Incompressible Poiseuille flows of Newtonian liquids with a pressure-dependent viscosity

Anna Kalogirou, Stella Poyiadji, Georgios C. Georgiou

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

The pressure-dependence of the viscosity becomes important in flows where high pressures are encountered. Applications include many polymer processing applications, microfluidics, fluid film lubrication, as well as simulations of geophysical flows. Under the assumption of unidirectional flow, we derive analytical solutions for plane, round, and annular Poiseuille flow of a Newtonian liquid, the viscosity of which increases linearly with pressure. These flows may serve as prototypes in applications involving tubes with small radius-to-length ratios. It is demonstrated that, the velocity tends from a parabolic to a triangular profile as the viscosity coefficient is increased. The pressure gradient near the exit is the same as that of the classical fully developed flow. This increases exponentially upstream and thus the pressure required to drive the flow increases dramatically. (C) 2011 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)413-419
Number of pages7
JournalJournal of Non-Newtonian Fluid Mechanics
Volume166
Issue number7-8
DOIs
Publication statusPublished - Apr 2011
Externally publishedYes

Keywords

  • Newtonian flow
  • Poiseuille flow
  • Pressure-dependent viscosity
  • Annular Poiseuille flow
  • NAVIER-STOKES EQUATIONS
  • POLYMER MELTS
  • FLUIDS
  • SHEAR
  • MANTLE

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