Nonlinear Phenomena in Complex Systems, 2002, Vol.5, No.1, pp.71-77

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2002, Vol.5, No.1, pp.71-77

Pattern Formation in Acoustic Cavitation
A.A. Doinikov

Cavitation bubbles in acoustic resonators, when the forcing is strong enough, are observed to arrange in branched filamentary structures resembling very much electrical discharge patterns. The filamentary cavitation structures, named acoustic streamers, consist of oscillating bubbles of small size that move towards the central pressure antinode, being free from coalescence. No satisfactory theory exists yet to explain the formation of such structures. The present paper seeks to establish a mechanism responsible for the acoustic streamer formation, based on the approximation of pairwise interactions between bubbles. To this end, using the Lagrangian formalism, equations of radial and translational motions of two spherical gas bubbles are derived, allowing for both coupling between the volume and translational bubble oscillations and mutual radiation interaction between the bubbles. The equations are then used in numerical investigation of translational motion of two small, driven well below resonance, bubbles in strong acoustic fields with pressure amplitudes exceeding 1 bar. It is shown that, if the forcing exceeds a threshold, the bubbles form a bound pair with a dynamical equilibrium spacing rather than collide and coalesce as they do in a weak field. This result, hopefully, seems to provide an explanation for the cavitation bubble patterns.
Key words: acoustic cavitation, acoustic streamer, bubble dynamics

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