Behavior of a particle-laden flow in a spiral channel

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 literatures 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.

Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature

“…Thus the flow, which comprises a primary flow down the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section. We make no assumptions of small channel torsion or slope and so extend the work of Stokes et al (2013) for channels of small centreline torsion, and of Lee et al (2014) for channels of small centreline slope. Using a non-orthogonal coordinate system, as in Lee et al (2014), we are, remarkably, able to find an exact solution of our thin-film model.…”

“…We make no assumptions of small channel torsion or slope and so extend the work of Stokes et al (2013) for channels of small centreline torsion, and of Lee et al (2014) for channels of small centreline slope. Using a non-orthogonal coordinate system, as in Lee et al (2014), we are, remarkably, able to find an exact solution of our thin-film model. Our use of a nonorthogonal coordinate system and accounting for a channel slope that varies with position across the channel width reveal corrections to the results of Stokes et al (2013).…”

“…In experiments performed by Holtham (1992) using two commercially-available spiral separators with an approximate width of 280mm, the fluid depth was 1-12mm, an aspect ratio δ < 0.1. Thus, Stokes et al (2004Stokes et al ( , 2013 and Lee et al (2014) have exploited the small depth of the flow to develop thin-film models of particle-free and particle-laden flow in helically-wound channels. These studies have considered limiting cases of channel geometry, such as small curvature, torsion or slope and indicate that the assumption made by Holland-Batt (1989, 2009) of a free-vortex primary flow in the channel is not, in general, valid in these limits.…”

“…In this paper we retain the assumption of small fluid depth but consider particle-free flow in channels of arbitrary curvature and torsion. In future work, the model will be extended using the approach of Lee et al (2014) to investigate particle-laden flow.…”

“…We extend the work of Stokes et al (2013) and Lee et al (2014) to channels with arbitrary curvature and torsion or, equivalently, arbitrary curvature and slope. We use a non-orthogonal coordinate system and, remarkably, find an exact steady-state solution.…”