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

Abstract

This paper presents the linear stability analysis of an interface between air and an insulating liquid subjected to a perpendicular electric field, in the presence of unipolar injection of charge. Depending on the characteristics of the liquid and the depth of the liquid layer two different instability thresholds may be found. One of them is characterized by a wavelength of the order of the liquid layer thickness and corresponds to the well-known volume instability of a liquid layer subjected to charge injection. The other one is characterized by a wavelength some ten times the liquid layer thickness and corresponds to the so-called rose-window instability, an instability associated to the balance of surface stresses. C 2014 AIP Publishing LLC.

Numerical analysis of electrohydrodynamic (EHD) instability in dielectric liquid-gas flows subjected to unipolar injection

“…The left and right sides of the domain are treated as periodic. In addition, the boundary conditions at the interface are as follows [39]:…”

“…Here, ρ c , µ c , ε c and K c are the characteristic physical properties. The obtained non-dimensional system of governing equations [39]:…”

“…Atten and Koulova-Nenova's work showed that the deformation of the interface will decrease the critical value for the bulk charge instability compared to a single-phase dielectric fluid system. Many subsequent works tried to find the critical value corresponding to the Rose-window instability [36][37][38] based on Atten and Koulova-Nenova's work and this was finally made by Chicón and Pérez [39]. The bulk charge instability threshold they found is close to Koulova-Nenova's result and a new criterion which is related to the Rose-window instability was obtained when the thickness of liquid layer is small enough.…”

“…The effect of deformability is discussed by Koulova-Nenova and Atten as mentioned before while the role of slip boundary has not been carefully studied. Based on the previous numerical studies on the single-phase EHD instability problem [40][41][42] and the latest analytical work [39], this work presents a numerical analysis of EHD instability of a horizontal liquidair interface subjected to unipolar charge injection with specifically developed finite-volume solver based on the open-source platform OpenFOAM ® . The effect of slip boundary condition on the bulk charge instability has been highlighted.…”

The Electric Honeycomb; an investigation of the Rose window instability

“…The results were verified against experiments in a subsequent study [ 5 ], wherein the RWI was investigated experimentally for low-conducting fluids in both the ohmic and non-ohmic regimes. More recent theoretical investigations have extended the stability analysis to consider the role of liquid motion [ 6 ] and the presence of an insulating liquid [ 7 ]. In this study, we extend experimental investigation of the RWI and explore the parametric space wherein the instability manifests itself.…”