The Influence of Gas–Liquid Interfacial Transport Theory on Numerical Modelling of Plasma Activation of Water

Abstract

Plasma activated water has shown great promise in a number of emerging application domains; yet the interaction between non-equilibrium plasma and liquid represents a complex multiphase process that is difficult to probe experimentally, necessitating the development of accurate numerical models. In this work, a global computational model was developed to follow the concentrations of aqueous reactive species in water treated using a surface barrier discharge in ambient air. While the two-film theory has long superseded other methods of modelling mass transfer in such areas of research as environmental and aerosol science, plasma modelling studies continue to use equilibrium and one-film theories. The transport of reactive species across the gas–liquid interface was therefore treated using the one-film and two-film theories, with the results compared to ascertain which is most appropriate for PAW modelling studies. Comparing the model-predicted concentrations to those measured, it was shown that concentrations of aqueous H+ and NO3− ions were better represented by the two-film theory, more closely fitting experimental measurements in trend and in magnitude by a factor of ten, while HNO2 and NO2− showed a slightly worse fit using this theory. This is attributed to the assumption in two-film theory of a gas-phase stagnant film which provides additional resistance to the absorption of hydrophilic species, which is absent in the one-film theory, which could be improved with a more accurate value of the Sherwood number for each species.

Plasma–liquid interactions in the presence of organic matter—A perspective

“…Adsorbed species can also solvate into the liquid and penetrate the bulk liquid, followed by diffusion in the bulk liquid. 27 The transport of species into the liquid has traditionally been described by the zero-film interfacial transport theory, 28 where there is no resistance to the flux of gaseous species into the liquid and the concentration equilibrates instantaneously in both phases. Henry's law is an example.…”

“…Species accumulate in the film until equilibrium with the gas phase is reached, preventing the uptake of more species until the concentration in the film is reduced by diffusion into the bulk liquid. 28 The two-film theory, widely used in environmental and aerosol science, provides further improvements by adding a second stagnant film at the interface. The presence of the second film on the gas side of the interface limits the transport of hydrophilic species, slowing their uptake into the liquid phase.…”

“…Hydrophobic species on the aqueous side experience a similar slowing of desorption from the liquid phase. 28 …”

“…has found the two-film theory superior in modeling the mass transfer across a gas–liquid interface. 28 A drawback of the two-film theory is the requirement of a Sherwood number, a dimensionless number representing the ratio of convective mass transfer to diffusive mass transport. The authors state that “due to the high reactivity of most plasma generated species, there is very little experimentally validated data.” 28 In addition to the lack of experimentally validated data, the complexity of the models and computational cost increase significantly when spatial dependences need to be resolved, i.e., if 1D or 2D models are applied.…”

“… 28 A drawback of the two-film theory is the requirement of a Sherwood number, a dimensionless number representing the ratio of convective mass transfer to diffusive mass transport. The authors state that “due to the high reactivity of most plasma generated species, there is very little experimentally validated data.” 28 In addition to the lack of experimentally validated data, the complexity of the models and computational cost increase significantly when spatial dependences need to be resolved, i.e., if 1D or 2D models are applied. For transport across the air–water interface, global models (0D) are often used where each region is solved separately and spatially averaged to reduce computing cost.…”