Effects of electrohydrodynamic charge transport on surface motion and deformation at a plasma–liquid interface

• Published in: Applied mathematical modelling Vol. 145; p. 116115
• Main Authors: Feng, Zhe, Klaseboer, Evert, Li, Hongying, Chan, Wai Hong Ronald
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.09.2025
• Subjects: Charge transport; Electrohydrodynamic flows; Interface deformation; Multi-phase flows; Phase-field method; Plasma–liquid interactions; Poisson–Nernst–Planck equations; Electrohydrodynamic flows; Poisson–Nernst–Planck equations; Multi-phase flows; Charge transport; Phase-field method; Plasma–liquid interactions; Interface deformation
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2025.116115

Two-dimensional multi-phase interactions between a weakly ionised single-fluid plasma and an incompressible liquid layer are studied through detailed numerical simulations of the Navier–Stokes and Poisson–Nernst–Planck equations, with relevance to liquid cooling in nuclear fusion reactor divertors, as well as ionic wind cooling. The plasma–liquid interface is captured using the conservative phase-field method to explore the effects of plasma-induced flow on and beneath the interface, as well as the characteristics of the interfacial deformation itself. 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 acts as a support for a pool of liquid. An ascending liquid flow is observed along the vertical axis of symmetry of the domain with a maximum speed close to experimentally measured values. Around the plasma–liquid interface, vortices comprising circulating liquid are generated with morphologies in general agreement with experiments. These vortices accumulate charge near the vertical symmetry axis and eventually enhance surface oscillations. A parametric study of the external voltage and strength of injected charge density indicates that external voltage is primarily responsible for promoting surface transport and charge accumulation. The observed surface oscillations, which are driven by Coulombic interactions, are primarily subject to the restoring action of gravity in the sense of oscillation period reduction. Our findings enable optimisation of mixing efficiencies in interfacial electrohydrodynamic flows that could be relevant for water purification and nitrogen fixation. •The phase-field method allows detailed analysis of plasma–liquid interfaces.•Electrohydrodynamic simulations are consistent with experimental flow speeds.•Our simulations demonstrate significant interfacial deformation and oscillations.•This surface behaviour is driven by charge accumulation beneath the interface.•The period of surface oscillations strongly depends on restoration by gravity.