Interaction of two nearly contacting gas bubbles pulsating in a liquid in an alternating pressure field

The conditions for the coalescence of two pulsating spherical bubbles in a liquid in a weak low-frequency acoustic pressure field, as well as the conditions for absence of such a fusion, have been studied. Since the frequency of the pressure field is much lower than natural frequencies, the bubbles pulsate with identical relative amplitudes and phases. At large distances, bubbles approach according to the Bjerknes law. However, viscous forces near a contact can compensate the attraction force and bubbles do not coalesce. It has been shown that bubbles coalesce when the ratio of radii is smaller than 3; otherwise, periodic oscillations are established at a small gap between the surfaces of bubbles and coalescence does not occur. These theoretical results have been confirmed by existing experiments.