Expansion and Contraction of Three Non-synchronously Appeared Bubbles

Joint dynamics of three equally spaced bubbles during their expansion and contraction has been studied. The bubbles arise in liquid (water) as small spherical gas nuclei located on a straight line, which corresponds to the production of bubble nuclei by liquid breakdown using either focused laser pulses or electric sparks. The bubble nuclei do not occur simultaneously: there is some time delay in the appearance of the lateral bubbles. At the moments of occurrence all the nuclei are spherical, equal in size and with equal high internal pressure. The bubble nuclei first expand due to their high initial pressure and then contract. Main attention is payed to the influence of the time delay in occurrence of the lateral bubble nuclei on the further joint dynamics of the three bubbles. The mathematical model used has been verified using some available experimental data. It has been found that the variation of the time delay in occurrence of the lateral bubbles leads to a quite large variety of scenarios of the dynamics of the three bubbles during their expansions and contractions until any of them becomes very largely deformed. By that moment, the bubbles can be significantly different in their shape and size. In particular, the central bubble can be nearly spherical, elongated along the symmetry axis without or with a radial dent, flattened along the symmetry axis without or with axial dents, be deformed with one radial and two axial dents, etc. The lateral bubbles can be spherical, with an axial dent directed to or from the central bubbles, with a protrusion directed to the central bubble, etc.