Chaos in bubbling—nonlinear analysis and modelling

Abstract

In the present paper, nonlinear features and analytical results for the chaotic bubbling from a submerged orifice are described. A chain of air bubbles was produced from the single orifice of 2 mm in diameter and micro-convection induced by the bubble generation was recorded using hot-probe anemometer located close to the orifice. The air flow rate was varied widely from q=100 to 2000 cc/ min and the aspects of bubbling were observed by high-speed video. The nonlinear analysis is performed for the time series data of hot-probe anemometer especially in the range of q=435– 1500 cc/ min . The calculated largest Lyapunov exponent shows that with increase of air volume flow rate, the time period for the process of liquid flow to lose stability becomes shorter and at high air flow rate such as q=1500 cc/ min , it is shorter than the time period between subsequent bubbles. To explain such chaotic behaviors of bubbling, a simple model has been proposed. The model simulates the process of interaction between the elastic bubble wall and liquid. Simulation results compared well with the analytical results of experimental data. Summarizing, it is concluded that one of the reasons for chaos appearance is the nonlinear character of interaction between an elastic bubble wall and the liquid stream.