Greek letter
drop breakup frequency, 1/s
the interfacial energy increase before and after drop breakup, J
the maximum interfacial energy increase during the drop breakup, J
the increase in viscous energy during the drop breakup process, J
the number of the broken drops
turbulent energy dissipation rate, m2/s3
eddy size, m
μd dispersed phase viscosity, Pa s
continuous phase density, kg/m3
dispersed phase density, kg/m3
σ interfacial tension, N/m
dispersed phase volume fraction
collision frequency between eddies and drops, 1/(m4s)
the size ratio between an eddy and a droplet

Reference

1. Maaß S, Kraume M. Determination of breakage rates using single drop experiments. Chem Eng Sci . 2012;70:146-164.
2. Solsvik J, Jakobsen HA. Single drop breakup experiments in stirred liquid–liquid tank. Chem Eng Sci . 2015;131:219-234.
3. Ashar M, Arlov D, Carlsson F, Innings F, Andersson R. Single droplet breakup in a rotor-stator mixer. Chem Eng Sci . 2018;181:186-198.
4. Herø EH, La Forgia N, Solsvik J, Jakobsen HA. Single drop breakage in turbulent flow: Statistical data analysis. Chem Eng Sci X . 2020;8:100082.
5. Vankova N, Tcholakova S, Denkov ND, Vulchev VD, Danner T. Emulsification in turbulent flow: 2. Breakage rate constants. J Colloid Interface Sci . 2007;313(2):612-629.
6. Andersson R, Andersson B. On the breakup of fluid particles in turbulent flows. AIChE J . 2006;52(6):2020-2030.
7. Galinat S, Masbernat O, Guiraud P, Dalmazzone C, Noı¨k C. Drop break-up in turbulent pipe flow downstream of a restriction. Chem Eng Sci . 2005;60(23):6511-6528.
8. Zhou H, Yu X, Jing S, Zhou H, Lan W, Li S. Measurement of droplet breakage in a pump-mixer. Chem Eng Sci . 2019;195:23-38.
9. Zhou H, Jing S, Yu X, Zhou H, Lan W, Li S. Study of droplet breakage in a pulsed disc and doughnut column-Part I: Experiments and correlations. Chem Eng Sci . 2019;197:172-183.
10. Zhou H, Yang J, Jing S, Lan W, Zheng Q, Li S. Influence of Dispersed-Phase Viscosity on Droplet Breakup in a Continuous Pump-Mixer.Ind Eng Chem Res . 2019;58(51):23458-23467.
11. Liu H, Jing S, Fang Q, Li S. Droplet Breakup in a Square-Sectioned Pulsed Disc and Doughnut Column. Ind Eng Chem Res . 2016;55(7):2242-2251.
12. Fang Q, Jing D, Zhou H, Li S. Population balance of droplets in a pulsed disc and doughnut column with wettable internals. Chem Eng Sci . 2017;161:274-287.
13. Zhou H, Yu X, Wang B, Jing S, Lan W, Li S. Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank.AIChE J . 2021;67(1):e17065.
14. Tsouris C, Tavlarides LL. Breakage and coalescence models for drops in turbulent dispersions. AIChE J . 1994;40(3):395-406.
15. Luo H, Svendsen HF. Theoretical model for drop and bubble breakup in turbulent dispersions. AIChE J . 1996;42(5):1225-1233.
16. Wang T, Wang J, Jin Y. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow. Chem Eng Sci . 2003;58(20):4629-4637.
17. Zhao H, Ge W. A theoretical bubble breakup model for slurry beds or three-phase fluidized beds under high pressure. Chem Eng Sci . 2007;62(1):109-115.
18. Coulaloglou CA, Tavlarides LL. Description of interaction processes in agitated liquid-liquid dispersions. Chem Eng Sci . 1977;32(11):1289-1297.
19. Han L, Luo H, Liu Y. A theoretical model for droplet breakup in turbulent dispersions. Chem Eng Sci . 2011;66(4):766-776.
20. Solsvik J, Skjervold VT, Han L, Luo H, Jakobsen HA. A theoretical study on drop breakup modeling in turbulent flows: The inertial subrange versus the entire spectrum of isotropic turbulence. Chem Eng Sci . 2016;149:249-265.
21. Zhou H, Jing S, Fang Q, Li S, Lan W. Direct measurement of droplet breakage in a pulsed disc and doughnut column. AIChE J . 2017;63(9):4188-4200.
22. Wang B, Zhou H, Yu X, et al. Determination of dynamic interfacial tension in a pulsed column under mass transfer condition. AIChE J . 2020;66(8):e16257.
23. Prince MJ, Blanch HW. Bubble coalescence and break‐up in air‐sparged bubble columns. AIChE J . 1990;36(10):1485-1499.
24. Zhou H, Yu X, Wang B, Jing S, Lan W, Li S. Modeling study on drop breakup time in turbulent dispersions. Chem Eng Sci . 2021;238:116599.
25. Kolmogorov AN. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Cr Acad Sci URSS . 1941;30:301-305.
26. Brodkey RS. The Phenomena of Fluid Motions . Courier Corporation; 1995.
27. Sreenivasan KR. On the scaling of the turbulence energy dissipation rate. Phys Fluids . 1984;27(5):1048-1051.
28. Batchelor GK. The Theory of Homogeneous Turbulence . Cambridge University Press; 1956.
29. Hesketh RP, Etchells AW, Russell TWF. Experimental observations of bubble breakage in turbulent flow. Ind Eng Chem Res . 1991;30(5):835-841.
30. Andersson R, Helmi A. Computational fluid dynamics simulation of fluid particle fragmentation in turbulent flows. Appl Math Model . 2014;38(17):4186-4196.
31. Bouaifi M, Mortensen M, Andersson R, et al. Experimental and Numerical Investigations of a Jet Mixing in a Multifunctional Channel Reactor: Passive and Reactive Systems. Chem Eng Res Des . 2004;82(2):274-283.
32. Maaß S, Gäbler A, Zaccone A, Paschedag AR, Kraume M. Experimental Investigations and Modelling of Breakage Phenomena in Stirred Liquid/Liquid Systems. Chem Eng Res Des . 2007;85(5):703-709.
33. Placek J, Tavlarides LL, Smith GW, Fořt I. Turbulent flow in stirred tanks. Part II: A two-scale model of turbulence. AIChE J . 1986;32(11):1771-1786.
34. Placek J, Tavlarides LL. Turbulent flow in stirred tanks. Part I: Turbulent flow in the turbine impeller region. AIChE J . 1985;31(7):1113-1120.
35. Karimi M, Andersson R. An exploratory study on fluid particles breakup rate models for the entire spectrum of turbulent energy.Chem Eng Sci . 2018;192:850-863.
36. Lehr F, Millies M, Mewes D. Bubble-Size distributions and flow fields in bubble columns. AIChE J . 2002;48(11):2426-2443.
37. Hert SCD, Rodgers TL. On the steady-state drop size distribution in stirred vessels. Part I: Effect of dispersed phase viscosity.AIChE J . 2018;64(9):3293-3302.