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

Published online by Cambridge University Press:  23 December 2014

D. J. Arnold ,
Y. M. Stokes  and
J. E. F. Green
D. J. Arnold
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
Y. M. Stokes*
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
J. E. F. Green
Affiliation:
School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Low-Reynolds-number flows: Lubrication theory Interfacial Flows (free surface): Thin films Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 76 - 94
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Copyright
© 2014 Cambridge University Press 

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