Numerical Simulation of Plasma--Droplet Interactions Under an Electric Field

Abstract

A coupled particle-in-cell and volume-of-fluid (PIC–VOF) framework is developed to simulate plasma–droplet interactions under a DC negative-corona discharge. The plasma is described by an electrostatic PIC model with Monte Carlo collisions that track electrons, N ${}_{2}^{+}$ , O ${}_{2}^{+}$ , and O ${}_{2}^{-}$ , resolving the negative-ion space charge that dominates the drift region self-consistently. The droplet is treated as a leaky-dielectric incompressible fluid governed by the Navier–Stokes equations with VOF interface tracking, a wall contact-angle boundary condition, and a Navier-slip moving-contact-line model; interfacial absorption of charged particles updates the droplet free charge self-consistently. The electric body force is the Korteweg–Helmholtz density, including Coulomb and dielectrophoretic (DEP) contributions, verified against a Maxwell stress control-surface integral within 3%. A multiscale coupling scheme with incremental PIC re-convergence renders the 360-ms transport simulation tractable. The computed corona current of $23~{\mu }$ A and the Warburg-type plate current profile (exponent ${n}=4.8\pm 0.3$ ) agree with the experiment of Li et al. within 5%, and the simulated droplet positions at five instants and the peak velocity of 0.061 m/s reproduce the measurements within the experimental reading uncertainty. Force decomposition shows that the DEP force dominates the transport, acting as a restoring force that reverses sign near the maxima of ${E}^{2}$ beneath the blade edges, while the Coulomb force is two to three orders of magnitude smaller because leaky-dielectric relaxation drains the deposited charge to the grounded substrate on a microsecond time scale, holding the droplet charge three to four orders of magnitude below the Pauthenier saturation limit. Sensitivity and control runs identify leaky-dielectric drainage as the controlling mechanism, and the uncertainty of the 2-D approximation is quantified at ±30%–50%.