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

The recently discovered polymer diffusive instability (PDI) in rectilinear flows of an Oldroyd-B fluid has wavelengths of the order of the size of the polymer for realistic polymer diffusivities, raising a question on the applicability of continuum constitutive equations. We show, using the Giesekus model (augmented with stress diffusion), that the PDI is rapidly suppressed as the anisotropy parameter is increased, suggesting that anisotropic diffusion needs to be incorporated in order to obtain physically consistent results, either in stability calculations or in direct numerical simulations.