Instability of an interface between air and a low conducting liquid subjected to charge injection

We study the linear stability of an interface between air and a low conducting liquid in the presence of unipolar injection of charge. As a consequence of charge injection, a volume charge density builds up in the air gap and a surface charge density on the interface. Above a certain voltage threshold the electrical stresses may destabilize the interface, giving rise to a characteristic cell pattern known as rose-window instability. Contrary to what occurs in the classical volume electrohydrodynamic instability in insulating liquids, the typical cell size is several times larger than the liquid depth. We analyze the linear stability through the usual procedure of decomposing an arbitrary perturbation into normal modes. The resulting homogeneous linear system of ordinary differential equations is solved using a commercial software package. Finally, an analytical method is developed that provides a solution valid in the limit of small wavenumbersMinisterio de Ciencia y Tecnología BFM2003-0173

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

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.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735 y P09-FQM-458