### BUBBLE INTERACTIONS

I have recently initiated an investigation of the interacting bubbles. This was a natural extension of my previous work on the drop-drop interaction. I believe with my insight into the drop-drop interaction I could contribute to the problem of bubble-bubble interaction. This proved to be a fruitful investigation, since we discovered certain physical phenomena that were never before reported. In my recent JFM paper in this area, I have shown that two bubbles may attract or repel each other under certain conditions, or may have a stable oscillatory behavior. I am currently extending this work to multi-bubble interaction. This work was supported by NASA micro-gravity program. The objective of this work was to find a technique to separate bubbles from melts, which is a problem in the crystal growth in the microgravity environment. The figure below tracks a resonany pair of bubbles in oscillation.

#### THREE BUBBLE OSCILLATION

Three-bubble oscillation was captured by chance with one bubble of 0.146 mm in the center and two bubble almost equal size around 0.133 mm on two sides. The levitated frequency is 22.5 kHz and acoustic pressure is around 950 Pa. This case is a little complicated than the two-bubble oscillations pattern because the middle bubble has resonance effects with the bubble from both sides. From the following figure, we can see the separation between two centers of bubbles in variation with time.

We studied the experimental result of separation between left/right bubble and the middle bubble versus time. The oscillations on both sides are almost in phase with a frequency of 16.6 Hz. The amplitude on right side is bounded by 4. 8 radii to 3.64 radii, and the left side is bounded by 4.6 radii to 3.58 radii. The oscillation frequency is relatively high for small dancing amplitude. It also compares the right/left side oscillation with the model prediction for the separation varying with time. Shown below is the ideal condition for three-bubble oscillation.

The model predicts the oscillation of 16.2 Hz and amplitude is bounded between 4.82 radii and 3.68 radii. The model prediction and experiment results match fairly well in general. However, the model only predicts the motion in an ideal condition and verifies the phenomenon in a long time scale. The real oscillations on both sides are not center symmetry in a strict sense since the left bubble and right bubble can never be exactly the same size and start oscillation at the same time at the same spacing.