## 4 Results and Discussions
### Effects of Different \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) Ratio and \(W_{\text{Hole}}\)  
Further simulation analyses were carried out to examine the effects of different \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratios ranging from 0.5 to 5.0 on the T-channel trapping with a \(W_{\text{Hole}}\) of 3 \(\upmu\)m. \(L_{\text{Main}}\) was manipulated to comply with the desired \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio. The hydrodynamic trapping concept was found to work accordingly for a T-channel with an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 2.0 and above as the yeast cell model was directed into the trap channel by the fluid stream and trapped in the trap channel (Figures 9 and 10). The fluid velocity profile and streamline field of the cell trapping model were analyzed to understand  
Figure 8: Simulation findings of fluid’s velocity streamline plots for model with \(W_{\text{Hole}}\) of 3 \(\upmu\)m and \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 3 during: (**A**) the initial position of cells; (**B**) cell trapping; and (**C**) after cell trapping. Figure 7: (**A**) Points representing velocity of fluid in the trap channel (**left** side) and main channel (**right** side); (**B**) graph representing velocity of fluid in trap channel and main channel for T-channel trapping model with \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 3.0 before and after cell trapping. the hydrodynamic trapping mechanism. Fluid velocity streamlines presented the direction where the fluid stream was heading, while velocity profiles represented the velocity value in the channel by the contour color. The velocity streamlines produced by the cell trapping model with an \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio of 1.0 and less were found to deviate from most of the streamlines headed to the main channel instead of the trap channel (Figure 9A). Therefore, the stream was unable to lead the cell into the trap channel. This finding is in agreement with the fluid's velocity distribution produced by the same model (Figure 10A). Results show that the main channel's fluid velocity for the single-cell trapping model with an \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio of 1.0 was higher compared to the trap channel's fluid velocity. Therefore the fluid stream will direct the yeast cell to flow into the main channel's path and bypass the trap channel. In contrast with the cell trapping model with an \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio of 2.0 and above (Figure 9B-D), the streamline profiles show the fluid flow diverging from the main channel into the trap channel; most streamlines were directed towards the trap channel. For models with an \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio of 2.0 (Figure 10B-D), the fluid's velocity in the trap hole was higher compared to the fluid's velocity in the main channel. These results show that the trap channel produces lower hydrodynamic resistance than the main channel and the mainstream will direct the yeast cell into the trap channel. Models with an \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio of 2.0-4.0 (Figure 10B-D) had similar fluid velocity patterns to provide an appropriate pressure drop for cell trapping. However, there are variations found in cell trapping time between different \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratios. A higher \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio requires a shorter time for the trapping process compared to a lower ratio. The graph in Figure 11 shows the results of trapping time for cell trapping models with a \(W_{\text{Hole}}\) of 3.0 and an\({}^{\prime}\!R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio ranging from 1.0 to 6.0. The graph shows that the trapping time decreases with increasing \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\). This was probably due to a higher \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\) ratio that enables velocity distribution in a shorter time compared to the lower \(R\!I_{\text{Main}}/R\!I_{\text{Trap}}\).