Abstract
We study pressure-driven channel flow of a simple viscoelastic fluid whose elastic modulus and relaxation time are both power-law functions of shear-rate. We find that a known linear instability for the case of constant elastic modulus (Wilson and Rallison, 1999) persists and indeed becomes more dangerous when the elastic modulus is allowed to vary. The most unstable scenario is a highly shear-thinning relaxation time with a slightly shear-thinning elastic modulus, and typical unstable perturbations have a wavelength comparable with the channel width. Inertia is mildly destabilising.We compare with microchannel experiments (Bodiguel et al., 2015), and find qualitative agreement on the critical flow rate for instability; however, because of the artificial nature of the power-law viscosity, we have excluded the sinuous modes of instability which are seen in experiment.
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