A numerical study of prediction method for terminal velocity of rising microbubbles in quiescent liquid by simplified rear stagnant cap model

Abstract A simplified rear stagnant cap model is employed to analyze the effect of contaminants on terminal velocity of microbubbles rising in quiescent liquid. A dataset of the terminal velocity of microbubbles rising in liquids is collected to validate the numerical method and evaluate the Hadamard‐Rybczynski (H–R) correlation and Stokes' law. Both the experimental data and numerical results indicate the inescapable effects from inertia and contaminants. The numerical results show that a steep fall in surface tangential velocity ahead of the stagnant cap results in a sharp increase in local pressure and the increase of the drag acting on a rising contaminated bubble. The evaluation work proved the rationality of the Sadhal–Johnson correlation, which realizes a quantitative prediction of the drag coefficients for contaminated microbubbles. Inclusive of both the contamination and inertia effects, prediction correlations of the upper and lower thresholds for normalization in the Sadhal–Johnson correlation are replaced by the Schiller–Naumann correlation and Mei et al. correlation, extending its application range from < 1 to < 100, applicable of predicting terminal rising velocities of microbubbles with maximum diameter around hundreds of microns.