Marangoni Instability Subject to Electrostatic Forcing

We investigate the effect of electrostatic potential on a thin liquid layer heated from below, with its free surface exposed to a hydrodynamically passive gas. The liquid and gas layers are confined between two horizontal plates. In the absence of a forced electrostatic potential, the liquid layer exhibits Marangoni instability if the temperature difference across the layer exceeds a threshold, which varies with the perturbation wavenumber. This threshold has two minima, corresponding to long- and short-wave instability modes, eventually leading to dryout. However, without the Marangoni effect, an electric field imposed on the liquid and gas layers, stable under gravity, causes instability through interfacial deflections, leading to the formation of pillars. Using linear stability analysis of the full governing equations, we derive an analytical expression for the critical potential. We also show that increasing the electrostatic potential reduces the critical Marangoni threshold, eventually making it negative. A negative Marangoni threshold indicates pillar formation due to electrostatic dominance, while a positive threshold indicates dry spot formation. These phenomena are confirmed by nonlinear interface evolution calculations using the long-wave model, specifically the Weighted Residual Integral Boundary Layer approach.