We consider the gravity-driven flow of a perfect dielectric, viscous, thin liquid film, wetting a flat
substrate inclined at a non-zero angle to the horizontal. The dynamics of the thin film is influenced
by an electric field which is set up parallel to the substrate surface – this nonlocal physical mechanism
has a linearly stabilizing effect on the interfacial dynamics. Our particular interest is in fluid films
that are hanging from the underside of the substrate; these films may drip depending on physical
parameters, and we investigate whether a sufficiently strong electric field can suppress such nonlinear
phenomena. For a non-electrified flow, it was observed by Brun et al. (Phys. Fluids 27, 084107, 2015)
that the thresholds of linear absolute instability and dripping are reasonably close. In the present
study, we incorporate an electric field and analyse the absolute/convective instabilities of a hierarchy
of reduced-order models to predict the dripping limit in parameter space. The spatial stability results
for the reduced-order models are verified by performing an impulse–response analysis with direct
numerical simulations (DNS) of the Navier–Stokes equations coupled to the appropriate electrical
equations. Guided by the results of the linear theory, we perform DNS on extended domains with
inflow/outflow conditions (mimicking an experimental set-up) to investigate the dripping limit for
both non-electrified and electrified liquid films. For the latter, we find that the absolute instability
threshold provides an order-of-magnitude estimate for the electric field strength required to suppress
dripping; the linear theory may thus be used to determine the feasibility of dripping suppression
given a set of geometrical, fluid and electrical parameters.