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Phys. Fluids 26, 043302 (2014);
Sungyon Lee1,2,a), Yvonne Stokes 3,b) , Andrea L. Bertozzi 1,c
1 Department of Mathematics and Applied Mathematics Laboratory, University of California, Los Angeles, California 90095, USA and
2 Department of Mechanical Engineering, Texas A&M, College Station, Texas 77843, USA and
3 School of Mathematical Sciences, The University of Adelaide, South Australia 5005, Australia
Abstract
Spiral gravity separators are devices used in mineral processing to separate particles based on their specific gravity or size. The spiral geometry allows for the simultaneous application of gravitational and centripetal forces on the particles, which leads to segregation of particles. However, this segregation mechanism is not fundamentally understood, and the spiral separator literature does not tell a cohesive story either experimentally or theoretically. While experimental results vary depending on the specific spiral separator used, present theoretical works neglect the significant coupling between the particle dynamics and the flow field. Using work on gravity-driven monodisperse slurries on an incline that empirically accounts for this coupling, we consider a monodisperse particle slurry of small depth flowing down a rectangular channel that is helically wound around a vertical axis. We use a thin-film approximation to derive an equilibrium profile for the particle concentration and fluid depth and find that, in the steady state limit, the particles concentrate towards the vertical axis of the helix, leaving a region of clear fluid.
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