110th anniversary: continuum modeling of granular mixing in a rotating drum

The mixing of granular materials is notoriously difficult to predict partly due to the complicated mixing mechanisms of particles and their variable flow kinematics. Despite many theoretical studies in idealized configurations of chute and rolling-mode drum, a generic macroscopic model for granular mixing has not been achieved. This paper proposes a continuum model for simulating the mixing of monodisperse particles by combining the μ(I) rheological theory and the convection-diffusion transport equation. The model, implemented via an operator-split scheme, is completely temporal-spatial and able to deal with both continuous flows and transient avalanches. Equipped with a rate-dependent diffusivity, it well recovers the particle concentration at different stages of mixing in slowly rotating drum. Moreover, having been used to simulate granular flow under different conditions, the proposed continuum model may have the potential as a general model to describe particle mixing in different processes.