The Stokes boundary layer for a power-law fluid

David Pritchard, Catriona R. McArdle, Stephen K. Wilson

Research output: Contribution to journalArticle

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Abstract

We develop semi-analytical, self-similar solutions for the oscillatory boundary layer (‘Stokes layer’) in a semi-infinite power-law fluid bounded by an oscillating wall (the so-called Stokes problem). These solutions differ significantly from the classical solution for a Newtonian fluid, both in the non-sinusoidal form of the velocity oscillations and in the manner at which their amplitude decays with distance from the wall. In particular, for shear-thickening fluids the velocity reaches zero at a finite distance from the wall, and for shear-thinning fluids it decays algebraically with distance, in contrast to the exponential decay for a Newtonian fluid. We demonstrate numerically that these semi-analytical, self-similar solutions provide a good approximation to the flow driven by a sinusoidally oscillating wall.

Original languageEnglish
Pages (from-to)745-753
Number of pages9
JournalJournal of Non-Newtonian Fluid Mechanics
Volume166
Issue number12-13
Early online date13 Apr 2011
DOIs
Publication statusPublished - Jul 2011

Keywords

  • Stokes’s second problem
  • power-law
  • Ostwald–de Waele
  • oscillatory boundary layer
  • Stokes layer

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