The effect of an electrostatic field on the rupture of a thin viscous static film by van der Waals attractions

Abstract

This research examines rupture phenomena of a horizontal static thin viscous layer on a solid plate under an electrostatic field generating from a charged foil above the film. The dynamics of the electrified liquid film is formulated to derive a long-wave evolution equation of local film thickness. It determines two-dimensional nonlinear behavior of the film subject to surface tension, viscous, electrically induced forces, and van der Waals attractions. Linear stability analysis is used to obtain the maximum growth rate of a periodic disturbance and its corresponding wavenumber. To see the development of film rupture the strongly nonlinear partial differential equation is numerically solved for the unlimited or limited foil length as part of an initial-value problem with spatially periodic boundary conditions. The stronger electric forces make the thin layer more unstable and speed up its rupture.