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Air-blown rivulet flow of a perfectly wetting fluid on an inclined substrate

Sullivan, J.M. and Wilson, S.K. and Duffy, B.R. (2008) Air-blown rivulet flow of a perfectly wetting fluid on an inclined substrate. In: Mathematics in Industry. Springer, pp. 774-778. ISBN 978-3-540-71991-5

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Thin-film flows occur in a variety of physical contexts including, for example, industry, biology and nature, and have been the subject of considerable theoretical research. (See, for example, the review by Oron, Davis and Bankoff [4].) In particular, there are several practically important situations in which an external airflow has a significant effect on the behaviour of a film of fluid, and consequently there has been considerable theoretical and numerical work done to try to understand better the various flows that can occur. (See, for example, the studies by King and Tuck [2] and Villegas-Díaz, Power and Riley [6].) The flow of a rivulet on a planar substrate subject to a shear stress at its free surface has been investigated by several authors, notably Myers, Liang and Wetton [3], Saber and El-Genk [5], and Wilson and Duffy [9]. All of these works concern a non-perfectly wetting fluid; the flow of a rivulet of a perfectly wetting fluid in the absence of a shear stress at its free surface has been treated by Alekseenko, Geshev and Kuibin [1], and by Wilson and Duffy [7,8]. In the present short paper we use the lubrication approximation to obtain a complete description of the steady unidirectional flow of a thin rivulet of a perfectly wetting fluid on an inclined substrate subject to a prescribed uniform longitudinal shear stress at its free surface.