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

Sullivan, J.M. and Wilson, S.K. and Duffy, B.R. (2008) A thin rivulet of perfectly wetting fluid subject to a longitudinal surface shear stress. Quarterly Journal of Mechanics and Applied Mathematics, 61 (1). pp. 25-61. ISSN 0033-5614

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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.