Effect of anisotropic mobility on the diffusive instability in viscoelastic shear flows.

The present work focusses on the linear stability analysis of inertialess viscoelastic plane Couette flow using the non-linear Giesekus model, which not only accounts for an anisotropic drag coefficient, but also predicts shear thinning of viscosity. Plane Couette flow has been found to be linearly unstable if polymer stress diffusion is included in the Oldroyd-B fluid. The unstable mode has been termed as the polymer diffusive instability (PDI). The conventional (non-diffusive) Giesekus model predicts plane Couette flow to be linearly stable. A similar analysis is carried out for the homogeneous diffusive Giesekus model using two different boundary conditions: no flux and no diffusion.



Our numerical results reveal that the PDI stabilises rapidly as anisotropic coefficient is increased, resulting in the shrinking of the neutral curves, for both boundary conditions. The critical Weissenberg number also diverges rapidly with increasing anisotropy for all the dimensionless diffusivity values studied. For higher solvent to solution viscosity ratio, system stabilises rapidly at smaller values of anisotropic coefficient, whereas for concentrated solutions, the system requires higher anisotropic coefficient to stabilize itself. The stabilization of the PDI is shown to be due to the anisotropic effects irrespective of the shear thinning nature of the Giesekus model. The PDI is found to be extremely sensitive to the boundary conditions.