Sound synchronization of bubble trains in a viscous fluid: experiment and modeling.

We investigate the dynamics of formation of air bubbles expelled from a nozzle immersed in a viscous fluid under the influence of sound waves. We have obtained bifurcation diagrams by measuring the time between successive bubbles, having the air flow (Q) as a parameter control for many values of the sound wave amplitude (A), the height (H) of the solution above the top of the nozzle, and three values of the sound frequency (fs). Our parameter spaces (Q,A) revealed a scenario for the onset of synchronization dominated by Arnold tongues (frequency locking) which gives place to chaotic phase synchronization for sufficiently large A.

Synchronization of two bubble trains in a viscous fluid: experiment and numerical simulation.

We investigate the interactions of two trains of bubbles, ejected by nozzles immersed in a viscous fluid, due only to the solution's circulation. The air fluxes (Q(1),Q(2)) are controlled independently, and we constructed parameter spaces of the periodicity of the attractors. We have observed complex behavior and many modes of phase synchronization that depend on these airflows as well as on the height (H) of the solution above the tops of the nozzles.

Period adding cascades: experiment and modeling in air bubbling.

Period adding cascades have been observed experimentally/numerically in the dynamics of neurons and pancreatic cells, lasers, electric circuits, chemical reactions, oceanic internal waves, and also in air bubbling. We show that the period adding cascades appearing in bubbling from a nozzle submerged in a viscous liquid can be reproduced by a simple model, based on some hydrodynamical principles, dealing with the time evolution of two variables, bubble position and pressure of the air chamber, through a system of differential equations with a rule of detachment based on force balance. The model further reduces to an iterating one-dimensional map giving the pressures at the detachments, where time between bubbles come out as an observable of the dynamics.