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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 BassomWe 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 MechanicsVolume
198Pagination
125-135ISSN
0377-0257Department/School
School of Natural SciencesPublisher
Elsevier Science BvPlace of publication
Po Box 211, Amsterdam, Netherlands, 1000 AeRepository Status
- Restricted