Predicting polydisperse granular segregation

Most granular materials in industrial applications and natural settings are size-polydisperse, but most models and simulations of segregation consider only bidisperse particle distributions. Here, we extend our recently developed theoretical advection–diffusion–segregation model to polydisperse particle distributions. To test the theoretical approach, we model and simulate grains log-normally distributed by size in a chute flow. In steady state, material near the free surface is dominated by large particles, whereas the lower regions are composed of mostly small particles. The segregation pattern depends on a single dimensionless control parameter, which is a function of the particle sizes, the diffusion coefficient, the shear rate, and the flowing layer depth. Interestingly, for all values of the control parameter, the overall log normal particle size distribution is approximately maintained at each spatial location, but with different mean and variance than the overall particle distribution. To confirm the theoretical results, we use discrete element method (DEM) simulations using a general purpose graphics processing unit. Quantitative agreement is found between theory and DEM simulations. Funded by the Dow Chemical Company

On Mixing and Segregation: From Fluids and Maps to Granular Solids and Advection–Diffusion Systems

In fluids, diffusive transport and fluid parameters are determined by the thermally driven movement of molecules, whereas in granular media, thermal effects play no role in transport. Despite this fundamental difference, mixing in fluids and mixing and segregation in granular solids share many similarities. The advection–diffusion equation formalism unites the two systems and can be used in both cases to predict and understand how and when mixing occurs, through the use of strategic simplifications. We illustrate this connection with a fluid mixing example (the rotated potential mixer) and a granular segregation example (the segregation of a bidisperse mixture flowing in a chute)