Satellite generation during bubble coalescence

We experimentally study the formation of a satellite bubble, during the coalescence of two larger bubbles. The daughter bubble is generated by capillary waves which propagate from the growing neck, connecting the two bubbles and focus on the opposite apex. As the successive waves converge on the top, their amplitude grows until a small daughter bubble is pinched off. The mechanism is robust over a large range of parameters. We have observed it in water for bubble diameters from 5.2mm down to 175 μm. For equally sized parent bubbles, the size of the daughter bubble is 0.10±0.03 times that of the mother bubble, but the daughter size also depends weakly on the approach velocity of the two initial bubbles. The effects of viscosity is to dampen the capillary waves, preventing the pinch-off for Ohnesorge number >6.5×10^-3, which is significantly smaller than the critical value observed for the coalescence cascade of a drop. The relative size of the parent bubbles has a large influence on the pinch-off, suppressing it when the size difference is too large. Linear wave-theory can reproduce the overall wave phenomenon and the amplitude evolution of the capillary waves, with the dominant mode number n ≃ 20.