Abstract
Axial segregation of polydisperse granular mixtures in rotating drums have been observed in several experimental and discrete particle simulation studies reported in the literature. A common thread to both experimental and numerical studies is the formation of (alternating) bands which eventually coarsen in the long-time limit due to logarithmic merging. Models to explain the experimental observations are generally limited to bidisperse mixtures, and often unable to reproduce band coarsening. One such mechanism for bidisperse mixtures argues that the grains eventually diffuse into axial bands as a consequence of concentration fluctuations in the free surface layer caused by friction-limited mobility. We generalise this model to multi-species mixtures and show that the solution produces banding that evolves more complexly than binary mixtures, with sinusoidal-like variations of the band structure that evolves non-linearly in time. In addition, we successfully recover band coarsening with time—an observation that is generally difficult to reproduce, even experimentally. Contrary to literature findings, the configurations herein did not produce bands within bands for ternary and quaternary mixtures.
Highlights
Segregation, and the dual phenomena of mixing, play a vital role in several industrial processes
We present a general formula to obtain the set of partial differential equations (PDEs) that describe axial segregation of any polydisperse mixture
We have shown previously [29] that: (a) band coarsening can be achieved by introducing a second order binomial expansion to the axial gradient operator; and to extend the theory to less than half full drums, a Bagnoldian shear stress assumption was required
Summary
Segregation, and the dual phenomena of mixing, play a vital role in several industrial processes. Some of the segregation mechanisms reported in the literature include gravity, stress gradients, granular temperature gradients and porosity gradients Particle properties such as size, density, inertia, surface roughness (friction) and shape often determines the extent to which a given segregation mechanism plays out. [26] experimentally investigated axial segregation of polydisperse mixtures in rotating drums. They used mixtures ranging from three to six different particle sizes with all other particle properties being identical. Notwithstanding the plethora of confounding factors influencing segregation, the literature does suggest that friction plays a major role in axial segregation within rotating drum flows. The time evolution of the resulting axial concentration profile is used to illustrate band formation and its eventual coarsening for binary, ternary and quaternary mixtures
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