Numerical simulation of electrohydrodynamics and surface deformation of a plasma–liquid interface

We study the two-dimensional interactions between a weakly ionised single-fluid plasma and an incompressible liquid layer through high-fidelity numerical simulations based on the Navier-Stokes and Poisson-Nernst-Planck equations, where the conservative phase-field method has also been incorporated to explore the effects of plasma-induced flow on a plasma-liquid interface. An electric potential difference is imposed across a nozzle-plate set-up, where the downward-pointing nozzle orifice serves as a source of positive ions and the bottom plate supports a pool of liquid above. Ascending flow is observed along the symmetric axis of the liquid phase with a maximum speed close to experimentally measured values. Around the plasma-liquid interface, circulation vortices occur with morphologies in general agreement with experiments. A parametric study of the sizes and maximum speeds of these vortices is conducted. Undulations in the interface are observed under certain conditions with the potential to develop interfacial instabilities that will require further experimental validation. Although the current numerical model is simplified and cannot reveal the full physics underlying plasma-liquid interactions, we have demonstrated its capacity to reproduce several preliminary and fundamental phenomena associated with these interactions, with an eye to the prediction of reactive species transport and self-organised patterns at plasma-liquid interfaces. Planned extensions of the model to compressible flows incorporating the energy equation will be discussed to elucidate the effects of thermal transport with reactions.