Characterization and control of chaotic bubble behavior

A knowledge of the properties and behavior of gas bubbles in liquid is a prerequisite to the detailed understanding of several chemical or other processes in which the essential action of the operation is centered about moving bubbles in liquid. The present investigation aims to add to this knowledge from the viewpoint of deterministic chaos. Special attention is given to bubble formation at a single submerged orifice as well as the movement of the bubbles in the system. The experimental investigation identified several dynamic features of the system such as low dimensionilty, periodic cycles, entrainment using sound or gas pulsing, and evaluation of spatio-temporal character. The period-doubling bifurcation route to chaos was experimentally verified as well. The system independent variable of gas flow was identified as the optimal feedback control variable. Taming of chaos was experimentally quantified by using periodic sound wave perturbation. Entrainment of chaotic bubble behavior to its periodic states was also obtainable by using a discrete gas pulsing method. The engineering need related to the control of the dynamics of chaotic bubble behavior was evaluated based on the OGY and Bruns nonlinear relay feedback control schemes. The advantage of these methods is that they do not require the model equations to describe the dynamics of the system. The sensitivity of a chaotic system to small perturbation provides a clue to implement these control models. Empirical difficulties in the sensitivity of the manipulated variable calculation to the experimental data used are effectively overcome. Results from this investigation provide useful and conclusive information for future work aimed at understanding bubble dynamics especially the control of chaotic bubble behavior.