Measurement of properties of chaotic bubble paths

The chaotic properties of bubble paths in bubble chain have been analysed. The bubbles have been generated from a brass cylindrical nozzle with inner diameter equal to 1 mm and placed at the centre of the bottom of rectangular tank (300 × 150 × 500 mm), which was filled with distilled water. Bubble departure diameter was about 5.5 mm. The mirrors system and high speed camera have been used for determining the 3D paths of subsequently departing bubbles. The chaotic changes of bubble path shapes have been observed. Bubble chains obtained for three different air volume flow rates have been analysed. The bubble departure frequencies were adequately 9.4 Hz, 11.6 Hz and 12.7 Hz. The method of Hurst exponent estimation for chaotic bubble paths has been proposed. The Hurst exponent has been calculated for bubble path projections on two orthogonal planes-parallel to the tank walls (shorter and wider). Obtained Hurst exponents confirm that bubble paths have deterministic chaos character. Also, sensitivity of the chaotic bubble paths on initial conditions and the structure of liquid flow around the bubble chain has been discovered. Proposed method allows us to detect anomalies of bubble paths. There has been discovered that predictability of bubble path projection varies depending on the plane which has been chosen for the projection. We can conclude that the method proposed in the paper is suitable for measurement of chaotic bubble path properties.