Predicting size and density segregation in granular flows*

As large and small particles flow, small particles fall between large particles to segregate in lower portions of a dense granular flow while displacing large particles upward, a process known as "percolation."  Similarly, heavy particles segregate below light particles as they flow due to "buoyancy."  The degree of segregation depends on the flow conditions and the differences between particles.  We address granular segregation in two ways.  The first approach is a continuum segregation model based on the advection-diffusion equation with a term added to account for particle segregation.  The model can predict mixing and segregation in both steady and transient flows for a variety of flow geometries and for a range of particle systems including multiple individual particle sizes, polydisperse particle size distributions, mixtures of particles varying in both size and density, and non-spherical particles.  Furthermore, the model's segregation velocity can be used to "design" non-segregating particle mixtures by adjusting particle size, density, and concentration.  The second approach is to consider the physics of granular segregation at the particle level via discrete particle simulations.  The result is the ability to predict the segregation force acting on an intruder particle as well as whether a single intruder particle will rise or sink in a bed of other particles.  These results have recently been extended from single intruder particles to cooperative phenomena in particle mixtures.  The ongoing challenge is to connect particle level forces to parameters in the continuum segregation model as well as to integrate the segregation model into constitutive models for granular flow.