## 3 Results and Discussion
### Two-Phase Flow Results  
#### 3.2.1 Velocity Fields  
Figure 9 shows the velocity field of magnetic particles measured at 200 \(\upmu\)m toward the center from the wall. The calculation area was approximately H 1000 \(\times\) W 424 \(\upmu\)m\({}^{2}\). Voids in the velocity field made up the areas where bubbles were present. Figure 9a shows magnetic particles present below the N\({}_{2}\) bubbles. The velocity of the magnetic particles becomes faster as the gap between the bubble and the wall becomes narrower, comparing with Figure 9b,c. The cross section becomes smaller, and the velocity increases because the velocity of a magnetic particle is greater than the N\({}_{2}\) velocity. In Figure 9b, magnetic particles and bubbles are shown in the middle. The velocities exhibited at the center and bottom of the N\({}_{2}\) bubbles are lower than the velocity at the top. In Figure 9c, magnetic particles are shown above the N\({}_{2}\) bubbles. Thus, the flow phenomenon changes completely depending on the size of the gap between the wall and the N\({}_{2}\) bubble. This phenomenon seems to be the result of the magnetic particles' velocity being greater than the N\({}_{2}\) velocity, which causes the bubbles to act as resistance. Figure 10 shows the velocity fields at the center of the solenoid nozzle. The center of the nozzle was located 1500 \(\upmu\)m away from the wall. The calculated area was approximately 212 \(\upmu\)m from either side of the center. In Figure 10a, the magnetic particles are shown below the bubble. In Figure 10b, magnetic particles are present between the bubbles which are located above and below. In Figure 10c, the magnetic particles are above the bubble. Higher velocities were measured in instances where magnetic particles were present above the bubble than when they were present below the bubble. Figure 8: Velocity profiles for magnetic and nonmagnetic particles and from theoretical calculations. Figure 9: Velocity fields of bubbly flow near the wall. The N\({}_{2}\) is located (**a**) above, (**b**) middle, (**c**) below. Since the magnetic particles flow in alignment with the external magnetic force, a generally uniform flow field was measured. Figure 11 shows graphs comparing the theoretical, single-phase nonmagnetic particle, single-phase magnetic particle, and two-phase experimental velocities near the wall and at the center. In Figure 11a, the red and blue profiles of the discontinuous points indicate the boundary of the bubble. These results show that the velocity at the bubble boundary is lower than that far from the bubble. Near to the wall, the velocity of the two-phase flow was found to be lower than those of the single-phase nonmagnetic and magnetic particle flow but higher than the theoretical velocity. At the center, all cases were affected by the external magnetic field, and lower velocities than the theoretical velocity were measured. Figure 12a shows the velocity field near the wall below the slug. Figure 12b shows the velocity field between the slug and the wall. In contrast to the phenomenon in the bubbly flow, high velocity near the wall was measured in the slug flow despite the external magnetic force acting as an opposing force. Figure 11: Comparison of the average velocity profiles of the bubbly flow (**a**) near the wall and (**b**) at the center. Figure 10: Velocity fields of bubbly flow at the center. The N\({}_{2}\) is located (**a**) above, (**b**) above and below, (**c**) below. The overall velocity of the magnetic particles appears to have increased because of the high N\({}_{2}\) velocity. Figure 13a shows the velocity field of a narrow place where the gap between slugs was 200 \(\upmu\)m. Figure 13b shows the velocity field of an area with a gap of at least 1000 \(\upmu\)m between slugs. While the theoretical velocity was 2 and the bubbly flow velocity was approximately 1, the velocity of an area with a narrow slug gap was measured to be over 1.5.