Modeling size segregation driven by pressure gradients in three-dimensional, dense, bidisperse granular mixtures

Dense granular systems that consist of particles of disparate size segregate based on size during flow, and size-based segregation in granular mixtures is a longstanding problem in industrial and geophysical processes. The two primary driving forces of size segregation are pressure gradients and shear strain-rate gradients, which we study using three-dimensional discrete-element method (DEM) simulations of dense, bidisperse spheres. In this study, we consider a granular flow configuration called antiplane shear flow (ASF) in which gravitational pressure gradients are perpendicular to the plane of shear, which allows for the isolation of pressure gradient driven segregation from strain-rate gradient driven segregation. Moreover, we consider inclined plane flow (IPF), in which gravitational pressure gradients are within the plane of shear. Based on DEM simulation data, we propose a three-dimensional constitutive equation for the relative flux of large and small particles due to pressure gradients, which accounts for the orientation of the pressure gradient vector relative to the stretching tensor (i.e., the strain-rate tensor). When coupled with the nonlocal granular fluidity model (a nonlocal continuum model for dense granular flow) we show that segregation dynamics may be captured using the continuum model across all considered variations in driving conditions and mixture properties for ASF and IPF.