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Instability of channel flow of a shear-thinning White-Metzner fluid

Wilson, HJ; Rallison, JM; (1999) Instability of channel flow of a shear-thinning White-Metzner fluid. Journal of Non-Newtonian Fluid Mechanics , 87 75 - 96. 10.1016/S0377-0257(99)00012-9.

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We consider the inertialess planar channel flow of a White-Metzner (WM) fluid having a power-law viscosity with exponent n. The case n=1 corresponds to an Upper Convected Maxwell (UCM) fluid. We explore the linear stability of such a flow to perturbations of wavelength 1/k. We find numerically that if n < nc ~ 0.3 there is an instability to disturbances having wavelength comparable with the channel width. For n close to nc, this is the only unstable disturbance. For even smaller n, several unstable modes appear, and very short waves become unstable and have the largest growth rate. If n exceeds nc, all disturbances are linearly stable. We consider asymptotically both the long wave limit which is stable for all n, and the short wave limit for which waves grow or decay at a finite rate independent of k for each n. The mechanism of this elastic shear-thinning instability is discussed.

Title:Instability of channel flow of a shear-thinning White-Metzner fluid
Keywords:Channel flow, Instability, Long wave, Short wave, Normal stresses, Shear-thinning, Power-law, White-Metzner, UCM
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics

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