Instability and dripping of electrified liquid films flowing down inverted substrates

Abstract

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. * ruben.tomlin11@imperial.ac.uk arXiv:1906.08757v2 [physics.flu-dyn]

On the effect of electrostatic surface forces on dielectric falling films

“…In the special case of perfectly dielectric fluids, an electric field in the normal direction to the substrate surface on which the falling film flows leads to destabilization by a pure surface force. At the same time, an electric field in the tangential direction to the surface has a stabilizing effect (Tomlin, Cimpeanu & Papageorgiou 2020). Owing to the orientation-dependent effect of the electric field, it is not surprising that films in an electric field have recently been compared to overlaying and hanging film flows (Tomlin et al 2020).…”

“…At the same time, an electric field in the tangential direction to the surface has a stabilizing effect (Tomlin, Cimpeanu & Papageorgiou 2020). Owing to the orientation-dependent effect of the electric field, it is not surprising that films in an electric field have recently been compared to overlaying and hanging film flows (Tomlin et al 2020). In hanging film flows, the component of gravity normal to the substrate surface causes an intensification of waves, finally leading to dripping (Rietz et al 2017;Rohlfs, Pischke & Scheid 2017;Kofman et al 2018).…”

“…Owing to the orientation-dependent effect of the electric field, it is not surprising that films in an electric field have recently been compared to overlaying and hanging film flows (Tomlin et al. 2020). In hanging film flows, the component of gravity normal to the substrate surface causes an intensification of waves, finally leading to dripping (Rietz et al.…”

“…Recently, Tomlin et al. (2020) studied the two-dimensional evolution of a dielectric suspended film stabilized by an electrostatic field in the tangential direction to the substrate surface. Based on direct numerical simulations and a simplified second-order WIBL model, they showed that a sufficiently strong electric field may ensure linear and nonlinear stability of the film.…”

Numerical-asymptotic models for the manipulation of viscous films via dielectrophoresis

“…The presence of non-zero conductivity has been found to have a significant effect on the interface stability, giving rise to pattern formation (Craster & Matar 2005; Wang & Papageorgiou 2016). More recent studies have considered the application of electric fields on perfectly conducting liquid films to control travelling wave flows on vertical fibres (Ding & Willis 2019) or to suppress dripping from inverted substrates (Tomlin, Cîmpeanu & Papageorgiou 2020).…”