Transition between Shear-Induced Segregation and Free-Sifting of Fines

Granular mixtures of particles with various properties (e.g., size, density, shape, and roughness) tend to segregate when subjected to mechanical excitation in a wide range of industrial processes and nature. For a mixture of size-bidisperse spherical particles, the large to small particle diameter ratio, R, determines whether shear-induced segregation (small R) or free-sifting (large R) occurs, but the transition between these two extremes remains largely unexplored. Using discrete element method simulations, we study percolation of small particles (fines) in static random packings of large particles and in free-surface flows with R ranging from 3 to 7.5. For the static case, there are three regimes. (i) For R>6.464 (the geometric trapping threshold, which characterizes the smallest opening formed by identical large particles), all fines fall through the voids between large particles due to gravity alone, and the average percolation velocity is constant and nearly independent of R. However, the percolation of fines is normally diffusive only for R>6.6 but anomalous for 6.464<R<6.6. (ii) A transition occurs for 4<R<6.464, where only a fraction of the fines percolates in a static bed of large particles, taking longer to do so and percolating an increasingly shorter distance as R is reduced. (iii) For R<4, particles do not appreciably penetrate the static bed. For the free-surface flow case (periodic chute flow), fines for R>5 percolate quickly (compared to the static bed) at a velocity that is only weakly dependent on R and the local shear rate, much like free-sifting in a static bed. For R<5 the small particle percolation velocity decreases with decreasing R, approaching zero in the monodisperse limit.