The Dean instability for shear-thinning fluids

• Published in: Journal of non-Newtonian fluid mechanics 2013-08, Vol.198, p.125-135
• Main Authors: Haines, Philip E., Denier, James P., Bassom, Andrew P.
• Format: Article
• Language: English
• Subjects: Aspect ratio; Bifurcation analysis; Dean vortices; Fluid flow; Instability; Mathematical analysis; Mathematical models; Navier-Stokes equations; Newtonian fluids; Shear-thinning fluid; Stability
• ISSN: 0377-0257; 1873-2631
• DOI: 10.1016/j.jnnfm.2013.05.004

•We consider the Dean instability for a generalised non-Newtonian fluid using an approximate power-law viscosity model.•The model incorporates a low-shear Newtonian plateau region.•The effect of channel aspect ratio is considered.•The results differ significantly from those for a Newtonian fluid.•The sensitivity of the results on the plateau region are considered. 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.