Particle Force-Based Continuum Model for Multicomponent Size Segregating Mixtures

Abstract

We investigate size difference driven segregation in dense granular flows of multicomponent mixtures down a periodic chute using continuum model and Discrete Element Method (DEM) simulations. A previously developed particle force-based segregation model for binary mixtures is systematically extended to mixtures comprising three or more particle species differing in size. The generalized model accounts for inter-species interactions by computing the net force on each component in the presence of all others, without relying on empirical percolation velocity. This segregation model is coupled with a mixture rheology model and incorporated into the species transport and momentum balance equations to develop a continuum model that predicts the spatial and temporal evolution of species concentration and velocity fields. The continuum model predictions are found to be in agreement with DEM simulation data for ternary and quaternary mixtures over a wide range of mixture compositions and chute inclinations at moderate size ratios for well-mixed and small-near-base configurations. For larger size ratios, the one dimensional model predictions capture the qualitative segregation trend while showing relatively larger quantitative differences from DEM data. For an initial configuration, having large particles near base and small particles near the free surface, a Rayleigh-Taylor like instability at early times is observed. Due to the presence of this instability, two dimensional evolution of the species concentration fields is present for initial part of the flow. Predictions of such features requires the extension of the one dimensional continuum model to two dimensions.