Mathematical modelling of gas–plasma jets interactions with liquids

An experimental and theoretical investigation of low velocity (up to $50\, \mathrm{m}\,\mathrm{s}^{-1}$) air jets and air plasmas interacting with a liquid was undertaken. Experimentally, a jet of air was directed in the laboratory towards a liquid (water) surface which was arranged both as a thin film on a substrate and also as bulk liquid. Various depths of liquid were investigated as well as different air flow rates. In addition, both air and helium plasma jets were considered but only air plasmas were analysed for chemical changes in the liquid.

Theoretically, the interaction of an air jet with water was considered using three different models. Two models used were direct numerical simulations (DNS), namely the Computational Fluid Dynamics (CFD) package in COMSOL Multiphysics version 5.3a and the volume-of-fluid Gerris package which is an open source software. In addition, a model using the thin-film approximation was used through decoupling the gas and liquid motion which is computationally very efficient.

Experimentally, the deformation of the liquid surface was measured by direct photography and the results compared to the models. For small air flow rates, a state was achieved with a dimple below the impinging jet which remained steady over long periods. At relatively high air flow rates, a steady state was not achieved and the surface underwent oscillations. The threshold for the onset of the oscillations was determined. The resulting surface shapes and onset of the oscillations were compared to the theoretical predictions with good agreement. In addition there was agreement between the two models with regards to streamline patterns and velocity fields were compared with good agreement.

When the liquid was very shallow, the thin film approximation was also compared to the experiments and the results of the DNS with better agreement than what the thin film approximation would suggest. In addition, for high flow rates, it was shown that the film could dewet from the surface and form an annular ring around the edge of the beaker in which the liquid was contained. Depending on the flow conditions and the liquid-substrate properties (hydrophilic or hydrophobic), this annulus was observed to remain after the jet was switched off. In other circumstances the film would form a central globule under the impinging jet.

In the case of the plasma interactions, it was shown that the associated electric field could deform the water surface, lessening the depth of the observed dimple. A simplified model of the air plasma which contained only 10 plasma species was used together with the flow patterns determined from the DNS to investigate the transfer of the species to the liquid and their subsequent chemical reactions. Experimentally, indigo dye was added to the liquid which is destroyed by ozone, produced during the chemical reaction process. This allowed a comparison with the theoretically predicted ozone production from the model.