Electric field stabilization of viscous liquid layers coating the underside of a surface

Abstract

We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a horizontal surface in the presence of an electric field applied parallel to the surface. The model includes the effect of bounding solid dielectric regions above and below the liquid-air system that are typically found in experiments. The competition between gravitational forces, surface tension, and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semispectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations using the volume-of-fluid methodology and assess the accuracy of the obtained solutions in the long-wave (thin-film) regime when varying the electric field strength from zero up to the point when complete stabilization occurs. We employ DNS to examine the limitations of the asymptotically derived behavior as the liquid layer thickness increases and find excellent agreement even beyond the regime of strict applicability of the asymptotic solution. Finally, the asymptotic and computational approaches are utilized to identify robust and efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.

Instability and dripping of electrified liquid films flowing down inverted substrates

“…We believe that the nonlocality of the problem is an important factor here. We emphasize that, unlike the electric field stabilization of the classical Rayleigh-Taylor instability [42,43], the mean flow gives rise to nontrivial bounded solutions (wave trains that do not drip) below the threshold of stabilization of the flat interface solution. For this reason, we do not investigate active control strategies.…”

“…Numerical solutions of the model accurately capture the primary collar and secondary lobe structures present in the early stages of finger formation (as validated with DNS). In both [42] and [43], the authors demonstrate numerically the possibility of active control of the underlying Rayleigh-Taylor instability and production of sustained nonlinear interfacial oscillations for arbitrarily long times. Such oscillations can enhance mixing, for example, as in [44].…”

“…We also provide electrified versions of two WIBL models derived by Ruyer-Quil and Manneville [33][34][35]. Temporal linear stability analyses of all three models show the stabilizing effect of the electric field, and complete stabilization of finite length systems (even in the absence of surface tension) as found in [42,43]. The major effort focuses on hanging films and the effect of the electric field on the A/C transition.…”

“…The use of horizontal electric fields to stabilize the Rayleigh-Taylor instability in stratified systems of dielectric fluids was considered by Cimpeanu et al [42] and Anderson et al [43]. The former work investigates an unbounded two-fluid system of viscous dielectric fluids with a less dense lower fluid.…”

“…DNS of the Navier-Stokes equations coupled with electrostatics was also carried out, and the parameters for which finger formation was suppressed was found to be in good agreement with the linear theory. In addition, Anderson et al [43] derived a nonlinear nonlocal evolution equation for the interfacial dynamics valid for sufficiently thin liquid layers. Numerical solutions of the model accurately capture the primary collar and secondary lobe structures present in the early stages of finger formation (as validated with DNS).…”