Thin-film flow in helically wound rectangular channels with small torsion

Y.M. Stokes, Brian R. Duffy, Stephen K. Wilson, H. Tronnolone

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Laminar gravity-driven thin-film flow down a helically-wound channel of rectangular cross-section with small torsion in which the fluid depth is small is considered. Neglecting the entrance and exit regions we obtain the steady-state solution that is independent of position along the axis of the
channel, so that the flow, which comprises a primary flow in the direction of the axis of the channel and a secondary flow in the cross-sectional plane, depends only on position in the two-dimensional cross-section of the channel. A thin-film approximation yields explicit expressions for the fluid velocity and pressure in terms of the free-surface shape, the latter satisfying a non-linear ordinary
differential equation that has a simple exact solution in the special case of a channel of rectangular cross-section. The predictions of the thin-film model are shown to be in good agreement with much more computationally intensive solutions of the small-helix-torsion Navier–Stokes equations. The
present work has particular relevance to spiral particle separators used in the mineral-processing industry. The validity of an assumption commonly used in modelling flow in spiral separators, namely that the flow in the outer region of the separator cross-section is described by a free vortex, is shown to depend on the problem parameters.
Original languageEnglish
Article number083103
Number of pages22
JournalPhysics of Fluids
Issue number8
Early online date21 Aug 2013
Publication statusPublished - 2013


  • thin-film
  • Navier–Stokes equations
  • spiral separators
  • Laminar gravity


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