Electric and capillary instability of liquid rising between heated/cooled parallel plates and subjected to phase change: DC on perfect dielectric liquids

Abstract

Based on Lucas–Washburn's seminal works, a simple model governing the flow inside a narrow channel, partly dipped into a large pool filled with a dielectric liquid, is presented. The channel walls are electrically polarized and can be warmer or cooler than the pool liquid using an appropriate heating and cooling device. The liquid dielectric constant is assumed varying linearly with temperature and evaporation or condensation can occur at the meniscus surface. Linear stability analysis is performed near the equilibrium position demonstrating various effects of dielectrophoretic, capillary, gravity and viscous forces. For the investigated liquid's volatility, it is shown that only sufficiently heated electrodes can exhibit instabilities about equilibrium position, whereas cooling these electrodes leads always to an asymptotically stable liquid motion. A numerical investigation is also performed on the transient regime showing either monotonic or damped oscillatory liquid motion depending on viscous, capillary and dielectric effects. If channel walls are heated and the electric field magnitude is above a specific and finite threshold, liquid can be pushed out of the gap, preventing reentrance. This effect can lead to undesirable walls dry-out that would be detrimental to two-phase heat transfer devices. A comparative survey is also performed on two liquids typically found in applications involving thermo-electrohydrodynamics, namely hfe-7100 and hfe-7300.