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.