## 3 Results and Discussion
### Computed Results
Figure 6:0 Distributions of mixture volume fractions (between 0 and 1) in mixing chambers: (**a**) with obstacles; and (**b**) without obstacles. The colors represent the volume fractions of the mixture; red corresponds to the blood (volume fraction = 0) and blue corresponds the plasma (volume fraction = 1). Figure 6:1 Distribution of flow streamlines and temperature over the mixing chamber without obstacles at: (**a**) 0 s; (**b**) 2 s; (**c**) 4 s; (**d**) 6 s; (**e**) 8 s; and (**f**) 10 s. Different temperatures are represented by different colors as shown in the color bar (in K). The volume fraction near \(\sim\)0.5 (see color bar in Figure 14) represented a perfect mixing between the two fluids injected into the mixing chamber. Apart from the degree of mixing, special attention would be paid on the spatial distribution of this mixture, which determined the path along which the mixture propagated in a particular mixing-chamber design. As shown by the flow profile Figure 14a, the mixing chamber with obstacles allowed a better mixing and at the same time directed the mixture of blood and plasma into the outlet nozzle. In contrast, the outlet zone in the mixing chamber without obstacles was almost completely filled with blood (see Figure 14b), and the blood at the center of the mixing chamber and the outlet nozzle did not have direct contact with the injected plasma from the side nozzles. In terms of treatment efficiency, it could be expected that the mixing chamber without obstacles would be less effective compared to one with obstacles, since the plasma which was initially present in the system was \"pushed out\" effectively by the blood without exhaustive mixing due to the higher density and dynamic viscosity of the blood (compared to the injected plasma). The volume fraction at the boundary of the outlet nozzle is quantitatively shown in Figure 6:2  
The average blood volume fractions scored over the outlet boundary of the nozzle for mixing chambers with and without obstacles are shown in Figure 6:3 When steady state was achieved after \(t>\sim\)2.0 s, the results for the two chambers overlapped, which showed that similar amounts of blood exited from the outlets of the chambers. As blood was injected into the chambers, the outlets started to get filled until saturation was reached. The blood volume fraction exiting the outlet boundary was found to be \(\sim\)0.66 after steady-state was achieved. The spatial distributions of volume fraction in the outlet nozzle for the mixing chambers (at \(t=10.0\) s) are also shown in Figure 6:4 Figure 16a shows that the blood and plasma were well-mixed in the presence of obstacles. In contrast, Figure 16b shows that, in the absence of obstacles, mixing was insignificant in the central part of the outlet nozzle, and became more significant towards the side walls of the chamber. Figure 6:5 Spatial distributions of volume fraction in the outlet nozzle for mixing chamber: (**a**) with obstacles; and (**b**) without obstacles at 10.0 s. Blue color (i.e., volume fraction = 0) represents blood while red color (i.e., volume fraction = 1) represents plasma. Figure 6:6 Average blood volume fractions scored over the outlet boundary of the nozzle (shown in blue) for mixing chambers with and without obstacles.