## 4 Results and Discussions  
### T-Channel Trapping Ability  
The finite element model for the T-channel trapping was developed to evaluate the channel's ability to trap single cells depending on the desired cell size. The model was designed to have two outlets that lead to the waste reservoir and to be operated by fluid infusion through the inlets. In the simulation analyses, the T-channel trapping model was developed to trap a 5-\(\upmu\)m yeast cell. Figure 5: (**A**) Schematic diagram of the experimental setup; (**B**) a close-up image of the trapping channel; (**C**) experimental setup; (**D**) a close-up real image of the T channel microfluidic chip positioned under the inverted microscope. A T-channel trapping model with a trap hole width (\(W_{\text{Hole}}\)) of 3.0 \(\upmu\)m was used to observe the appropriate flow resistance ratio of the main channel to the trap channel (\(Rh_{\text{Main}}/Rh_{\text{Trap}}\)) for single particle/cell trapping. The main channel's length (\(L_{\text{Main}}\)) was manipulated to create an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio ranging from 0.5 to 5. Increasing the \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio is proportional with the increase in the main channel's (main path) length. Figure 6 represents the result of cell trapping for a model with an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio ranging from 1 to 6 at the 25 s point of the simulation time. A yeast cell model was trapped when a \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 2 or higher was used with various cell positions in the trap channel during a simulation time of 25 s (Figure 6B-E). A higher \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio produced faster cell trapping. Models with an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 1 or less were not able to trap the cell, causing the cell to bypass the trap channel to enter the main channel (Figure 6A). The simulation results show that an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 2 or above is able to trap single cells using the hydrodynamic trapping concept. The fluid's velocity inside the main channel and trap channel were further investigated to analyze the fluid's velocity profile in the channels before and after cell trapping occurred. A T-channel model with a \(W_{\text{Hole}}\) 3 and \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 3 was chosen for the analysis. Figure 7A represents the fluid's velocity position in the trap and main channel and the graph in Figure 7B presents the fluid's velocity measurement in the trap and main channel before and after trapping. Before cell trapping occurred, the fluid's velocity inside the trap was higher than in the main channel; conversely, after the cell was trapped, the fluid's velocity inside the trap channel decreased dramatically while the fluid's velocity in the main channel increased instantly. When the velocity of fluid in the trap channel is higher than the main, it leads to a lower hydrodynamic resistance in the trapping site, which creates a trapping stream directing the cell into the trap channel. further blocks the trap hole and drastically decreases the fluid's velocity inside the trap channel. This finding supports the principle of hydrodynamic trapping in which, when the trapping site is empty, the trap channel will have lower flow resistance compared to the main channel. The direction of fluid flow diverges from the trap channel to the main path (main channel); therefore, subsequent cells will be directed to the main path. These findings were supported by the simulation outcome using three cells and a T-channel model with an \(Rh_{\text{Main}}/Rh_{\text{Trap}}\) ratio of 3 and a \(W_{\text{Hole}}\) width of 3 \(\upmu\)m. The analyses were carried out to investigate the movement of subsequent cells after trapping occurred. Results obtained show that the first cell moved into the trap channel (Figure 8B) and subsequent cells bypassed the trap channel (Figure 8C).