## 3 Results and Discussion
### Computed Results  
Due to employment of a finer mesh and a relatively long simulation time of 10.0 s, the present numerical simulation was executed on a computer cluster with Intel(r) Xeon E5-2670 2.60 GHz using 48 physical cores and hyper-threaded to 96. The computation time to complete the simulations for mixing chambers with and without obstacles was \(\sim\)2.96 \(\times\) 10\({}^{4}\) and \(\sim\)7.24 \(\times\) 10\({}^{3}\) s, respectively. To make sure that the system had reached the steady-state over the simulation time of 10.0 s, the average velocity in the mixing chamber domain was scored, and the results are shown in Figure 8a,b for chambers with and without obstacles, respectively. Figure 5: Comparisons between 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 obtained experimentally [48] (squares) and from the present model (circles). Figure 6: Contour plots of the 2.77 \(\times\) 10\({}^{-3}\) m air bubble rising through the water column at: (**a**) 0; (**b**) 0.02; and (**c**) 0.04 s. Blue color represents water and red color represents the air bubble. Figure 7: Comparisons between the heights of a 4.2 \(\times\) 10\({}^{-3}\)-m-diameter water droplet impacting onto a solid surface with a contact angle of 50\({}^{\circ}\)[49] (squares) and from the present model (curve). The velocity magnitudes averaged over the mixing chamber domain for the two different conceptual designs of the mixing chamber are shown in Figure 8. The velocities in the mixing chamber domain with obstacles showed fluctuations for \(t\) < 2.0 s, mainly due to two reasons: (1) the steady-state was not yet reached for \(t\) < 2.0 s; and (2) the presence of obstacles to the flow when chamber was getting filled would significantly affect the flow pattern and the velocity magnitude. In contrast, the velocity variations in the mixing chamber without obstacles were found negligible since a major part of the flow remained undistorted (the center part of the flow that was away from the mixing chamber walls). However, the steady-state for the designs without any obstacles would also be fully achieved at \(t\) \(\sim\) 2.0 s. After the steady-state was fully achieved, the velocity magnitude in the mixing chamber domain would not fluctuate noticeably. Therefore, the velocity of the flow would remain almost constant while the mixing chamber was in operation (i.e., when the blood and cold plasma were injected from the embedded nozzles). Snapshots for spatial evolution of the velocity over the mixing chamber domains are shown in Figures 9 and 10, for mixing chambers with and without obstacles, respectively. Figure 8: Average velocity magnitude of the mixture of fluids over the mixing chamber domain with and without obstacles (Note: the mixing chamber domain is marked in blue). Figure 9: Distribution of velocity streamlines over the mixing chamber with obstacles at: (**a**) 0 s; (**b**) 2 s; (**c**) 4 s; (**d**) 6 s; (**e**) 8 s; and (**f**) 10 s. Different velocities are represented by different colors as shown in the color bar (in m s\({}^{-1}\)). The spatial evolutions of velocities in the mixing chamber domain are shown in Figures 9 and 10 for mixing chamber with and without obstacles, respectively. For \(t>2.0\) s, the velocities did not change noticeably. These results together with those shown in Figure 8 supported that steady state was achieved for \(t>2.0\) s. Moreover, velocities away from the walls were higher than those closer to the no-slip walls due to adhesion between the fluid and solid. The initial temperature of blood was set to be 310 K [38] and the initial cold plasma temperature was set to be at 303 K [39].