## 2 Idea and Concept
From Equation (1), by estimating that the pressure drop across the trap and the main channel are the same (\(\Delta P_{\text{Trap}}=\Delta P_{\text{Main}}\)), the flow rate ratio (\(Q_{\text{Trap}}/Q_{\text{Main}}\)) or flow resistance ratio (\(Rh_{\text{Main}}/Rh_{\text{Trap}}\)) between the trap channel and the main channel can be given as follows [50]:  
\[\frac{Q_{\text{Trap}}}{Q_{\text{Main}}}-\frac{Rh_{\text{Main}}}{Rh_{\text{Trap }}}=\left(\frac{C_{\text{Main}}}{C_{\text{Trap}}}\right)\left(\frac{L_{\text{ Main}}}{L_{\text{Trap}}}\right)\left(\frac{P_{\text{Main}}}{P_{\text{ Trap}}}\right)^{2}\left(\frac{A_{\text{Trap}}}{A_{\text{Main}}}\right)^{3} \tag{2}\]  
Figure 1: Schematic illustration of single cell T-channel trapping model and the hydrodynamic resistance. Figure 2: Schematic illustration of the fluid’s hydrodynamic resistance in the microchannels for two different conditions; (**A**) empty trap channel (before cell trapping occurs); (**B**) after cells have been trapped. By using a relationship of \(A=W\times H\) and \(P=2\left(W+H\right)\), where \(W\) and \(H\) are the width and height of the channel, respectively, Equation (2) can be defined as:  
\[\frac{Q_{\text{Trap}}}{Q_{\text{Main}}}=\frac{Rh_{\text{Main}}}{Rh_{\text{Trap}}} =\left(\frac{C_{\text{Main}}}{C_{\text{Trap}}}\right)\left(\frac{L_{\text{ Main}}}{L_{\text{Trap}}}\right)\left(\frac{W_{\text{Main}}+H_{\text{Main}}}{W_{ \text{Trap}}+H_{\text{Trap}}}\right)^{2}\left(\frac{W_{\text{Trap}}H_{\text{Trap} }}{W_{\text{Main}}H_{\text{Main}}}\right)^{3} \tag{3}\]  
From Equations (2) and (3), it is noted that the flow rates of the trap channel (\(Q_{\text{Trap}}\)) and the main channel (\(Q_{\text{Main}}\)) are distributed depending on the corresponding \(Rh\). For the trap to work, the flow rate along the trap channel must be greater than the main channel (\(Q_{\text{Trap}}>Q_{\text{Main}}\)). In other words, the flow resistance along the main channel must be greater than the trap channel (\(Rl_{\text{Main}}>Rl_{\text{Trap}}\)). Therefore, a single cell can be trapped by manipulating the flow resistance ratio (\(Rl_{\text{Main}}/Rh_{\text{Trap}}\)), which is determined by the geometric parameters of the channels. A single-cell trapping model is developed to produce a finite element single-cell trapping system in which the optimization of a channel's geometry and adjustment of desired cell size could be performed. The geometry of the trapping channel is a variable for optimization (see Equation (3)) and subject to the size of cells and the application that will be carried out in the channel after the cells are trapped. An example of a channel's geometry optimization was presented in this paper using a 5-\(\upmu\)m yeast cell model. For other cell sizes, some guidelines in designing and optimizing the cell trapping channel are discussed. Firstly the diameter of the viable cells/particle in suspension should be determined to estimate the range of suitable \(W_{\text{Hole}}\) sizes. The trap channel's geometry size is dependent on the trapped cells'/particles' applications. For example, if adherence cells are used and need to be cultured inside the trapping platform, the \(W_{\text{Trap}}\) should be bigger than the diameter of the cell (viable cells in suspension before adhesion) because suspended cells will need space for cell adhesion, spreading and growing in time. In different applications, an individual ciliate protozoan, _Tetrahymena thermophila_[30], needs to be trapped and maintained in the trap channel for long-term monitoring of cell behavior. Therefore, no expansion in size is expected after the trapping process and the trap channel's width does not require space for expansion. In summary, the geometry of channels is a variable (\(L\), \(H\), and \(W\); see Equation (3)) for optimization, subject to the size, type and the application performed to the trapped cells.