Multi-scale Poincare<acute accent> analysis of three-dimensional gas bubble trajectories in liquid

This study presents an investigation of the three-dimensional trajectories of gas bubbles in a liquid medium, utilizing multi-scale Poincare<acute accent> analysis, Lyapunov exponent and dimensionless numbers such as Reynolds, Bond, and Weber. The research was conducted using a glass tank filled with distilled water, where gas bubbles were generated by nozzles of inner diameters equal to 1.1 mm and 1.2 mm, air volume flow rates from: 0.00016 l/min to 0.008 l/min, with a step of 0.00016 l/min. High-speed photography and advanced image processing techniques allowed for precise tracking and reconstruction of the trajectory of the geometric center of each bubble. Multi-scale Poincare<acute accent> plots provided important information on the dynamics of bubble motion at different heights and scales. The results indicated that using larger nozzles and higher airflows led to more stable and predictable bubble trajectories, characterized by more negative Lyapunov exponents and consistent patterns in multi-scale Poincare<acute accent> plots. Notably, the 1.2 mm nozzle operating at higher airflow rates achieved a more uniform distribution of bubbles and reduced chaotic behavior, as opposed to the concentrated and turbulent flow patterns associated with smaller nozzles and lower airflows. The findings emphasize the need for complementary analytical methods to fully capture both global and local dynamics of bubble flows. While Lyapunov exponents provide insights into overall flow stability, the multi-scale Poincare<acute accent> analysis uncovers localized variations, revealing the complexity of interactions within the flow. These combined approaches are crucial for understanding the chaotic transitions and for optimizing industrial processes involving two-phase flow systems.