Travelling-wave similarity solution for unsteady flow around a dry patch driven by gravity and constant surface shear stress

Yazariah Mohd Yatim, Brian Duffy, Stephen Wilson

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In this paper we use the lubrication approximation to analyse three-dimensional unsteady flow of a thin film of Newtonian fluid around a symmetric slender moving dry patch on an inclined planar substrate. The flow being driven by gravity and a prescribed constant shear stress at the free surface. We obtain a novel unsteady travelling-wave similarity solution for the dry patch of uniform thickness, in which the dry patch travels at constant speed. This solution predicts that the dry patch has a parabolic shape which may be concave up or concave down the substrate. In all
cases investigated numerically the film thickness is found to increase monotonically away from the contact line.
Original languageEnglish
Title of host publicationProceedings of the 2nd International Symposium on Frontiers of Computational Sciences 2012
Number of pages11
Publication statusPublished - 2012
Event2nd international symposium on frontiers of computational sciences - Islamabad, Pakistan
Duration: 28 Jun 201229 Jun 2012


Conference2nd international symposium on frontiers of computational sciences


  • travelling-wave
  • similarity solutions
  • Newtonian fluid
  • dry patch
  • thin-film flow

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