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An improved model for low viscous droplet breakage has been developed. Unlike the previous work that considered the inertia subrange and adopted the assumption of binary breakage, this work considered the breakage of droplets in the framework of the multiple fragments and the wide energy spectrum (i.e., including the dissipation range, the inertia subrange, and the energy containing range simultaneously). The previous interactions between the droplet and the surrounding fluids have been considered through introducing the interaction forces. The effect of the surface deformation and oscillation resulting from these interactions on the constraints of multiple breakages has been accounted for. These factors have been neglected in the existing models. The wide energy spectrum distribution was found to have an important effect on the nonmonotone evolution of breakage frequency with increasing parent droplet size. The cumulative volume fractions predicted by this work showed a better agreement with the experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2147–2168, 2015

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An unsteady-state model for predicting mass-transfer coefficient k L of bubbles with mobile surface was developed for turbulent gas-liquid dispersions. This model was derived from an unsteady-state convection and diffusion equation through a characteristics method. Unlike the previous work, this model considered the contributions of the amount of fluid structures of different scales (i.e., eddies) existing in the turbulent flows, the frequency of eddies arriving at the surface, the deformation and oscillation of bubbles to mass transfer. This model was based on the framework of wide energy spectrum and can account for the role of eddies of different sizes in mass transfer. Thus the assumption adopted by the previous models that mass transfer was controlled by eddies of certain sizes is no more needed. The overall k L predicted by the proposed model showed a better agreement with the reported experimental data. Derivation of liquid-side mass-transfer coefficientAccording to the points of (1) and (3) mentioned above, the convection-diffusion equation for the solute concentration in the thin concentration layer close to surface can take the form of à c is the dimensionless distance. It can be seen from Figure 5a that this distance increases with the increasing s. Nevertheless, our calculations indicate that y c will not be changed obviously when s > 1.0 under the action of the convections of eddies, which are responsible to sweep the surface and remove the solute-enriched liquid to the bulk fluid. As shown in Figure 5b, the turbulent dissipation rate e, the diffusion coefficient D and the size of eddy k affect the solute concentration distribution Figure 4. The variation of R L with f min .

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