Oxford Mathematician John Allen, Professor Emeritus of Engineering Science, talks about his and his collaborators' work on the electrohydrodynamic stability of a plasma-liquid interface.
"The study of plasma-liquid interactions is an increasingly important topic in the field of plasma science and technology with applications in nanoparticle synthesis, catalysis of chemical reactions, material processing, water treatment, sterilization and plasma medicine. This particular work is motivated by the plasma-liquid interactions inherent in magnetic confinement fusion devices, such as tokamaks, either due to melt damage of the metal walls or in new liquid metal divertor concepts. The ejection of molten droplets has been observed in both cases and is of considerable concern to the operation of a successful fusion device. Understanding the stability of the liquid metal surface is a critical issue.
Previously-studied instabilities of liquid metal surfaces in tokamaks include a Kelvin-Helmholtz instability due to plasma flow across the metal surface, a Rayleigh-Taylor instability driven by the j × B force due to a current flowing in the metal, a Rayleigh-Plateau instability of the liquid metal rim around a cathode arc spot crater, and droplet emission from bursting bubbles which are formed by liquid boiling or absorption of gases from the plasma. However, none of these studies considers the effect of the strong electric fields and ion flows in the sheath region between the plasma and the liquid surface despite the observations of electrical effects such as arcing, which cause considerable damage to the tokamak wall, and enhanced droplet emission rates from electrically-biased surfaces. Furthermore electrostatic breakup has been identified as an important process for liquid droplets in plasmas.
Instabilities driven by electric fields, i.e. electrohydrodynamic (EHD) instabilities, at the interface between a conducting liquid and and vacuum, were originally studied by Melcher and subsequently by Taylor and McEwan. Melcher’s marginal stability criterion was invoked by Bruggeman et al. in order to explain the filamentary structure of a glow discharge over a water cathode and, additionally, to explain the instability of an electrolytic water solution cathode from an earlier experiment. Earlier evidence for EHD instabilities of the plasma-liquid interface appears in an experiment on unrelated work where an arc spot occasionally formed on an electrically-isolated mercury pool which was in contact with the plasma. Another EHD effect, the deformation of a liquid surface into a Taylor cone, has recently been used to form the cathode of a corona discharge.
Our work investigates the EHD stability of a plasma-liquid interface with a linear perturbation analysis. Melcher’s stability criterion is found to apply to short-wavelength perturbations of the surface. However the fast-moving ions in the sheath provide a significant pressure on the liquid surface which can overcome the electric stress for long-wavelength perturbations. This effect hasbeen neglected in previous studies and provides an overall increase in the critical voltage which must be applied to the surface in order to make it unstable. This effect is encouraging for the ongoing development of new plasma-liquid technologies."