Experimental investigation of single bubbles rising in stagnant liquid: Statistical analysis and image processing

Abstract

Despite the large effort devoted to the study of single bubbles rising in a stagnant liquid, the complex phenomena involved have resulted in a large scatter in the terminal velocity. Providing new experimental data where the statistical uncertainty is thoroughly evaluated is therefore necessary. Single bubble experiments were conducted in a tall vertical column containing stagnant liquid at ambient conditions. To track the bubbles over the spatial range, high-speed cameras were mounted on a linear unit drive. The tall column allowed us to study the effect of hydrostatic pressure and late developed bubble dynamics on the bubble motion. The bubble properties, i.e., the bubble velocity, size, shape, and trajectory, were evaluated using an image analysis processing method. The analysis includes a quantitative evaluation of important parameters involved in the handling of the raw data. Several of the existing correlations for the terminal velocity were validated against the experimental data. The data are well predicted by the correlation proposed by Tomiyama et al. [“Terminal velocity of single bubbles in surface tension force dominant regime,” Int. J. Multiphase Flow 28, 1497–1519 (2002)]. The uncertainty in the experimental data has been emphasized, providing a quantitative evaluation based on several statistical methods. The number of experimental events necessary to obtain statistical significance was evaluated using a 95% confidence interval. Satisfying precision is found to be fulfilled for 10–15 bubble rise events. For bubbles of comparable size, the statistically significant terminal velocity data were found to exhibit a small scatter.