15. Kuschel M, Siebler F, Takors R (2017) Lagrangian trajectories to predict the formation of
population heterogeneity in large-scale bioreactors. Bioengineering 4(4):27. https://doi.org/10.
3390/bioengineering4020027
16. Wang G, Haringa C, Tang W, Noorman H, Chu J, Zhuang Y, Zhang S (2020) Coupled
metabolic-hydrodynamic modeling enabling rational scale-up of industrial bioprocesses.
Biotechnol Bioeng 117(3):844–867. https://doi.org/10.1002/bit.27243
17. Nieß A, Löffler M, Simen JD, Takors R (2017) Repetitive short-term stimuli imposed in poor
mixing zones induce long-term adaptation of E. Coli cultures in large-scale bioreactors:
experimental evidence and mathematical model. Front Microbiol 8(Jun):1–9. https://doi.org/
10.3389/fmicb.2017.01195
18. Zieringer J, Takors R (2020) Data-driven in-silico prediction of regulation heterogeneity and
ATP demands of Escherichia coli in large-scale bioreactors
19. Morchain J, Gabelle JC, Cockx A (2014) A coupled population balance model and CFD
approach for the simulation of mixing issues in lab-scale and industrial bioreactors. AICHE J
60(1):27–40. https://doi.org/10.1002/aic.14238
20. Morchain J, Pigou M, Lebaz N (2017) A population balance model for bioreactors combining
interdivision time distributions and micromixing concepts. Biochem Eng J 126:135–145.
https://doi.org/10.1016/j.bej.2016.09.005
21. Pigou M, Morchain JÔ (2015) Investigating the interactions between physical and biological
heterogeneities in bioreactors using compartment, population balance and metabolic models.
Chem Eng Sci 126(April):267–282. https://doi.org/10.1016/j.ces.2014.11.035
22. Haringa C, Tang W, Wang G, Deshmukh AT, van Winden WA, Chu J, van Gulik WM, Heijnen
JJ, Mudde RF, Noorman HJ (2018b) Computational fluid dynamics simulation of an industrial
P. chrysogenum fermentation with a coupled 9-pool metabolic model: towards rational scaledown and design optimization. Chem Eng Sci 175:12–24. https://doi.org/10.1016/j.ces.2017.
09.020
23. Haringa C, Vandewijer R, Mudde RF (2018c) Inter-compartment interaction in multi-impeller
mixing: part i. experiments and multiple reference frame CFD. Chem Eng Res Des 136
(June):870–885. https://doi.org/10.1016/j.cherd.2018.06.005
24. Haringa C, Vandewijer R, Mudde RF (2018d) Inter-compartment interaction in multi-impeller
mixing. Part ii. Experiments, sliding mesh and large eddy simulations. Chem Eng Res Des 136
(June):886–899. https://doi.org/10.1016/j.cherd.2018.06.007
25. Siebler F, Lapin A, Hermann M, Takors R (2019) The impact of CO gradients on C. ljungdahlii
in a 125 m3 bubble column: mass transfer, circulation time and lifeline analysis. Chem Eng Sci
207:410–423. https://doi.org/10.1016/j.ces.2019.06.018
26. Kuschel M, Takors R (2020) Simulated oxygen and glucose gradients as a prerequisite for
predicting industrial scale performance a priori
27. Heins AL, Fernandes RL, Gernaey KV, Lantz AE (2015) Experimental and in silico investigation of population heterogeneity in continuous Saccharomyces cerevisiae scale-down fermentation in a two-compartment setup. J Chem Technol Biotechnol 90(2):324–340. https://doi.org/
10.1002/jctb.4532
28. Wang T, Wang J, Jin Y (2005) Population balance model for gas - liquid flows: influence of
bubble coalescence and breakup models. Ind Eng Chem Res 44(19):7540–7549. https://doi.org/
10.1021/ie0489002
29. Venneker BCH, Derksen JJ, Van den Akker HEA (2002) Population balance modeling of
aerated stirred vessels based on CFD. AICHE J 48(4):673–685. https://doi.org/10.1002/aic.
690480404
30. Lapin A, Schmid J, Reuss M (2006) Modeling the dynamics of E. coli populations in the threedimensional turbulent field of a stirred-tank bioreactor-A structured-segregated approach. Chem
Eng Sci 61(14):4783–4797. https://doi.org/10.1016/j.ces.2006.03.003
31. Dehbi A (2008) A CFD model for particle dispersion in turbulent boundary layer flows. Nucl
Eng Des 238(3):707–715. https://doi.org/10.1016/j.nucengdes.2007.02.055
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
251
population heterogeneity in large-scale bioreactors. Bioengineering 4(4):27. https://doi.org/10.
3390/bioengineering4020027
16. Wang G, Haringa C, Tang W, Noorman H, Chu J, Zhuang Y, Zhang S (2020) Coupled
metabolic-hydrodynamic modeling enabling rational scale-up of industrial bioprocesses.
Biotechnol Bioeng 117(3):844–867. https://doi.org/10.1002/bit.27243
17. Nieß A, Löffler M, Simen JD, Takors R (2017) Repetitive short-term stimuli imposed in poor
mixing zones induce long-term adaptation of E. Coli cultures in large-scale bioreactors:
experimental evidence and mathematical model. Front Microbiol 8(Jun):1–9. https://doi.org/
10.3389/fmicb.2017.01195
18. Zieringer J, Takors R (2020) Data-driven in-silico prediction of regulation heterogeneity and
ATP demands of Escherichia coli in large-scale bioreactors
19. Morchain J, Gabelle JC, Cockx A (2014) A coupled population balance model and CFD
approach for the simulation of mixing issues in lab-scale and industrial bioreactors. AICHE J
60(1):27–40. https://doi.org/10.1002/aic.14238
20. Morchain J, Pigou M, Lebaz N (2017) A population balance model for bioreactors combining
interdivision time distributions and micromixing concepts. Biochem Eng J 126:135–145.
https://doi.org/10.1016/j.bej.2016.09.005
21. Pigou M, Morchain JÔ (2015) Investigating the interactions between physical and biological
heterogeneities in bioreactors using compartment, population balance and metabolic models.
Chem Eng Sci 126(April):267–282. https://doi.org/10.1016/j.ces.2014.11.035
22. Haringa C, Tang W, Wang G, Deshmukh AT, van Winden WA, Chu J, van Gulik WM, Heijnen
JJ, Mudde RF, Noorman HJ (2018b) Computational fluid dynamics simulation of an industrial
P. chrysogenum fermentation with a coupled 9-pool metabolic model: towards rational scaledown and design optimization. Chem Eng Sci 175:12–24. https://doi.org/10.1016/j.ces.2017.
09.020
23. Haringa C, Vandewijer R, Mudde RF (2018c) Inter-compartment interaction in multi-impeller
mixing: part i. experiments and multiple reference frame CFD. Chem Eng Res Des 136
(June):870–885. https://doi.org/10.1016/j.cherd.2018.06.005
24. Haringa C, Vandewijer R, Mudde RF (2018d) Inter-compartment interaction in multi-impeller
mixing. Part ii. Experiments, sliding mesh and large eddy simulations. Chem Eng Res Des 136
(June):886–899. https://doi.org/10.1016/j.cherd.2018.06.007
25. Siebler F, Lapin A, Hermann M, Takors R (2019) The impact of CO gradients on C. ljungdahlii
in a 125 m3 bubble column: mass transfer, circulation time and lifeline analysis. Chem Eng Sci
207:410–423. https://doi.org/10.1016/j.ces.2019.06.018
26. Kuschel M, Takors R (2020) Simulated oxygen and glucose gradients as a prerequisite for
predicting industrial scale performance a priori
27. Heins AL, Fernandes RL, Gernaey KV, Lantz AE (2015) Experimental and in silico investigation of population heterogeneity in continuous Saccharomyces cerevisiae scale-down fermentation in a two-compartment setup. J Chem Technol Biotechnol 90(2):324–340. https://doi.org/
10.1002/jctb.4532
28. Wang T, Wang J, Jin Y (2005) Population balance model for gas - liquid flows: influence of
bubble coalescence and breakup models. Ind Eng Chem Res 44(19):7540–7549. https://doi.org/
10.1021/ie0489002
29. Venneker BCH, Derksen JJ, Van den Akker HEA (2002) Population balance modeling of
aerated stirred vessels based on CFD. AICHE J 48(4):673–685. https://doi.org/10.1002/aic.
690480404
30. Lapin A, Schmid J, Reuss M (2006) Modeling the dynamics of E. coli populations in the threedimensional turbulent field of a stirred-tank bioreactor-A structured-segregated approach. Chem
Eng Sci 61(14):4783–4797. https://doi.org/10.1016/j.ces.2006.03.003
31. Dehbi A (2008) A CFD model for particle dispersion in turbulent boundary layer flows. Nucl
Eng Des 238(3):707–715. https://doi.org/10.1016/j.nucengdes.2007.02.055
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
251