A bubble coalescence model for a solution with a nonionic surfactant and with a small bubble approach velocity was developed, in which the mechanism of how coalescence is hindered by Marangoni stress was quantitatively analyzed. The bubble coalescence time calculated for ethanol-water and MIBC-water systems were in good agreement with experimental data. At low surfactant concentrations, the Marangoni stress and bubble coalescence time increased with bulk concentration increase. Conversely, in the high concentration range, the Marangoni stress and coalescence time decreased with bulk concentration. Numerical results showed that the nonlinear relationship between coalescence time and surfactant concentration is determined by the mass transport flux between the film and its interface, which tends to diminish the spatial concentration variation of the interface, i.e., it acts as a “damper”. This damping effect increases with increased surfactant concentration, therefore decreasing the coalescence time at high concentrations.

To account for the effect of liquid viscosity, the bubble breakup model considering turbulent eddy collision based on the inertial subrange turbulent spectrum was extended to the entire turbulent spectrum that included the energy-containing, inertial, and energy-dissipation subranges. The computational fluid dynamics-population balance model (CFD-PBM) coupled model was modified to include this extended bubble breakup model for simulations of a bubble column. The effect of turbulent energy spectrum on the bubble breakup and hydrodynamic behaviors was studied in a bubble column under different liquid viscosities. The results showed that when the liquid viscosity was < 80 mPas, the bubble breakup and hydrodynamics were almost independent on the turbulent spectrum. At liquid viscosity > 80 mPas, the bubble breakup rate and gas holdup were significantly under-predicted when the inertial turbulent spectrum was used, and when using the entire turbulent spectrum the predictions were more consistent with experimental data.