From single-bubble theory to macroscopic mass transfer coefficients in polydisperse bubbly flows

Abstract We develop an analytical approach that bridges single-bubble mass-transfer models and macroscopic transfer coefficients in gas–liquid systems with polydisperse bubble populations. Bubble radii and slip velocities are represented by probability density functions, and representative separable and conditional closures are developed for their joint statistics. Starting from representative Sherwood-type correlations, we derive closed-form expressions for the mean interfacial mass flux, the liquid-side mass-transfer coefficient K₋ K L, and the volumetric coefficient K₋a K L a in terms of gas holdup and the parameters of the adopted distributions. The analysis clarifies when replacing the full bubble population by a single characteristic diameter can bias the predicted transfer coefficients and identifies regimes in which turbulence weakens the direct dependence of K₋ K L on bubble size. The proposed formulation provides a transparent route from mesoscopic bubble-population statistics to macroscopic transfer characteristics and can serve as a theoretical basis for future calibration against bubble-resolved experiments and computer-vision data.