Elastic instabilities in pressure-driven channel flow of thixotropic-viscoelasto-plastic fluids

We study the stability of pressure-driven channel flow of a thixotropic-viscoelasto-plastic fluid. Several recent experiments have shown that channel flows of shear-thinning polymer solutions can be linearly unstable even at very low Reynolds numbers. We use the Bautista-Manero-Puig model (BMP) to attempt to capture the physics of these instabilities. We obtain an analytic solution for the steady-state velocity profile, dependent on our fluid parameters, that is able to predict a large variety of base states. We derive dimensionless groups to compare the effects of viscoelasticity, thixotropy and plasticity on the flow stability. We find that sinuous perturbations are slightly more unstable than varicose modes, and we identify the values of our model parameters for which the instability has its strongest effects. We conclude that dominant thixotropy can stabilise the flow, but instability occurs when the characteristic timescale of viscoelasticity is much longer than both those of plasticity and thixotropy. The most dangerous situation is a plug flow with an apparent yield surface just within the channel, and we find that the growth rate of the instability scales with the rate of thixotropic structure recovery.