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The Dean instability for shear-thinning fluids

journal contribution
posted on 2023-05-18, 15:44 authored by Haines, PE, Denier, JP, Andrew BassomAndrew Bassom
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.

History

Publication title

Journal of Non-Newtonian Fluid Mechanics

Volume

198

Pagination

125-135

ISSN

0377-0257

Department/School

School of Natural Sciences

Publisher

Elsevier Science Bv

Place of publication

Po Box 211, Amsterdam, Netherlands, 1000 Ae

Repository Status

  • Restricted

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