Accurate low-order modeling of electrified falling films at moderate Reynolds number

The two- and three-dimensional spatio-temporal dynamics of a falling, electrified leaky dielectric film are studied. The method of weighted residuals is used to derive high-order models that account for both inertia as well as second-order electrostatic effects. The models are validated against both linear theory and direct numerical simulations of the Navier-Stokes equations. It is shown that a simplified model offers a rapid computational option at the cost of a minimal decrease in accuracy. This model is then used to perform a parametric study in three dimensions.