Axial segregation of granular flows in rotating drums - Ahmed, Elbasher M E (Department of Physics, 2023)
A mechanistic model of axial segregation in rotating drums is presented for mixtures of granular material. We show that grains composed of different material properties which are heuristically argued to manifest as differences in frictional properties at the continuum scale-diffuse into axial bands as a consequence of concentration fluctuations in the free surface layer caused by friction- limited mobility. The model is composed of two new ingredients that success- fully recover the well-known phenomenon of axial banding and subsequent band coarsening in the long-time evolution: (1) A Bagnoldian stress assumption facilitated band formation at drum fill levels < 50% that have hitherto not been possible with a Newtonian shear stress ansatz, through the formation of an asymmetric free surface profile that is experimentally verified by the nuclear imaging technique of Positron Emission Particle Tracking. (2) The geometric slope corresponding to the gravity-driven axial flux between adjacent bands is (binomially) expanded to second order thereby ensuring band coarsening in the long-time limit for all boundary conditions investigated. Numerical implementation of the axial diffusion model is shown to be sensitive to the boundary conditions of the tumbling mill (particle size, volume concentration, mill speed, average friction, end wall friction, drum length and drum diameter). The explicit solutions for a binary-, ternary-, quaternary- and n-species granular mixture was developed with numerical implementation up to n = 4. Consistent with experimental observations in the literature, the 3-species mixture successfully captures bands within bands, while the 4-species mixture successfully recovers bands within bands, within bands.