# Elasto-Inertial Particle Focusing in Microchannel with T-Shaped Cross-Section
## 3 Results and Discussion
### Viscoelastic Particle Focusing under Non-Newtonian Fluid  
First, we investigated and observed the focusing and migration of particles under a viscoelastic fluid in three kinds of microchannels with different T-shaped cross-sections. Furthermore, experiments were carried out for two sizes of particles (5 and 13 \(\upmu\)m diameter), which is one of the important parameters for determining elasto-inertial particle focusing behaviors [20]. Figure 4 shows the particle focusing at a flow rate of 100 \(\upmu\)L/min according to the location from the inlet of the Type 3 microchannel in non-Newtonian viscoelastic fluid (PEO500). At the location near the inlet (1 cm), no focusing was observed for either particle size due to the insufficient elastic forces developed. As the channel length was increased to 7 cm, particles were focused in a single stream located at the center, with a flow rate of 100 \(\upmu\)L/min. The lateral migration speed was strongly dependent upon particle size [21, 22], so tighter particle focusing was obtained for the 13 \(\upmu\)m particle 7 cm downstream from the inlet. Figure 5 presents the optical images of particle focusing (top and side view) in the microchannel with different T-shaped cross-sections for different flow rates and particle sizes in non-Newtonian viscoelastic fluid. All optical images were captured 7 cm downstream. The dotted lines are the boundaries of the microchannel from the top and side view, which were obtained from the bright-field optical images. Figure 6 presents the normalized fluorescent intensity profiles presenting the particle distribution at various flow rates in the microchannel with different T-shaped cross-sections including a microchannel with a square cross-section which was prepared for comparison. As shown in Figure 5a,c,e, when viewed from the side, 13 \(\upmu\)m particles were observed to focus to a single line near the bottom side for all types of channels. Furthermore, the effect of elasto-inertial force was dominant for low flow rates ((below 50 \(\upmu\)L/min, Re \(\approx\) 0 and Wi \(>\) 0) so the particles moved to the centerline for all types of channels (top view). The experimental results show that there was only one stream from both front and side views, meaning that true 3D elasto-inertial particle focusing was achieved for the tested condition. On the other hand, when the flow rate increased and reached 50 \(\upmu\)L/min (Re \(>\) 0 and Wi \(>\) 0), the single-line particle focusing changed to double-line focusing in the Type 1 channel, but there was no change in the Type 2 and Type 3 channels. For the higher flow rate of 100 \(\upmu\)L/min (inertial force dominant regime), due to the relatively strong inertial force at the high flow rate [6], the focused particles were more or less dispersed around the centerline in the Type 2 channel and the triple-line focusing was observed in the Type 3 channel. This implies that the lateral migration of particles in a non-Newtonian fluid is strongly affected by the inertial force rather than the elastic force [20]. Figure 3: SEM images of microchannels with a T-shaped cross-section. (**a**) Type 1, (**b**) Type 2, (**c**) Type 3. As shown in Figure 5b,d,f, particles with a relatively small particle size (5 \(\upmu\)m) were randomly dispersed and not focused at specific points in the Type 1 and Type 2 channels for low flow rates (below 50 \(\upmu\)L/min, Re \(\approx\) 0 and Wi \(>\) 0). In the case of the Type 3 channel, however, small particles were slightly focused in the centerline for low flow rates. As the flow rate increased up to 50 \(\upmu\)L/min (Re \(>\) 0 and Wi \(>\) 0), the particles were focused in the center of the microchannels under the influence of elasto-inertial force. However, unlike the large particles (13 \(\upmu\)m), the small particles were not completely focused in the center, showing wider focused bands. This was due to the competition between the non-negligible inertial lift force and the relevant elastic force under viscoelastic fluid flowing [6,20].