# Elasto-Inertial Particle Focusing in Microchannel with T-Shaped Cross-Section
## 3 Results and Discussion
### Simulation Results
Note that the \(x\)-directional net  
Figure 9: Variation in (**a,b**) x-directional and (**c,d**) y-directional net elasto-inertial force exerted on 5 and 13 \(\upmu\)m particles suspended in the Type 2 channel. Measurements were made for various particle locations along the x and y axis illustrated in Figure 2.  
forces are only considered in this case since y-directional net forces for Type 3 have the same trend and equilibrium point as those of Type 2. It should also be noted that the maximum flow rate increases at 150 \(\upmu\)L/min as the characteristic drift for the larger particles started to occur at the flow rate of 150 \(\upmu\)L/min in the present experiment. Figure 10 shows the variation in the \(x\)-directional net force exerted on two different particles varying with the flow rates. For the case of the 5 \(\upmu\)m particle, the first two lowest flow rates (i.e., T\({}_{3}\)D5Q1 and T\({}_{3}\)D5Q10) generate multiples of the zero crossing in the x-directional force, indicating an absence of the particle focusing in the lateral direction, as shown in Figure 10a. With an increase in flow rate, however, a consistent directional force occurs and pushes the 5 \(\upmu\)m particle toward the origin of Type 3, indicating a single train of the particle focusing along the lateral centerline from 100 \(\upmu\)L/min. These migrating patterns for the smaller particle agreed well with the results of the experiment, as seen in Figure 5f. The case of 13 \(\upmu\)m particle, however, shows unique migrating behavior as the flow rate increases. When increasing the flow rate up to 100 \(\upmu\)L/min, as shown in Figure 10b, \(F_{x,net}\) becomes more consistent, moving the particle toward the lateral origin with a single equilibrium point. This is supported by our experimental observations, shown in Figure 5e, that the intensity of the fluorescent particles focused at the lateral centerline becomes higher, up to a flow rate of 100 \(\upmu\)L/min. Interestingly, at the flow rate of 150 \(\upmu\)L/min, the migrating pattern in the lateral direction for 13 \(\upmu\)m particle case remarkably changes in the Type 3 channel. As shown in Figure 10b, \(F_{x,net}\) at the maximum flow rate is characterized by two negative convexes and a positive plateau between them. This indicates two possible points of the particle focusing each at \(x=0\) and \(x=55\) \(\upmu\)m, which is not observed in the case of 5 \(\upmu\)m particles at the same flow rate. The interesting pattern of the particle focusing in Type 3 depending on the particle size could be attributed to the coupled effect between the sharp edge at the junction and the bottom wall (see Figure 8d). As was discussed earlier, the shallow channel depth with a protruded sharp edge as in Type 3 resonates with the effect of the shear rate on its cross-plane. Thus, the Type 3 channel preferentially segregates the large particle (i.e., 13 \(\upmu\)m) with two lateral locations for the particle focusing. In contrast, the small particle (i.e., 5 \(\upmu\)m) consistently drifts toward a single focusing point at the lateral origin at a flow rate of 150 \(\upmu\)L/min. This numerical result has excellent agreement with our experimental result at the same flow rate in the same microchannel. Furthermore, the current observation suggests a potential implication of the particle separation depending on its size when the aspect ratio of the T-shaped microchannel and the flow rate are appropriately leveraged.