Physica A 308 (2002) 15–24 www.elsevier.com/locate/physa Explosion of chaotic bubbling A. Tufaile ∗ , M.B. Reyes, J.C. Sartorelli Instituto de F  isica, Universidade de S˜ ao Paulo, Caixa Postal 66318, 05315-970 S˜ ao Paulo, Brazil Received 22 November 2001 Abstract We have studied a saddle-node bifurcation= explosion of air bubble formation driven by a sound wave, whose amplitude is the control parameter. The bubbles are formed in a nozzle submerged in a water= glycerol solution inside a cylindrical tube, and the sound wave is tuned to the air column above the uid. The nonlinear interaction between sound wave and the uid oscillations, caused by the air bubbles passage through the liquid, results in a route to chaos via quasi-periodicity, with some resonant states characterized by the rational winding numbers W = f s =f b , where f s is the sound wave frequency and f b is the bubbling rate. We also have shown that the bubble dynamics is similar to the one observed in the two-dimensional circle map. c  2002 Elsevier Science B.V. All rights reserved. PACS: 05.45.-a Keywords: Bubble dynamics; Explosion; Circle map 1. Introduction Recent studies on air bubble formation under sound wave stimuli have identied a variety of rich dynamics [1–3]. Besides synchronization [1] and H enon-like behav- ior [2], we have observed that the sound wave= bubbling system can be represented by the two-dimensional circle map dynamics [3]. The identication of the geometry of bifurcations obtained from a sound wave= bubbling system provides the framework for understating the dynamics of a pulsating two-phase ow interacting with a wave. It is presented an experimental exploration of a route to chaos via quasi-periodicity, followed by the occurrence of a saddle-node bifurcation in air bubble formation sub- jected to dierent values of sound wave amplitude. We also related these behaviors * Corresponding author. E-mail address: tufaile@if.usp.br (A. Tufaile). 0378-4371/02/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-4371(02)00571-X