Electrohydrodynamic Stability of Falling Films with Odd Viscosity and Wall Slip Effects

Abstract The hydrodynamic instability of a thin liquid film possessing odd viscosity and flowing down a slippery inclined substrate is investigated under the combined influence of an imposed tangential shear stress and a normal electric field. Employing long-wave approximation techniques, a nonlinear evolution equation is derived that incorporates the effects of odd viscosity, slip length, normal electric field, and bidirectional tangential shear. Linear stability analysis reveals that odd viscosity and reverse-direction tangential shear exert stabilizing influences, whereas slip length, the normal electric field, and forward-direction tangential shear promote destabilization. The critical Reynolds number is determined analytically and its dependence on the governing system parameters is examined systematically. Through multi-scale analysis, the weakly nonlinear instability is investigated by deriving a complex Ginzburg–Landau equation that delineates four distinct dynamical regimes: subcritical instability, unconditional stability, explosive instability, and supercritical stability. These regimes are characterized by the signs of the coefficients appearing in the amplitude equation. Parametric studies demonstrate that, within the supercritical stable regime, the nonlinear wave amplitude and phase velocity increase with the electrical parameter in the flow direction but diminish with increasing odd viscosity coefficient. The present results show excellent agreement with established theoretical and experimental investigations reported in the literature.