On the boundary-layer equations for power-law fluids

James P. Denier*, Paul P. Dabrowski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

65 Citations (Scopus)

Abstract

We reconsider the problem of the boundary-layer flow of a non-Newtonian fluid whose constitutive law is given by the classical Ostwald-de Waele power-law model. The boundary-layer equations are solved in similarity form. The resulting similarity solutions for shear-thickening fluids are shown to have a finite-width crisis resulting in the prediction of a finite-width boundary layer. A secondary viscous adjustment layer is required in order to smooth out the solution and to ensure correct matching with the far-field boundary conditions. In the case of shear-thinning fluids, the similarity forms have solutions whose decay into the far field is strongly algebraic. Smooth matching between these inner algebraically decaying solutions and an outer uniform flow is achieved via the introduction of a viscous diffusion layer.

Original languageEnglish
Pages (from-to)3143-3158
Number of pages16
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume460
Issue number2051
DOIs
Publication statusPublished - 8 Nov 2004
Externally publishedYes

Keywords

  • Boundary layer
  • Non-newtonian fluid
  • Power law

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