Three-dimensional model for particle-size segregation by shaking

Abstract

A three-dimensional model for particle-size segregation by shaking has been developed and used to study the upward motion of a large sphere in a random packing of smaller spheres. In this model segregation occurs only for values of the diameter ratio (\ensuremath{\Phi}) above a critical value ${\mathrm{\ensuremath{\Phi}}}_{\mathit{c}}$\ensuremath{\simeq}2.8. The ratio of the upward velocity of the large particles to their diameter is greatest for values of \ensuremath{\Phi} just larger than ${\mathrm{\ensuremath{\Phi}}}_{\mathit{c}}$. The simulation results can be understood in terms of a simple theoretical model that becomes exact in the limit \ensuremath{\Phi}\ensuremath{\rightarrow}\ensuremath{\infty}.