Yield stress destabilizes viscoelastic fluid flow

Motivated by the ubiquitous flows of viscoelastic fluids possessing yield stress in industrial applications and natural settings, the linear stability of sliding and plane Couette flows of White and Metzner (WM) fluid, which exhibits elasticity and yield stress, is analyzed. After yielding, the WM fluid behaves as an Upper Convected Maxwell fluid. In the creeping-flow limit, in the absence of yield stress, two linearly stable discrete Gorodtsov and Leonov (GL) modes exist for an arbitrary high value of the Weissenberg number. As the yield stress effect (i.e., Bingham number) increases, the GL modes become unstable, leading to an unstable flow. Analysis reveals that these modes originate near the walls due to the ‘extra normal stress’ arising from the synergistic effects of fluid yield stress and elasticity. The extra normal stress is an inherent feature of a WM fluid. Thus, the predicted instability is expected to be present in wall-bounded flows of WM fluid in the creeping-flow limit. The dispersion curves exhibit weak Hadamard instability, which is removed by incorporating a stress diffusivity term into the constitutive equation. The outcomes of the present study are potentially relevant to the WM fluid flows in geophysical and biological settings and industrial processes.