Nonlinear elastic instability of gravity-driven flow of a thin viscoelastic film down an inclined plane

Feng Kang, Kangping Chen

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

A nonlinear evolution equation for the thickness of a thin viscoelastic film flowing down an inclined plane is derived for an Oldroyd-B fluid, using a long wave approximation. The evolution equation is valid to the second order in a small parameter which measures the relative thickness of the film to a typical wavelength. For a very thin film, viscoelasticity dominates the stability of the film and it can cause a purely elastic instability. The weakly nonlinear development of a monochromatic wave resulting from this elastic instability is studied using the second-order evolution equation which allows us to investigate the effects of inclination angle on the bifurcation. It is found that although extremely long waves bifurcate subcritically, the linearly most amplified wave does bifurcate supercritically when the surface tension parameter J > 13.8035. It is demonstrated that for a fixed bifurcation parameter δ = Wi - Wic, increasing the inclination angle can reduce the equilibrium amplitude for a supercritical bifurcating wave.

Original languageEnglish (US)
Pages (from-to)243-252
Number of pages10
JournalJournal of Non-Newtonian Fluid Mechanics
Volume57
Issue number2-3
DOIs
StatePublished - May 1995

Keywords

  • Bifurcation
  • Elastic instability
  • Thin viscoelastic films

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics

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