With the growing scarcity of water resources and increasing demand in energy, research efforts in effective water treatment and liquid waste management have been expanding steadily. The ability of UV light present in various electric discharges to disinfect water makes the use of plasma based technologies an effective alternative to the traditional methods like reverse-osmosis, distillation, etc. The interaction of plasmas with liquids has been a subject of current research and the present thesis includes both experimental and theoretical work done to better understand the physics of contact glow discharge electrolysis applied to waste water treatment.

Other aspects of the interaction between electric fields and electrolytes have also been analyzed in this work. For instance, electric double layer theory has been used to model the interaction between electric field and liquid waste close to the solid surface incorporating joule heating and evaporation. The presence of the electric field results in a coupling of the momentum, energy, and mass transfer equations which are solved simultaneously with the Poisson-Boltzmann equation that describes the electric potential distribution. The results show that the rate of evaporation at the air-liquid interface is a strong function of the applied electric field and bulk ion-concentration.

Temperature patterns observed in electrolytic cell experiments has been explained using buoyancy-driven flow model. As the heating element does not extend along the entire axial length of the cylindrical tank, this configuration displays very particular vortex patterns inside the cell and divides the domain into two regions of different temperatures.

To model electrohydrodynamics accurately, boundary conditions for Navier-Stokes equations are revisited and a new formulation has been proposed to numerically solve the Navier-Stokes equations. The proposed formulation is particularly suitable for transient problems including start-up problems. In addition, a novel projection scheme has been proposed which is coupled with Navier-Stokes algorithm to produce numerical solutions on non-staggered grids, which is 2$^{nd}$ order accurate in both space and time. The proposed projection scheme is also suitable for generating compatible initial data from given initial data at the start of any numerical simulation. The methodology developed can be adapted to study the dynamics of plasma based on a two-fluid formulation.