Effects of Frequency and Joule Heating on Height Rise between Parallel Electrodes with AC Electric Fields

High strength AC electric fields generate a body force on a dielectric medium confined between two electrodes. The body forces are due to two factors. First is the variation in permittivity across an interface such as liquid-air present between the electrodes. The second is a change in the dielectric property of the medium due to a variation in the thermodynamic properties such as temperature. The height rise of a dielectric medium between two electrodes is one of the consequences of these electrical body forces and is used here as a comparatively simple way to study these forces. In an aqueous solution with finite conductivity, the effects of the frequency of the supplied voltage source and the temperature change due to Joule heating on height rise have never been studied in this context. This study focuses on systems where the contributions of surface forces are negligible and highlights the interplay between solution conductivity, applied electric field, and the solution height/temperature behavior. Using a generic thermodynamic model for an aqueous solution under the application of an alternating current electric field, it is shown that for low conductivity solutions the resulting temperature and height rise change weakly with the applied field frequency and strongly with the applied electric field. For higher conductivity solutions, the behavior becomes more complex with respect to the electric field strength. As compared to Pellat's original model, the height rise varies from strongly suppressed to enhanced.