## 3 Results and Discussions
### The Closed-Microchannel Structure  
Scientists have performed several studies on fluid dynamics for devices consisting of parallel channels separated by arrays of micropillars [24; 25; 31]. They have tried to modify the dimensions of the micropillar structure and the inlets and outlets in order to analyse how these geometrical features affect the velocity, shear stress and pressure within the device. [PERSON] et al. [25] performed a fluid dynamic analysis on a device consisting of three parallel channels separated by two rows of micropillars for performing 3D and 2D human cardiomyocyte cell culture, signifying that cardiomyocytes proliferated better in 3D than in 2D conditions. Additionally, [PERSON] et al. [30] analysed the effect of gap spacing between the micropillars on wall shear stress. Their results demonstrated tunable shear stress gradients by changing the number of micropillar rows and their size. However, in this study, we designed a microfluidic device with three parallel channels that were separated by two rows of micropillars (Figure 4a) to assess the velocity, shear stress, and pressure within the microdevice using six different flow rates within the channels. This design is used to address the presence of a flow rate in the main microchannel, which can affect the shear stress and velocity profile, as well as how the different geometrical dimensions of the micropillars could affect the fluid dynamic parameters. Furthermore, this design can be utilised to analyse how different gaps between the pillars can affect shear stress and velocity. The wall shear stress was calculated prior to the simulation using Equation (4). The calculated wall shear stress for the side microchannels using flow rates of 2, 6 and 10 \(\mu\)L/min is 0.02, 0.06, and 0.1 Pa, respectively, and the calculated wall shear stress for the main microchannels using 3, 5 and 7 \(\mu\)L/min is 0.007, 0.04, and 0.05 Pa, respectively. The simulation results are shown below (Figure 8a-c). Figure 8a shows the low-velocity profile at the same flow rate (2 \(\mu\)L/min) used for the side channels and the flow rate of 3 \(\mu\)L/min used for the main microchannel. However, increasing the flow rates at the side and main microchannels produced a higher velocity in the main microchannel, which can cause flow through the micropillars to the main channel (Figure 8b). The same results were obtained for Figure 8c, which shows a higher velocity profile in the main microchannel as we increased the flow rate in the side microchannels. Figure 8a-c shows the movement of fluid from the side microchannels towards the main microchannel when flow rates are applied to both the side and main microchannels. This can lead to an increase in the value of wall shear stress within the main microchannel. The wall shear stress was increased by increasing the flow rates at the main microchannel, showing higher wall shear stress in Figure 8e,\(f\) using the flow rates of 5 and 7, respectively. For this geometry, the pressure distribution inside a rectangular cross-section microfluidic device is also calculated using Equation (6) [40]:  
\[\Delta\mathrm{P}=\frac{12\mu\mathrm{LQ}}{\mathrm{wh}^{3}} \tag{6}\]  
As shown in Figure 8g-i, when the flow rate increases, the pressure within the channels increases and, according to Equation (6), the two values (pressure and flow rates) are directly proportional. Figure 8j depicts the generated mesh study of the closed microchannel structure and the micropillars showing a total of 283,958 elements, which is adequate to guarantee a grid-independent solution. Moreover, the results of the velocity profile, wall shear stress and pressure for all the six flow rates within the side and main microchannels were plotted for evaluation versus the width of the channels (Figure 9). Figure 8: Simulated shear stress and velocity magnitude along the red line.