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Steady symmetric low-Reynolds-number flow past a film-coated cylinder

Published online by Cambridge University Press:  11 September 2012

L. R. BAND ,
J. M. OLIVER ,
S. L. WATERS  and
D. S. RILEY
L. R. BAND
Affiliation:
Centre for Plant Integrative Biology, University of Nottingham, Sutton Bonington Campus, Loughborough, LE12 5RD, UK email: leah.band@nottingham.ac.uk School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK email: david.riley@nottingham.ac.uk
J. M. OLIVER
Affiliation:
Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK email: oliver@maths.ox.ac.uk, waters@maths.ox.ac.uk
S. L. WATERS
Affiliation:
Mathematical Institute, 24-29 St Giles’, Oxford OX1 3LB, UK email: oliver@maths.ox.ac.uk, waters@maths.ox.ac.uk
D. S. RILEY
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK email: david.riley@nottingham.ac.uk
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Abstract

In this study, we examine a steady two-dimensional slow flow past a rigid cylinder coated with a thin layer of immiscible fluid. The Reynolds number for the external bulk flow is assumed small and flow within the film is driven by the action of the bulk fluid’s tangential viscous stress acting at the interface. Using double asymptotic expansions based on the bulk fluid’s Reynolds number and the aspect ratio of the film thickness to the cylinder’s radius, we derive the leading- and first-order equations governing the steady-state film dynamics, and obtain analytical solutions, in terms of the film thickness, for the bulk flow. We solve the governing film equations, finding that solutions feature a drained region. We briefly discuss the influence of the Capillary number and fluid viscosities, and conclude by showing how the presence of the film affects the drag on the film-coated cylinder.

Keywords

thin-film flowStokes flowasymptotic expansions
Type
Papers
Information
European Journal of Applied Mathematics , Volume 24 , Issue 1 , February 2013 , pp. 1 - 24
Copyright
Copyright © Cambridge University Press 2012

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