Nonlinear correlation of bubble departures from two adjacent needles during chaotic fluctuations in the gas supply systems.

In the present paper, the chaotic nature and synchronization of the bubble departure process were investigated. In the experiment, gas bubbles were generated from twin needles submerged in water. During the experiment, the time series of pressure fluctuations in the gas supply systems and of liquid movement into the needles were recorded. Time series were analyzed using Fast Fourier Transform (FFT) and Cross Recurrence Quantification Analysis (CRQA). The CRQA included representative cross recurrence plots, temporal evolution of recurrence measures, distribution analysis, and non-parametric statistical comparisons between the investigated airflow conditions. It was shown that the FFT method cannot always be used as a measure of synchronization of bubble departure from twin needles, but it can help estimate it when combined with parameters obtained from the CRQA method. Among the investigated recurrence measures, Determinism and Longest Diagonal Line provided the strongest discrimination between operating conditions, whereas Laminarity and Longest Vertical Line supplied complementary information on laminar behavior and intermittent dynamics. The robustness of the proposed methodology was further confirmed through a sensitivity analysis of the phase-space reconstruction parameters. Overall, the results demonstrate that CRQA provides complementary information to conventional frequency analysis by revealing changes in nonlinear coupling and trajectory coherence that cannot be inferred from bubble departure frequencies alone.