The geometric axial surface profiles of granular flows in rotating drums

A mechanistic description of axial segregation in rotating drum flows remains an open question. Consequently, optimal mixing of grinding balls and rocks for efficient breakage, maximum production of fines, and slurry transport is seldom achieved. Experimental and numerical studies of granular mixtures in rotating drums identify alternating axial bands that eventually coarsen in the long-term limit. Most models of axial segregation are limited to binary mixtures and cannot always predict the logarithmic coarsening effects observed experimentally. A key missing factor is a robust description of the axial free surface profile that is valid across a wide range of flow regimes. We present a practical model of the axial free surface profile by linking it to readily-derived geometric features of the cross-sectional S-shaped free surface profile. A parametric study shows good agreement with experimental measurements reported in the literature and heuristically valid trends.