Physics of bubble oscillations

Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.