  There is a growing interest in the study of plasma-liquid interactions with
application to biomedicine, chemical disinfection, agriculture, and other
fields. This work models the momentum, heat, and neutral species mass transfer
between gas and aqueous phases in the context of a streamer discharge; the
qualitative conclusions are generally applicable to plasma-liquid systems. The
problem domain is discretized using the finite element method. The most
interesting and relevant model result for application purposes is the steep
gradients in reactive species at the interface. At the center of where the
reactive gas stream impinges on the water surface, the aqueous concentrations
of OH and ONOOH decrease by roughly 9 and 4 orders of magnitude respectively
within 50 $\mu$m of the interface. Recognizing the limited penetration of
reactive plasma species into the aqueous phase is critical to discussions about
the therapeutic mechanisms for direct plasma treatment of biological solutions.
Other interesting results from this study include the presence of a 10 K
temperature drop in the gas boundary layer adjacent to the interface that
arises from convective cooling and water evaporation. Accounting for the
resulting difference between gas and liquid bulk temperatures has a significant
impact on reaction kinetics; factor of two changes in terminal aqueous species
concentrations like H$_2$O$_2$, NO$_2^-$, and NO$_3^-$ are observed if the
effect of evaporative cooling is not included.
