The Dean instability for shear-thinning fluids

Philip E. Haines, James P. Denier*, Andrew P. Bassom

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We investigate the Dean instability for a generalised Newtonian fluid which satisfies an approximately power-law viscosity model, albeit modified to incorporate a low-shear Newtonian plateau. Infinite aspect ratio linear stability results are presented for both a narrow-gap width and a finite radius of curvature. These results reveal a surprising sensitivity to the details of the low-shear Newtonian region. Finite element solutions of the axisymmetric Navier-Stokes equations for flow through a finite aspect ratio duct confirm this sensitivity and, in addition, demonstrate the potential for hysteresis on the primary branch of vortices. A detailed bifurcation analysis over a range of the aspect ratio reveals that the nonlinear structure of the problem is qualitatively similar to that for a Newtonian fluid despite the apparently quite distinctive behaviour when a comparison is made at a fixed aspect ratio.

Original languageEnglish
Pages (from-to)125-135
Number of pages11
JournalJournal of Non-Newtonian Fluid Mechanics
Publication statusPublished - Aug 2013
Externally publishedYes


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