## 3 Results and Discussion  
### Experimental Benchmarking  
The main aim of the present model was to simulate the mixing phenomena in two-phase fluid systems, which was coupled with the heat transfer module to keep track of temperature dispersion during mixing. In order to exhaustively benchmark the present model, the previous experimental results from [PERSON] et al. [43] regarding the propagation of plasma plume in ambient air were used, where the measurements were focused on temperature variations versus distance away from the outlet nozzle. Furthermore, experimental data on temperature variations associated with mixing between the discharged plume and the ambient air were needed for the present benchmarking. Therefore, it is remarked that the present experimental benchmarking directly focused on the mixing between the two fluids (in this case plasma plume and air) with subsequent temperature dispersion. In addition, for the sake of benchmarking, a similar experimental setup of [PERSON] et al. [43] was modeled. The results of this benchmarking are shown in Figure 4.  
The results from the present model were in a good agreement with previously obtained experimental data; this proved the capability of the present model to precisely predict the mixing and the subsequent heat distribution during plasma discharge in air. The small deviations between the experimental data and theoretical predictions were likely due to unknown and uncontrollable external factors involved in the experiments.  
Furthermore, since the present work dealt with mixing of blood (liquid) with helium plasma, the present model was also benchmarked using experimental results with liquid and gas interface, including those for: (1) an air bubble rising in a water column; and (2) a water droplet moving in air and impacting a surface. For (1), the vertical velocities of a 2.77 \(\times\) 10\({}^{-3}\) m air bubble at different heights above the bottom nozzle that released the air bubble into the water column were employed [48]. Comparisons between vertical velocities obtained by the experiment and from the present model are shown in Figure 5, which show good agreement. To ensure preservation of the interface between the air bubble and water, the contour plots for the bubble at 0, 0.02 and 0.04 s are shown in Figure 6. The capability of our present model in preserving the interface between the air bubble and water (i.e., the liquid-gas system) was shown. The gradual change in the volume fraction around the air bubble (shown in red) in the water column (shown in blue) demonstrated that the present model could accurately track the degree of mixing between the gas (i.e., air) and the liquid (i.e., water) throughout the simulation. For (2), the variations with time in the height of a 4.2 \(\times\) 10\({}^{-3}\)-m-diameter water droplet impacting onto a solid surface with a contact angle of 50\({}^{\circ}\)[49] were employed. Comparisons between heights obtained by the experiment and from the present model are shown in Figure 7, which show good agreement. The accuracy of the present model in simulating two-phase fluids (i.e., liquid-gas) system was demonstrated by the benchmarking above.  
Figure 4: Comparison between temperatures at different distances from the outlet for 6 kV operating voltage obtained experimentally by [PERSON] et al. [43] and from theoretical predictions.