Travelling-wave similarity solutions for a steadily translating slender dry patch in a thin fluid film

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Abstract

A novel family of three-dimensional travelling-wave similarity solutions describing a steadily translating slender dry patch in an infinitely wide thin fluid film on an inclined planar substrate when surface-tension effects are negligible is obtained, the flow being driven by gravity and/or a prescribed constant shear stress on the free surface of the film. For both driving mechanisms, the dry patch has a parabolic shape (which may be concave up or concave down the substrate), and the film thickness increases monotonically away from the contact lines to its uniform far-field value. The two most practically important cases of purely gravity-driven flow and of purely surface-shear-stress-driven flow are analysed separately.
Original languageEnglish
Article number052103
Number of pages27
JournalPhysics of Fluids
Volume25
Issue number5
Early online date21 May 2013
DOIs
Publication statusPublished - May 2013

Keywords

  • film flow
  • flow instability
  • liquid films
  • shear strength
  • substrates
  • thin films
  • waves

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