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Type: Journal article
Title: Thin-film flow in helically-wound rectangular channels of arbitrary torsion and curvature
Author: Arnold, D.
Stokes, Y.
Green, J.
Citation: Journal of Fluid Mechanics, 2015; 764:76-94
Publisher: Cambridge University Press
Issue Date: 2015
ISSN: 0022-1120
Statement of
D. J. Arnold, Y. M. Stokes, and J. E. F. Green
Abstract: Laminar helically-symmetric gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section is considered. We extend the work of Stokes et al. (Phys. Fluids, vol. 25 (8), 2013, 083103) and Lee et al. (Phys. Fluids, vol. 26 (4), 2014, 043302) 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. We find that the free-surface shape and flow have a complicated dependence on the curvature, slope and flux down the channel. Moderate to large channel slope has a significant effect on the flow in the region of the channel near the inside wall, particularly when the curvature of the channel is large. This work has application to flow in static spiral particle separators used in mineral processing.
Keywords: lubrication theory; thin films; waves/free-surface flows
Rights: © Cambridge University Press 2014
DOI: 10.1017/jfm.2014.703
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Mathematical Sciences publications

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