### Abstract

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.

Language | English |
---|---|

Article number | 083103 |

Number of pages | 22 |

Journal | Physics of Fluids |

Volume | 25 |

Issue number | 8 |

Early online date | 21 Aug 2013 |

DOIs | |

Publication status | Published - 2013 |

### Fingerprint

### Keywords

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

### Cite this

*Physics of Fluids*,

*25*(8), [083103]. https://doi.org/10.1063/1.4818628

}

*Physics of Fluids*, vol. 25, no. 8, 083103. https://doi.org/10.1063/1.4818628

**Thin-film flow in helically wound rectangular channels with small torsion.** / Stokes, Y.M.; Duffy, Brian R.; Wilson, Stephen K.; Tronnolone, H.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Thin-film flow in helically wound rectangular channels with small torsion

AU - Stokes, Y.M.

AU - Duffy, Brian R.

AU - Wilson, Stephen K.

AU - Tronnolone, H.

PY - 2013

Y1 - 2013

N2 - 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 thechannel, 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 ordinarydifferential 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. Thepresent 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.

AB - 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 thechannel, 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 ordinarydifferential 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. Thepresent 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.

KW - thin-film

KW - Navier–Stokes equations

KW - spiral separators

KW - Laminar gravity

UR - http://www.scopus.com/inward/record.url?scp=84883423412&partnerID=8YFLogxK

U2 - 10.1063/1.4818628

DO - 10.1063/1.4818628

M3 - Article

VL - 25

JO - Physics of Fluids

T2 - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 8

M1 - 083103

ER -