A three-dimensional continuum model for coupled size segregation and flow in dense, bidisperse granular materials

When a non-monodisperse granular system undergoes flow, particles of similar sizes tend to gather together, a phenomenon known as size segregation, which can result in complex, non-homogeneous fields for the average particle size. The ability to predict how granular mixtures segregate is important in the design of industrial processes and the understanding of geophysical phenomena. At the continuum level, the two main drivers of size segregation are pressure gradients and strain-rate gradients. In this talk, we discuss a continuum model for the dynamics of segregation in bidisperse, dense granular flows that accounts for both driving mechanisms. Combined with the nonlocal granular fluidity (NGF) model (a nonlocal continuum model for dense granular flow), the coupled model is capable of quantitatively predicting segregation fields in quasi-one-dimensional flow configurations, such as vertical chute flow and inclined plane flow. Moreover, we have developed a finite-element-based numerical approach for solving the segregation dynamics equation (SDE) and the NGF model simultaneously. Our implementation is applied to a few three-dimensional inhomogeneous flow configurations: notably, annular shear flow with gravity and split-bottom flow with gravity, and we show that the coupled continuum model is capable of qualitatively capturing the segregation dynamics observed in three-dimensional discrete-element method simulations.