Interfacial Area Transport Equation for Bubble Coalescence and Breakup: Developments and Comparisons

Bubble coalescence and breakup play important roles in physical-chemical processes and bubbles are treated in two groups in the interfacial area transport equation (IATE). This paper presents a review of IATE for bubble coalescence and breakup to model five bubble interaction mechanisms: bubble coalescence due to random collision, bubble coalescence due to wake entrainment, bubble breakup due to turbulent impact, bubble breakup due to shearing-off, and bubble breakup due to surface instability. In bubble coalescence, bubble size, velocity and collision frequency are dominant. In bubble breakup, the influence of viscous shear, shearing-off, and surface instability are neglected, and their corresponding theory and modelling are rare in the literature. Furthermore, combining turbulent kinetic energy and inertial force together is the best choice for the bubble breakup criterion. The reviewed one-group constitutive models include the one developed by Wu et al., Ishii and Kim, Hibiki and Ishii, Yao and Morel, and Nguyen et al. To extend the IATE prediction capability beyond bubbly flow, two-group IATE is needed and its performance is strongly dependent on the channel size and geometry. Therefore, constitutive models for two-group IATE in a three-type channel (i.e., narrow confined channel, round pipe and relatively larger pipe) are summarized. Although great progress in extending the IATE beyond churn-turbulent flow to churn-annual flow was made, there are still some issues in their modelling and experiments due to the highly distorted interface measurement. Regarded as the challenges to be addressed in the further study, some limitations of IATE general applicability and the directions for future development are highlighted.

An Investigation on the Bubble Breakup Characteristics by Recirculation Flow in a Venturi Channel

Discrete bubbles can be effectively cracked and dispersed in a Venturi channel with its unique structural characteristics, and the general Venturi channel has been widely used in the practical engineering. Bubble breakup mechanisms based on Venturi channels have been extensively studied, but most of them are based on single bubble or bubble flow pattern. In this paper, the transport process of slug flow in a Venturi channel was explored through visualization experiments, and the characteristics of recirculation flow were indicated by numerical simulation method. The liquid velocity sensitively affects the bubble generation process. With the increase of the liquid velocity, the initial bubble is no longer detached from the gas injector hole, and the gas-liquid flow pattern changes from bubbly flow to slug flow. The slug bubble extends to the diverging section and experiences the process of interface instability, sub-bubble detachment and bubble collapse. The average Sauter bubble diameter decreases with the increase of liquid velocity, and the fitting function is Log Normal. There is a recirculation flow in the side wall region of the diverging section, and the area of the recirculation flow increases with the increase of the liquid velocity at the inlet. The numerical simulation results indicated that there is a large velocity gradient in the boundary region of the recirculation flow under slug flow pattern, which contribute to the bubble collapse.

Breakup of bubbles in Advanced-Flow Reactor at low Reynolds numbers

In order to study the behavior and mechanism of the bubble breakup in Advanced-Flow Reactor (AFR), visualization experimental study was carried out in a single Corning G1 module. The results show that the breakup behavior in AFR has a significant regularity at low Reynolds numbers (Re<1000), which is closely related to the capillary number Ca and the virtual length l0 of bubbles, and the criterions is also obtained. Most of bubbles in arc-shaped junction divergence of AFR are breakup with permanent obstruction (POB), which could be divided into two stages: squeezing stage and rapid pinch-off stage. The modified equation obtained in this paper can roughly describe the change of the bubble neck at the squeezing stage of POB. The research results provide a theoretical basis for industrial application of AFR and the development of next-generation reactors.

Influence of Interfacial Force Models and Population Balance Models on the kLa Value in Stirred Bioreactors

Optimal oxygen supply is vitally important for the cultivation of aerobically growing cells, as it has a direct influence on cell growth and product formation. A process engineering parameter directly related to oxygen supply is the volumetric oxygen mass transfer coefficient kLa. It is the influences on kLa and computing time of different interfacial force and population balance models in stirred bioreactors that have been evaluated in this study. For this investigation, the OpenFOAM 7 open-source toolbox was utilized. Firstly, the Euler–Euler model with a constant bubble diameter was applied to a 2L scale bioreactor to statistically examine the influence of different interfacial models on the kLa value. It was shown that the kL model and the constant bubble diameter have the greatest influence on the calculated kLa value. To eliminate the problem of a constant bubble diameter and to take effects such as bubble breakup and coalescence into account, the Euler–Euler model was coupled with population balance models (PBM). For this purpose, four coalescence and five bubble breakup models were examined. Ultimately, it was established that, for all of the models tested, coupling computational fluid dynamics (CFD) with PBM resulted in better agreement with the experimental data than using the Euler–Euler model. However, it should be noted that the higher accuracy of the PBM coupled models requires twice the computation time.

Gas-liquid mass transfer intensification for bubble generation and breakup in micronozzles

The local gas-liquid mass transfer was characterized during bubble generation in T-contactors and in an adjacent micronozzle. A colorimetric technique with the oxygen sensitive dye resazurin was investigated to visualize gas-liquid mass transfer during slug flow, bubble deformation, as well as laminar and turbulent bubble breakup in the wake of a micronozzle. Two optimized nozzle geometries from previous studies were evaluated concerning volumetric mass transfer coefficients for low pressure loss, narrow residence time distribution, or high dispersion rates. Highest values in kla up to 60 s−1 were found for turbulent bubble breakup and an optimized micronozzle design in respect to pressure drop and dispersion rate. The achieved mass transfer coefficients were correlated with the energy dissipation rate within the micronozzles and with the inverse Kolmogorov time scale in vortex dissipation in good agreement for laminar and turbulent breakup regimes. Graphical abstract

A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media

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.