Applicability of the 3D Advection-Diffusion Model to a Bladed Granular Mixer

The one-dimensional form of the advection-diffusion equation has been used to model axial mixing in rotating drums in a number of studies.  This work attempts to examine whether granular mixing in more complex geometries can be modeled using the three-dimensional form of the advection-diffusion equation.  A horizontal, cylindrical granular mixer with rotating impeller blades is the system under consideration.  The inputs required for the advection-diffusion model (convective velocities and diffusion coefficients) are obtained from a discrete element method (DEM) simulation of the granular mixer.   The variation in concentration of a tracer species with location is computed using a finite difference numerical solution of the 3D advection-diffusion equation.  The results obtained from the advection-diffusion model are compared against measurements from the DEM simulation, which is considered as the “exact solution”.  This proposed methodology presents an efficient multi-scale modeling technique that uses measurements from short DEM simulations as inputs for predicting mixing performance over longer time scales.