## 3 Results and Discussions
### Three Parallel Microchannels  
The microfluidic geometry consisting of parallel channels which were separated by rows of micropillars was analysed by different groups of researchers either to study the  
Figure 6: Simulated shear stress and velocity magnitude along the red line plotted versus the width of the microchannel using three different flow rates: 2, 6 and 10 \(\upmu\)L/min. (**a–c**) fluid flow; (**d–f**) wall shear stress simulations of the longitudinal microchannel with a height of 200 \(\upmu\)m; (**g**) the velocity profile; (**h**) wall shear stress profile at the bottom of the microchannel (h = 0 \(\upmu\)m- solid lines) and at the middle of the microchannel (h = 100 \(\upmu\)m- dotted lines); (**i**) generated mesh density study of the longitudinal microchannel. distribution of specific compound concentrations inside the channels at different time points [58], to increase the accuracy of in vitro drug screening [33] or to investigate the distributions of velocity and shear stress within the channels [22; 30]. This particular microfluidic geometry attracted the interest of many scientists as it allows the cells and the culture medium to be introduced separately. The cells are cultured in the main or middle channel, while the culture medium is supplied through the side channels and gets diffused to the cells across the micropillar structures. However, in this study, the three parallel microchannels were designed to investigate the wall shear stress and velocity profile distribution through the inlets of the two side microchannels using different flow rates (Figure 3a). The fluid distribution within the microchannel was evaluated using a streamline plot (Figure 7a-c). Figure 7a-c shows that in the side microchannels, the fluid moves parallel to the walls, while in the main microchannel, the fluid diffuses from the side microchannels to the middle microchannel through the micropillars. The wall shear stress for both the side and main microchannel using three different flow rates (2, 6 and 10 \(\mu\)L/min) was calculated using Equation (4). The calculated wall shear stress for the side microchannels (250 \(\mu\)m) using three different flow rates is 0.02, 0.06, and 0.1 Pa. The results obtained from the simulations show low values of shear stress in the main microchannel (no fluid flow) and higher values of shear stress in the side microchannels. Additionally, since the width of the side channels was smaller compared to the main microchannel, the velocity and wall shear stress values were greater within the side microchannels. However, as we increased the flow rates to 6 and 10 \(\mu\)L/min, the velocity and wall shear stress increased (Figure 7d-f). Maintaining the shear stress within the physiological range is critical, as excessively large values of shear forces can alter the cytoskeletal structure of cells as well as cell viability in a microfluidic cell culture. Additionally, the velocity and wall shear stress profiles (bottom and middle of the microchannels) were simulated versus the width of all the microchannels (Figure 7g,h). As shown in the figure, the minimum velocity occurred not only near the walls due to the non-slip condition but also near the micropillars, which acted as a barrier between the side and main microchannels. In fact, Figure 7g,h indicated that in the proximity of the micropillars (about 280 \(\mu\)m and 830 \(\mu\)m on the width axis), the velocity decreased near the walls. Furthermore, the velocity started to have higher values in the side microchannels than in the main microchannel. This phenomenon is due to the absence of flow rate in the main microchannel. Figure 7h shows the wall shear stress profiles at two different height positions of the device (h = 0 \(\mu\)m representing the bottom of the microchannels and h = 100 \(\mu\)m representing the middle of the microchannels).