Bubble-Size distributions and flow fields in bubble columns
Abstract
Abstract Bubble‐size distributions and flow fields in bubble columns are calculated numerically. The population balance is simplified and reduced to a balance equation for the average bubble volume. Models developed predict the rate of bubble breakup and coalescence based on physical principles. The flow fields are numerically calculated for bubble columns with cylindrical cross sections using the Euler‐Euler method. The newly derived balance equations for the average bubble volumes are implemented into a commercial CFD code. The solutions of the balance equation for high superficial gas velocities result mainly in two fractions: one for the fraction with small and the other for the fraction with large bubble diameters. Both are considered pseudocontinuous phases, in addition to the liquid phase. The calculated flow fields are characterized by several large‐scale vortices. The local volume fractions of gas and liquid are locally inhomogeneous and highly time‐dependent. The time‐averaged flow field is axisymmetric and stationary. The calculated volume fractions, velocities, and bubble‐size distributions agree well with existing and previously published experimental results for bubble columns up to 0.3 m in diameter.
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An advantage of the model of Lehr et al. [276] is that for small bubbles a breakage in two bubbles of equal size has the highest probability, while an unequal size breakage has a higher probability if the size of the bubbles increases.
“An advantage of the model of Lehr et al. [276] is that in the case of small bubbles a breakage in two bubbles of equal size has the highest probability, while an unequal size breakage has a higher probability if the size of the bubbles increases.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] based their breakage model on a mechanism where bubbles deform due to turbulent flow, become stretched, neck, and break, with assumptions that break-up is due to collision of eddies of different sizes with a bubble, only binary break-up is considered, break-up is determined by balance between interphase forces and inertial forces of the eddy, and only eddies smaller than the
“Lehr et al. [276] based their breakage model on the following mechanism of the bubble rupture. First, bubbles deform due to the action of the turbulent flow field. Subsequently, they become stretched in one direction, leading to necking in the shape, and finally, bubbles break. The assumptions used to develop the break-up kernel are that the break-up of bubbles in a turbulent flow field is due to”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] assume that eddies with bigger sizes only transport bubbles and eddies with smaller sizes do not have sufficient energy to affect bubble motion.
“It is assumed that eddies with bigger sizes only transport bubbles and eddies with smaller sizes do not have sufficient energy to affect bubble motion.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] consider coalescence of more than two bubbles at the same time as a time series of subsequent binary coalescence events.
“Lehr et al. [276] consider the coalescence of more than two bubbles at the same time as a time series of subsequent binary coalescence events.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] assume that collisions arise due to turbulent fluctuations and from the difference in rising velocity of bubbles of different sizes.
“Collisions are assumed to arise due to turbulent fluctuations and from the difference in the rising velocity of bubbles of different sizes.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] assume that coalescence of bubbles occurs in three steps: bubbles collide retaining liquid, liquid drains to a final critical thickness, and coalescence occurs once the final thickness is attained; if contact time is not sufficiently long, coalescence does not occur and bubbles bounce back.
“They assume that the coalescence of bubbles occurs in three steps. First, bubbles collide retaining a small amount of liquid between them. Second, the liquid drains until a final critical liquid thickness is reached. Third, coalescence occurs once the final liquid thickness is attained. If the contact time is not sufficiently long, coalescence does not occur and bubbles bounce back.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Lehr et al. [276] experimentally determined the critical velocity to be ucrit = 0.08 m/s for air-water systems.
“The authors experimentally determined the critical velocity to be ucrit = 0.08 m/s for air-water systems.”
From Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review (2022) · cites this paper as [276]
Cites
Leal, L. G. (1979) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(79)90021-1 · Cited by 5,328 · see citing works
Mathematical Modeling of Two-Phase Flow
Drew, D. A. (1983) · Annual Review of Fluid Mechanics · doi:10.1146/annurev.fl.15.010183.001401 · Cited by 1,472 · see citing works
Theoretical model for drop and bubble breakup in turbulent dispersions
Luo, H., & Svendsen, H. F. (1996) · AIChE Journal · doi:10.1002/aic.690420505 · Cited by 1,250 · see citing works
Bubble coalescence and break-up in air-sparged bubble columns
Prince, M. J., & Blanch, H. W. (1990) · AIChE Journal · doi:10.1002/aic.690361004 · Cited by 1,238 · see citing works
Howarth, L. (1963) · Physics Bulletin · doi:10.1088/0031-9112/14/9/009 · Cited by 708 · see citing works
Chesters, A. A. (1991) · TU/e Research Portal · Cited by 572 · see citing works
Momentum and heat transfer in two-phase bubble flow—I. Theory
Yoshifusa, S. A. T. O., SADATOMI, M., & SEKOGUCHI, K. (1981) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(81)90003-3 · Cited by 554 · see citing works
Hills, J. H. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)85172-8 · Cited by 533 · see citing works
Foundation of the interfacial area transport equation and its closure relations
Kocamustafaogullari, G., & Ishii, M. (1995) · International Journal of Heat and Mass Transfer · doi:10.1016/0017-9310(94)00183-v · Cited by 503 · see citing works
MARTÍNEZ-BAZÁN, C., MONTAÑÉS, J. L., & LASHERAS, J. C. (1999) · Journal of Fluid Mechanics · doi:10.1017/s0022112099006680 · Cited by 476 · see citing works
Bubble Wake Dynamics in Liquids and Liquid–Solid Suspensions
(1990) · Elsevier eBooks · doi:10.1016/c2009-0-24002-5 · Cited by 347 · see citing works
Multiphase reactors – revisited
Duduković, M. P., Larachi, F., & Mills, P. L. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(98)00367-4 · Cited by 331 · see citing works
Flow structure in a three‐dimensional bubble column and three‐phase fluidized bed
Chen, R. C., Reese, J., & Fan, L. (1994) · AIChE Journal · doi:10.1002/aic.690400702 · Cited by 325 · see citing works
Pfleger, D., Gomes, S., Gilbert, N., & Wagner, H.-G. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00261-4 · Cited by 313 · see citing works
Dynamic numerical simulation of gas-liquid two-phase flows Euler/Euler versus Euler/Lagrange
Sokolichin, A., Eigenberger, G., Lapin, A., & Lübert, A. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(96)00425-3 · Cited by 292 · see citing works
Sokolichin, A., & Eigenberger, G. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(98)00420-5 · Cited by 270 · see citing works
Modeling of Vertical Bubble-Driven Flows
Jakobsen, H. A., Sannæs, B. H., Grevskott, S., & Svendsen, H. F. (1997) · Industrial & Engineering Chemistry Research · doi:10.1021/ie970276o · Cited by 262 · see citing works
Radial Nonuniformity of Velocity and Voidage in a Bubble Column
Hills, J. H. (1974) · Cited by 231 · see citing works
Gas-liquid-solid fluidization engineering
Homsy, G. M. (1990) · International Journal of Multiphase Flow · doi:10.1016/0301-9322(90)90047-m · Cited by 230 · see citing works
Experimental study of gas‐induced liquid‐flow structures in bubble columns
Degaleesan, S., Duduković, M. P., & Pan, Y. (2001) · AIChE Journal · doi:10.1002/aic.690470904 · Cited by 225 · see citing works
Numerical simulation of gas–liquid dynamics in cylindrical bubble column reactors
Sanyal, J., Vasquez, S. A., Roy, S., et al. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00235-3 · Cited by 215 · see citing works
Breakage and Coalescence in Dispersed Phase Systems
Valentas, K. J., & Amundson, N. R. (1966) · Industrial & Engineering Chemistry Fundamentals · doi:10.1021/i160020a018 · Cited by 212 · see citing works
Development of a k-ε Model for Bubbly Two-Phase Flow
de Bertodano, M. L., Lahey, R. T., & Jones, O. C., Jr. (1994) · Journal of Fluids Engineering · doi:10.1115/1.2910220 · Cited by 210 · see citing works
Two- and three-dimensional simulations of a bubble plume using a two-fluid model
Mudde, R. F., & Simonin, O. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00234-1 · Cited by 185 · see citing works
Krishna, R., Urseanu, M. I., van Baten, J. M., et al. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00211-0 · Cited by 182 · see citing works
Liquid velocity field in a bubble column: LDA experiments
Mudde, R. F., Groen, J. S., & den Akker, H. E. A. V. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(97)88935-x · Cited by 181 · see citing works
BUBBLE BREAKUP AND COALESCENCE IN TURBULENT GAS-LIQUID DISPERSIONS
Lee, C.-H., Erickson, L. E., & Glasgow, L. A. (1987) · Chemical Engineering Communications · doi:10.1080/00986448708911986 · Cited by 178 · see citing works
Experimental study on interfacial area transport in bubbly two-phase flows
Hibiki, T., & Ishii, M. (1999) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(99)00014-9 · Cited by 161 · see citing works
Bubble breakage in pipeline flow
Hesketh, R. P., Etchells, A. W., & Russell, T. W. F. (1991) · Chemical Engineering Science · doi:10.1016/0009-2509(91)80110-k · Cited by 149 · see citing works
Bubble break-up in gas—liquid bioreactors: Break-up in turbulent flows
Walter, J. F., & Blanch, H. W. (1986) · The Chemical Engineering Journal · doi:10.1016/0300-9467(86)85011-0 · Cited by 145 · see citing works
Computational Fluid Dynamics Applied To Chemical Reaction Engineering
Kuipers, J. A. M., & Swaaij, W. P. M. V. (1998) · Advances in chemical engineering · doi:10.1016/s0065-2377(08)60094-0 · Cited by 144 · see citing works
Borchers, O., Busch, C., Sokolichin, A., & Eigenberger, G. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00181-5 · Cited by 142 · see citing works
Modelling of slurry reactors. A fundamental approach
Torvik, R., & Svendsen, H. F. (1990) · Chemical Engineering Science · doi:10.1016/0009-2509(90)80112-r · Cited by 135 · see citing works
Experimental and numerical studies of the hydrodynamics in a bubble column
Laı́n, S., Bröder, D., & Sommerfeld, M. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00212-2 · Cited by 135 · see citing works
Krishna, R., van Baten, J. M., & Urseanu, M. I. (2000) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00582-5 · Cited by 133 · see citing works
A three-dimensional CFD model for gas–liquid bubble columns
Delnoij, E., Kuipers, J. A. M., & Swaaij, W. P. M. V. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(98)00362-5 · Cited by 129 · see citing works
Dynamic simulation of bubbly flow in bubble columns
Pan, Y., Duduković, M. P., & Chang, M. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(98)00453-9 · Cited by 116 · see citing works
Numerical investigation of gas‐driven flow in 2‐D bubble columns
Pan, Y., Duduković, M. P., & Chang, M. (2000) · AIChE Journal · doi:10.1002/aic.690460303 · Cited by 112 · see citing works
Physical aspects and scale-up of high pressure bubble columns
Wilkinson, P. M. (1991) · University of Groningen research database (University of Groningen / Centre for Information Technology) · Cited by 98 · see citing works
Interfacial area density in bubbly flow
Millies, M., & Mewes, D. (1999) · Chemical Engineering and Processing - Process Intensification · doi:10.1016/s0255-2701(99)00022-7 · Cited by 94 · see citing works
Self-citationChaotic flow in bubble column reactors
Devanathan, N., Duduković, M. P., Lapin, A., & Lübbert, A. (1995) · Chemical Engineering Science · doi:10.1016/0009-2509(95)00070-l · Cited by 92 · see citing works
Investigations and modelling of bubble columns
Grienberger, J., & Hofmann, H. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)87037-q · Cited by 87 · see citing works
The influence of gas density and liquid properties on bubble breakup
Wilkinson, P. M., Schayk, A. V., Spronken, J. P. M., et al. (1993) · Chemical Engineering Science · doi:10.1016/0009-2509(93)81003-e · Cited by 86 · see citing works
Interfacial area concentration in steady fully-developed bubbly flow
Hibiki, T., & Ishii, M. (2001) · International Journal of Heat and Mass Transfer · doi:10.1016/s0017-9310(00)00365-3 · Cited by 84 · see citing works
CFD simulation of bubble column reactors: importance of drag force formulation
Thakre, S. S., & Joshi, J. B. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00232-8 · Cited by 72 · see citing works
Optimization of affinity and ion-exchange chromatographic processes for the purification of proteins
Mao, Q., & Hearn, M. T. W. (2000) · Biotechnology and Bioengineering · doi:10.1002/(sici)1097-0290(19961020)52:2 · Cited by 36 · see citing works
Webb, C., Que, F., & Senior, P. R. (1992) · Chemical Engineering Science · doi:10.1016/0009-2509(92)85039-e · Cited by 32 · see citing works
Liquid circulation in columns due to bubble drift
Millies, M., & Mewes, D. (1992) · Chemical Engineering & Technology · doi:10.1002/ceat.270150408 · Cited by 4 · see citing works
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A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow
Wang, T., Wang, J., & Jin, Y. (2003) · Chemical Engineering Science · doi:10.1016/j.ces.2003.07.009 · Cited by 260 · see citing works
Two-Phase Bubble Columns: A Comprehensive Review
Besagni, G., Inzoli, F., & Ziegenhein, T. (2018) · ChemEngineering · doi:10.3390/chemengineering2020013 · Cited by 190 · see citing works
Theoretical prediction of flow regime transition in bubble columns by the population balance model
Wang, T., Wang, J., & Jin, Y. (2005) · Chemical Engineering Science · doi:10.1016/j.ces.2005.04.027 · Cited by 141 · see citing works
Modelling of a RDC using a combined CFD-population balance approach
Vikhansky, A., & Kraft, M. (2004) · Chemical Engineering Science · doi:10.1016/j.ces.2004.02.016 · Cited by 59 · see citing works
Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review
Luzi, G., & McHardy, C. (2022) · Energies · doi:10.3390/en15113966 · Cited by 44 · see citing works
Coalescence and Break-Up in Bubble Columns: Euler-Lagrange Simulations Using a Stochastic Approach
Gruber, M. C., Radl, S., & Khinast, J. G. (2013) · Chemie Ingenieur Technik · doi:10.1002/cite.201300024 · Cited by 18 · see citing works
- Authors
- Lehr, F., Millies, M., & Mewes, D.
- Affiliations
- Leibniz University Hannover (DE)
- Corresponding author
- Mewes, D.
- ORCID
- Mewes, D.
- Venue
- AIChE Journal
- Publisher
- Wiley
- Published
- 2002-11
- Volume
- 48
- Issue
- 11
- Pages
- 2426-2443
- ISSN
- 0001-1541 (ISSN-L)
- 1547-5905
- OpenAlex
- W2166225626
- Cited by
- 567
- References
- 48
- Citations by year
- 2026: 34 · 2025: 49 · 2024: 42 · 2023: 43 · 2022: 27 · 2021: 49 · 2020: 33 · 2019: 42 · 2018: 31 · 2017: 21 · 2016: 30 · 2015: 17 · 2014: 21 · 2013: 18 · 2012: 14
- FWCI
- 6.22
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- AIChE Journal (publishedVersion)
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Fluid Dynamics and Mixing
- Physical Sciences › Environmental Science › Water Science and Technology › Minerals Flotation and Separation Techniques
- Physical Sciences › Engineering › Computational Mechanics › Granular flow and fluidized beds
- Keywords
- bubble column, bubble size distribution, bubble breakup, bubble coalescence, population balance, Euler-Eulerian two-phase model, large-scale vortices, void fraction, superficial gas velocity
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