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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on January 3, 2008
The Quarterly Journal of Mechanics and Applied Mathematics 2008 61(1):25-61; doi:10.1093/qjmam/hbm023
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Q. Jl Mech. Appl. Math, Vol. 61. No. 1 © The author 2008. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress

J. M. Sullivan, S. K. Wilson{dagger} and B. R. Duffy

( Department of Mathematics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH )

{dagger} < s.k.wilson{at}strath.ac.uk>

Received 26 January 2007. Revise 7 September 2007. Accepted 11 October 2007.


  Abstract

The lubrication approximation is used to obtain a complete description of the steady unidirectional flow of a thin rivulet of perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal surface shear stress. The quasi-steady stability of such a rivulet is analysed, and the conditions under which it is energetically favourable for such a rivulet to split into one or more subrivulets are determined.


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