Instability in a non-ohmic/ohmic fluid interface under a perpendicular electric field and unipolar injection

Abstract

We set the equations for the linear electrohydrodynamic instability of an interface between two fluids, subjected to a perpendicular field and a unipolar charge injection. One of the fluids is modeled as being in non-ohmic regime ͑insulating͒, whereas the other is ohmic. A new interfacial instability mechanism is described, which may account for the Rose-window instability. The equations are analytically solved in the limit of long wavelength and neglecting the fluid motion. We show that this limit applies well to the case of an air-ohmic liquid interface. The applicability to a liquid-liquid interface is also analyzed.

The stability of a horizontal interface between air and an insulating liquid subjected to charge injection

“…5 The possibility of deformation of the initially flat free interface between liquid and air is another source of potential instability. In the Ohmic case, Vega and Pérez 18 showed that the electric pressure is a decreasing function of the liquid layer thickness. This is a potentially unstable situation, since any fluctuation leading to the decrease of the layer thickness would be amplified.…”

Spreading of a dielectric droplet through an interfacial electric pressure

“…Therefore, the effect of film thickness on the current density and electric pressure can be neglected. This assumption is particularly valid for thin dielectric liquid films (h S ), which are exposed to stronger corona discharge at larger electrode separations (Vega & Pérez 2002). Current density, surface charge density and electric field in the presence of uniform electric field are saturated and they can be expressed as (Mott & Gurney 1964;Vega & Pérez 2002):…”

“…However, the corona discharge over the interface was assumed to be strong enough, so that the current density change owing to the film thickness variation becomes negligible. Applying both conditions, the implicit current density expression presented in the study of Mott & Gurney (1964) is reduced to the well-known Mott's steady-state space-charge-limited conduction (SCLC; Vega & Pérez (2002)), -the electric pressure has two components: (i) electric pressure owing to the surface charge (electrophoretic component) and (ii) electric pressure owing to the interfacial jump in 1/23E 2 (dielectrophoretic component). According to the observations, as the electrostatic field in the absence of ion injection does not influence the interface, the dielectrophoretic component was neglected, and -the main voltage drop is assumed to occur in air gap.…”

“…The electric field enhancement coefficient, a equals 1 for strong uniform ion injection in an infinite film layer (Mott's steady-state SCLC; Mott & Gurney (1964), Vega & Pérez (2002)). The details of the field enhancement coefficient calculation can be found in the electronic supplementary material.…”

The combined effect of polarization and free surface charges on the electric pressure jump in an ohmic/ohmic fluid interface

“…The results may reproduce the instability criterions in the t i t of long wavelength of previous works for all cases where overstahility is not present. Given the simplic-ity of the system of equations used and the fact that capillary forces, coming into play for lower instahility wavelengths [5, 6], have a much lower influence than the electrical pressure [l], the following analysis is useful as a fast track estimation of instability thresholds when overstability is not possible [2,3]. Besides, this study provides a very intuitive idea on the mechanical process that occurs in the interface due to the action of electrical pressure.…”