Convective and absolute instabilities in electrohydrodynamic flow for viscoelastic fluid

The convective and absolute instabilities in electrohydrodynamic-Poiseuille mixed convection for viscoelastic fluids with the Oldroyd-B model are examined. In the absence of Poiseuille flow, based on the stationary and oscillatory characteristics at the onset of convection, we distinguish weakly and strongly elastic fluid, dominated by viscosity effects and elasticity effects, respectively. Their borderline of the two effects in terms of the critical electric Weissenberg W_{ec} satisfies the relation W_{ec}=a/(1-β)+b where β is viscosity ratio, and the parameters a and b depend on dimensionless ion mobility. In the presence of Poiseuille flow, with an increase in shear strength, the convective and absolute instability thresholds increase in both weakly and strongly elastic fluids, and the jump of phase speed and saddle point shift are observed at low polymer concentration with sufficient elasticity, causing the faster transverse rolls (TRs) to propagate downstream. However, at the high polymer concentration of large W_{e}, instead of downstream moving TRs, the upstream moving TRs can be the most unstable at the onset of absolute instability. Kinetic energy budget analysis reveals that with an increase in shear strength and elasticity, the suppressive effect of polymeric stresses on instability is enhanced in viscosity effects-dominated flow, while it is reduced in elasticity effects-dominated flow. Besides, the energy transfer from the wall-normal gradient of the perturbed electric field to the wall-normal gradient of the perturbed wall-normal velocity under the effect of the wall-normal gradient of the base electric field becomes the most destabilizing factor in the very strongly elastic fluids.