike previous models for segregation, our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters, and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi-twodimensional bounded heaps. The model yields two dimensionless control parameters, both of which are only functions of control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, Pe, captures the interplay of advection and diffusion, and the second dimensionless parameter, A, describes the interplay between segregation and advection. A parametric study of A and Pe demonstrates how the particle segregation configuration depends on the interplay of advection, segregation and diffusion. The model can be readily adapted to other flow geometries.
AB - Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation and diffusion in size bidisperse granular materials. The fluxes associated with these three driving factors depend on the underlying kinematics, whose characteristics play key roles in determining particle segregation configurations. Unlike previous models for segregation, our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters, and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi-twodimensional bounded heaps. The model yields two dimensionless control parameters, both of which are only functions of control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, Pe, captures the interplay of advection and diffusion, and the second dimensionless parameter, A, describes the interplay between segregation and advection. A parametric study of A and Pe demonstrates how the particle segregation configuration depends on the interplay of advection, segregation and diffusion. The model can be readily adapted to other flow geometries.
KW - Granular media
KW - Granular segregation
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U2 - 10.1017/jfm.2013.680
DO - 10.1017/jfm.2013.680
M3 - Article
AN - SCOPUS:84901808963
VL - 741
SP - 252
EP - 279
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
SN - 0022-1120
ER -