Measurement of multifractal character of bubble paths using image analysis

Abstract

The trajectory of the virtual mass centers of sequentially departing gas bubbles in water flow has been analyzed in this study. The bubbles were generated from a brass nozzle of 1 mm inner diameter in a glass tank (300 × 150 × 500 mm3), filled with distilled water maintained at 21 ± 1 °C. A three-mirror system was used to obtain two frames of the workspace in a single shot of a Phantom v1610 high-speed camera. A three-dimensional computer reconstruction algorithm was developed, which consisted of a blur filter, canny edge filter, region of interest (ROI), and Kalman filter. This algorithm was used to obtain the coordinates of the center of mass of each individual gas bubble. We analyzed the bubble trajectories obtained for three different air volumetric flow rates. A multifractal analysis was used to evaluate the gas bubble dynamics. The wavelet transform modulus maxima method was used to obtain the singularity spectra of the bubble paths. The local Hölder exponent value proved that the gas bubble motion trajectories tended to behave in a deterministic and chaotic manner. In addition, the sensitivity of the chaotic bubble paths to small- and large-scale fluctuations of the lateral bubble displacement was investigated. In conclusion, the proposed approach allows us to distinguish between deterministic chaotic dynamics and the stochastic evolution of bubble paths.