Mathematical Modeling of Turbulent Gas–Liquid Mass Transfer Accounting for Bubble Dynamics

A physics-based mathematical model is developed for interfacial mass transfer in turbulent gas–liquid media. The formulation derives characteristic bubble-scale quantities governing the volumetric mass-transfer coefficient kLa from the bubble response to turbulent velocity fluctuations. Bubble translation is described by a reduced equation of motion that retains the added-mass contribution and quasi-steady drag. Kolmogorov-type estimates are used to characterize turbulent fluctuations, and the fluctuation length governing the mean bubble–liquid slip velocity is selected by maximizing the bubble response. A characteristic bubble diameter is estimated from a turbulent–capillary balance, while the liquid-side coefficient is evaluated using a Higbie-based finite-exposure formulation, with the characteristic exposure time related to the bubble diameter and the critical slip velocity. The resulting analytical relation expresses kLa in terms of gas holdup, molecular diffusivity, drag coefficient, liquid density, surface tension, turbulent energy dissipation rate, and a bubble-size factor. In its bubble-size-based form, the model predicts the scaling kLa∝ε7/10, providing a mechanistic interpretation of the approximately 0.7 power-input exponent encountered in established empirical correlations. Consistency is assessed through comparison with representative literature correlations. The same analytical relation is additionally evaluated using hydrodynamic quantities supplied by an illustrative CFD calculation, demonstrating how spatially non-uniform flow information can be converted into distributed mass-transfer estimates. The proposed formulation provides a compact and physically interpretable route from bubble-scale dynamics to apparatus-scale mass-transfer prediction in gas–liquid contactors, bioreactors, and related non-equilibrium dispersed systems.