*3.1. Bubble Shape and Moving Path*

Figure 2 shows the bubbles' shape changing with the gas flow rate. At a low gas flow rate of 20–40 mL/min, the bubbles with diameters of 2–3 mm were spherical in shape. At an increased gas flow rate of 60–500 mm, the shape of the injected bubbles changed to be ellipsoidal and the bubbles' diameters were 3–5 mm. With a further increase of gas flow (1000–1500 mL/min), the bubbles became mushroom-shaped and more irregular. The bubbles' sizes were about 10–20 mm.

**Figure 2.** Bubble shape at different gas flow rate with oil phase viscosity of 50 cSt.

Figure 3 shows the bubble movement path and the interface fluctuation when it passed through the water–oil interface. The gas formed spherical bubbles after being ejected through the nozzle, and the shape of the bubbles subsequently changed from ellipsoidal or coronal during ascension because of the difference in internal and external pressures. When a bubble was close to the water–oil interface, its movement path deviated, resulting in a different ascending trajectory because of interface fluctuation caused by the impact of previous bubbles. The velocity of a bubble decreased rapidly, and the bubble surface pressure became uniform when it passed through the water–oil interface. It then ascended in a spherical shape while driving the interface upward. In addition, when the bubble entered the oil phase from the water, the surface of the bubble covered the water-phase liquid film, resulting in entrainment.

**Figure 3.** Bubble shape, movement path, and interfluctuation.

### *3.2. Bubble Residence Time at Liquid–Liquid Interface*

Figure 4 shows that the heights to which the bubble rose varied with time when oil phases with different viscosities were used. The difference in density and interfacial tension between the oil phases is very small (Table 1). Parameters *T*1, *T*2, and *T*<sup>3</sup> are the times for a bubble to cross the water–oil interface. The interface is more easily broken when the oil has a low kinematic viscosity, thus, the bubble would cross using a shorter route and in less time. With an increase in the oil kinematic viscosity, the "elasticity" of the interface is enhanced, where bubbles should overcome the higher viscous resistance to rising. The bubbles require more time to cross an oil phase with higher viscosity.

**Figure 4.** Bubble rising heights at different times (*Q* = 50 mL/min).

#### *3.3. Bubble Rising Velocity*

Figure 5 shows the distribution of bubble velocity at different heights with a low gas flow rate *Q* = 50 mL/min. As a result of the low gas flow rate, bubbles formed with lower frequency, lower velocity, and a smaller size after the gas was emitted from the nozzle. Thus, small bubbles interacted one by one with the water–oil interface. This figure reveals that the velocity of bubbles increased linearly in the water-phase (black points) and decreased when they began to pass through the interface (red points). When a bubble left the surface, its velocity was minimum. It then entered the oil phase. However, the velocity was lower in the oil phase than in the water-phase because of the high viscosity of the silicone oil (blue points). In addition, region 2 became larger with increasing oil viscosity.

As shown in Figure 6, about five bubbles were tracked to measure the bubbles' rising velocity. The blue points show the bubbles with a decreasing velocity caused by interface interaction, the red points show bubbles with a decreasing velocity caused by bubble breakage and the green points show the bubbles with an increasing velocity caused by bubble aggregation. When the gas flow rate was increased, the bubble flow was no longer one by one but rather continuous and even. The shape of the interface, therefore, changed dramatically. Because of the instability of the bubble shape, fragmentation, accumulation, and the influence of interface fluctuation, the change in large-bubble velocity can be divided into four stages during the rising process. The bubble velocity varied with height. In region 1, the bubbles' velocity increased during the rising process. When the bubble moved to region 2, the velocity of a bubble was reduced because the shape of the bubble changed during ascent. The shape and velocity of the bubble affected each other, so the velocity changed periodically. In region 3, the improvement in bubble shape caused the increasing of bubbles' velocity. The velocity was hampered by the fluctuation of the interface in region 4. As the viscosity increases, the difference in velocity between the bubbles at the top and bottom becomes smaller and the location of bubble aggregation becomes closer to the nozzle.

**Figure 5.** Rising-bubble velocity distribution (*Q* = 50 mL/min).

**Figure 6.** Rising-bubble velocity distribution (*Q* = 1000 mL/min).
