Nonlinear dynamics of a liquid film flow over a solid substrate in the presence of external shear stress and electric field

Abstract

Using approximation techniques, long-wave length framework and boundary-layer, the effects of electrostatic force and induced shear stress on the flow behavior down an inclined solid substrate are investigated. In general case, the considered model accounts in the presence of inertia regime and streamwise viscous diffusion with the influence of normal electric field and an imposed shear stress. Using the Galerkin weighted residual, two coupled evolution equations for the flow rate and film thickness are extracted. In the appropriate limit cases, the evolution equations obtained by previous authors are recovered. The primary instability has been analyzed using the Whitham wave hierarchy framework. In the nonlinear regime, the behavior of solitary waves arose on the surface of liquid film due to the effects of electrostatic force and imposed shear stress throughout three-dimensional dynamical systems. Some bifurcation points are reported. In both extremely viscous and electrogravity regimes, the Benney-like equation is extracted in a new form. By excluding contribution of external shear stress and viscous dispersion parameter, the interesting results of previous authors are recovered. In both weakly nonlinear and inertialess regimes, the bifurcation points of the three dynamical systems are discussed within the Kuramoto–Sivashinsky type equation.