Multiphase Science and Technology A Quarterly

ISSN for PRINT: 0276-1459

For Online Access

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2005, Volume17

Issue 4

84 pages

DOI: 10.1615/MultScienTechn.v17.i4

Issue price - $140.00

S. Konovalova
Institute of Mechanics, Ufa Branch of the Russian Academy of Sciences, Ufa, Russia

I. S. Akhatov
Dept. of Mechanical Engineering & Applied Mechanics, North Dakota State University, Fargo, ND, USA

Bubble clouds forming in a liquid subject to a strong acoustic excitation, that is called acoustic cavitation, show a complicated slowly varying filamentary structure. This bubbly mixture represents a multiphase system whose physical origin is still not completely understood. Basic physical interactions in such bubbly liquid comprised of nonlinear bubble dynamics, Bjerknes and drag forces, interaction between bubbles, wave dynamics, etc. In the introduction section a brief overview of various theoretical approaches to this phenomenon is presented. The paper gives a systematic representation of particle model for describing the structure formation process in a bubbly liquid. In the framework of the particle model all bubbles are treated as interacting objects that move in the liquid.
A mathematical model for coupled, radial and translational, motion of a small spherical cavitation bubbles driven below its resonance frequency in a strong acoustic field (P_a > 1 bar, f = 20 kHz) is presented. Numerical analysis of the dynamics of a single bubble shows that, within the limits of harmonic resonances of the system, period-doubling bifurcations cascades with transitions to chaos and back to regular dynamics take place. A possible mechanism for the erratic dancing mode of bubble motion is proposed. Besides erratic dancing, the low-frequency quasi-periodic translational motion (periodic dancing) mode is observed at certain values of bubble radii. For a pair of interacting bubbles various dynamic modes are obtained: simple attraction, periodic motion and asymptotic motion, when the bubbles tend to take steady positions on a vertical line crossing the pressure antinode. In the last two cases bubbles do not coalesce, but are bound into couples, which cannot be predicted by a classic linear theory. This is explained by so-called giant response of small bubbles. Thus, the nonlinear effects can result in self-organization of bubble clouds. Structure formation processes in bubble clouds are simulated numerically. The characteristic bubble sizes in the structures, as well as dimension and shape of the structures are in qualitative agreement with the experimental observations.

DOI: 10.1615/MultScienTechn.v17.i4.30 Download article, 343-371 pages

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