Using electric fields to induce patterning in leaky dielectric fluids in a rod-annular geometry

Abstract

The stability and axisymmetric deformation of two immiscible, viscous, perfect or leaky dielectric fluids confined in the annulus between two concentric cylinders are studied in the presence of radial electric fields. The fields are set up by imposing a constant voltage potential difference between the inner and outer cylinders. We derive a set of equations for the interface in the long-wavelength approximation which retains the essential physics of the system and allows for interfacial deformations to be as large as the annular gap hence accounting for possible touchdown at the inner or outer electrode. The effects of the electric parameters are evaluated initially by performing a linear stability analysis which shows excellent agreement with the linear theory of the full axisymmetric problem in the appropriate long wavelength regime. The nonlinear interfacial dynamics are investigated by carrying out direct numerical simulations of the derived long wave models, both in the absence and presence of electric fields. For non-electrified thin layer flows (i.e. one of the layers thin relative to the other) the long-time dynamics agree with the lubrication approximation results found in literature. When the liquid layers have comparable thickness our results demonstrate the existence of both finite time and infinite time singularities (asymptotic touching solutions) in the system. It is shown that a two-side touching solution is possible for both the non-electrified and perfect dielectric cases, while only one-side touching is found in the case of leaky dielectric liquids, where the flattened interface shape resembles the pattern solutions found in literature. Meanwhile the finite-time singular solution agrees qualitatively with the experiments of Reynolds (1965).

On the effect of electrostatic surface forces on dielectric falling films

“…In this case, a cusped interfacial shape is observed. Very similar results for leaky dielectric fluids have been presented by Wang & Papageorgiou (2016). Dryout and electrode touching phenomena have similarly been found for stratified multilayer flows in horizontal channels under the influence of electric forces (Barannyk et al.…”

Deformation and stability of a viscous electrolyte drop in a uniform electric field

“…These characteristics are not captured by the perfect dielectric and perfect conductor models. To explain these features, Taylor proposed the so-called leaky dielectric [19] or Taylor-Melcher (TM) model [2] for weakly conducting fluids, which has been widely and successfully applied to many problems in electrohydrodynamics (see, e.g., [20][21][22][23][24][25][26] in addition to the references below). The leaky dielectric model allows charge to accumulate at a fluid-fluid interface, and tangential electric stresses generated by this surface charge along with charge convection are found to be important for predicting oblate steady-state drop shapes, steady fluid motion, and unsteady breakup in isolated drops acted on by an electric field [27,28].…”

Nonlinear dynamics of unstably stratified two-layer shear flow in a horizontal channel

“…In the absence of the shear flow (so when the upper wall is stationary), the finger pattern in the interfacial profile retains the symmetry of the initial condition (3.1) approximately (see related studies on static liquid film configurations, for example those by Yiantsios & Higgins (1989), Bertozzi & Pugh (1998), Tseluiko & Papageorgiou (2007), Wang, Mählmann & Papageorgiou (2009), Barannyk et al. (2015) and Wang & Papageorgiou (2018)). Here the symmetry is broken by the superimposed shear flow and consequently the interfacial profile tends to drift in the positive direction.…”