Dynamic Behavior of Microbial Populations in Stirred Bioreactors Simulated with Euler–Lagrange Methods: Traveling along the Lifelines of Single Cells
Abstract
In the present work, an Euler−Lagrange approach has been applied to characterize the behavior of a heterogeneous cell population in a stirred-tank bioreactor with nonideal mixing. It allows one to describe population behavior as the outcome of the interaction between the intracellular state of its individual cells and the turbulent flow field in the reactor. The modeling approach and the numerical method employed are based on an Euler−Lagrange formulation of the system combined with a fractional-step method to allow for a stable, accurate, and numerically efficient solution of the underlying equations. This strategy permits one to account for the heterogeneity present in real reactors in both the fluid and cellular phases, respectively. Three examples are used to illustrate the application of this approach. The suggested method is easily transferable to similar problems requiring a segregated and high-dimensional description of the internal structure of the corpuscular phase, which usually precludes the application of population balance equations.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Despite its simplicity, the model allows study of the time evolution of a representative population of algae in the fluid flow and to draw conclusions about trapped algae in vortices, the quality of mixing, and the induced shear stress.
“In summary, despite its simplicity, the model allows us to study the time evolution of a representative population of algae in the fluid flow and to draw conclusions about trapped algae in vortices, the quality of mixing, and the induced shear stress [13], respectively.”
From Comprehensive Computational Model for Coupled Fluid Flow, Mass Transfer, and Light Supply in Tubular Photobioreactors Equipped with Glass Sponges (2022) · cites this paper as [13]
Cites
Computational Methods for Fluid Dynamics
Ferziger, J. H., & Perić, M. (2002) · Springer eBooks · doi:10.1007/978-3-642-56026-2 · Cited by 3,904 · see citing works
On the Construction and Comparison of Difference Schemes
Strang, G. (1968) · SIAM Journal on Numerical Analysis · doi:10.1137/0705041 · Cited by 3,616 · see citing works
Numerical Methods for Conservation Laws
LeVeque, R. J. (1990) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-5116-9 · Cited by 795 · 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
Self-citationThe Inventor Mentor: Programming Object-Oriented 3d Graphics With Open Inventor, Release 2
Wernecke, J. (1994) · International Linear Collider · Cited by 272 · see citing works
Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth
von Meyenburg, H. K. (1969) · Archives of Microbiology · doi:10.1007/bf00414585 · Cited by 252 · see citing works
Fractional step methods applied to a chemotaxis model
Tyson, R. C., Stern, L. G., & LeVeque, R. J. (2000) · Journal of Mathematical Biology · doi:10.1007/s002850000038 · Cited by 154 · see citing works
K�enzi, M. T., & Fiechter, A. (1969) · Archives of Microbiology · doi:10.1007/bf00417021 · Cited by 142 · see citing works
Oscillations in continuous cultures of budding yeast: A segregated parameter analysis
Porro, D., Martegani, E., Ranzi, B. M., et al. (1988) · Biotechnology and Bioengineering · doi:10.1002/bit.260320402 · Cited by 121 · see citing works
Costes, J., & Couderc, J. P. (1988) · Chemical Engineering Science · doi:10.1016/0009-2509(88)80018-6 · Cited by 115 · see citing works
Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation
Wolf, J., & Heinrich, R. (2000) · Biochemical Journal · doi:10.1042/bj3450321 · Cited by 114 · see citing works
Jenne, M., & Reuß, M. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00093-7 · Cited by 110 · see citing works
General hybrid multizonal/CFD approach for bioreactor modeling
Bezzo, F., Macchietto, S., & Pantelides, C. C. (2003) · AIChE Journal · doi:10.1002/aic.690490821 · Cited by 110 · see citing works
Bioreaction Engineering: Modeling and Control
Schügerl, K., & Bellgardt, K. ‐. (1987) · Medical Entomology and Zoology · Cited by 106 · see citing works
Strässle, C., Sonnleitner, B., & Fiechter, A. (1988) · Journal of Biotechnology · doi:10.1016/0168-1656(88)90042-9 · Cited by 102 · see citing works
Coupling of mixing and microbial kinetics for evaluating the performance of bioreactors
Bajpai, R. K., & Reuss, M. (1982) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.5450600308 · Cited by 95 · see citing works
Self-citationMünch, T., Sonnleitner, B., & Fiechter, A. (1992) · Journal of Biotechnology · doi:10.1016/0168-1656(92)90150-8 · Cited by 93 · see citing works
Control strategies of continuous bioprocesses based on biological activities
Meyer, C., & Beyeler, W. (1984) · Biotechnology and Bioengineering · doi:10.1002/bit.260260816 · Cited by 83 · see citing works
Integration of Physiology and Fluid Dynamics
Schmalzriedt, S., Jenne, M., Mauch, K., & Reuß, M. (2003) · Advances in biochemical engineering, biotechnology · doi:10.1007/3-540-36782-9_2 · Cited by 79 · see citing works
Cyclic AMP mediates the cell cycle dynamics of energy metabolism in Saccharomyces cerevisiae
Müller, D., Exler, S., Aguilera‐Vázquez, L., Guerrero‐Martín, E., & Reuß, M. (2003) · Yeast · doi:10.1002/yea.967 · Cited by 79 · see citing works
Self-citationA concept for multi-scale modeling of bubble columns and loop reactors
Bauer, M., & Eigenberger, G. (1999) · Chemical Engineering Science · doi:10.1016/s0009-2509(99)00264-x · Cited by 68 · see citing works
Münch, T., Sonnleitner, B., & Fiechter, A. (1992) · Journal of Biotechnology · doi:10.1016/0168-1656(92)90039-c · Cited by 63 · see citing works
Cell population modelling of yeast glycolytic oscillations
Henson, M. A., MÜLLER, D., & Reuß, M. (2002) · Biochemical Journal · doi:10.1042/bj20021051 · Cited by 62 · see citing works
Self-citationA finite representation model for an asynchronous culture of E. coli
Domach, M. M., & Shuler, M. L. (1984) · Biotechnology and Bioengineering · doi:10.1002/bit.260260810 · Cited by 60 · see citing works
Physiology of Saccharomyces cerevisiae during cell cycle oscillations
Duboc, P. (1996) · Journal of Biotechnology · doi:10.1016/0168-1656(96)01566-0 · Cited by 59 · see citing works
Population balance models of autonomous microbial oscillations
Hjortsø, M. A., & NIELSEN, J. K. (1995) · Journal of Biotechnology · doi:10.1016/0168-1656(95)00086-6 · Cited by 52 · see citing works
Oscillatory metabolism of Saccharomyces cerevisiae: an overview of mechanisms and models
Patnaik, P. R. (2003) · Biotechnology Advances · doi:10.1016/s0734-9750(03)00022-3 · Cited by 51 · see citing works
Multiscale modeling of hydrodynamics, mass transfer and reaction in bubble column reactors
Bauer, M., & Eigenberger, G. (2001) · Chemical Engineering Science · doi:10.1016/s0009-2509(00)00323-7 · Cited by 44 · see citing works
Kim, B., & Shuler, M. L. (1990) · Biotechnology and Bioengineering · doi:10.1002/bit.260360605 · Cited by 35 · see citing works
Simulation of the growth pattern of a single cell of Escherichia coli under anaerobic conditions
Ataai, M. M., & Shuler, M. L. (1985) · Biotechnology and Bioengineering · doi:10.1002/bit.260270714 · Cited by 29 · see citing works
Cell cycle‐dependent protein secretion by Saccharomyces cerevisiae
Frykman, S., & Srienc, F. (2001) · Biotechnology and Bioengineering · doi:10.1002/bit.10003 · Cited by 25 · see citing works
Kromenaker, S. J., & Srienc, F. (1994) · Cytotechnology · doi:10.1007/bf00749617 · Cited by 22 · see citing works
2nd International Conference on Bioreactor Fluid Dynamics
King, R. W. (1988) · Elsevier eBooks · Cited by 18 · see citing works
Plasmid stability in a recombinant S cerevisiae strain secreting a bifunctional fusion protein
Altintas, M. M., Kırdar, B., Önsan, Z. İ., & Ülgen, K. Ö. (2001) · Journal of Chemical Technology & Biotechnology · doi:10.1002/jctb.424 · Cited by 17 · see citing works
A model of transient mixing in a stirred tank
Smith, F. G. (1997) · Chemical Engineering Science · doi:10.1016/s0009-2509(96)00472-1 · Cited by 16 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Mink, A., Schediwy, K., Posten, C., Nirschl, H., Simonis, S., & Krause, M. J. (2022) · Energies · doi:10.3390/en15207671 · Cited by 30 · see citing works
- Authors
- Lapin, A., Müller, D., & Reuss, M.
- Affiliations
- University of Stuttgart (DE)
- Venue
- Industrial & Engineering Chemistry Research
- Publisher
- American Chemical Society (ACS)
- Published
- 2004-06-25
- Volume
- 43
- Issue
- 16
- Pages
- 4647-4656
- ISSN
- 0888-5885 (ISSN-L)
- 1520-5045
- OpenAlex
- W1974033770
- Cited by
- 131
- References
- 35
- Citations by year
- 2026: 8 · 2025: 10 · 2024: 11 · 2023: 6 · 2022: 17 · 2021: 4 · 2020: 10 · 2019: 4 · 2018: 12 · 2017: 9 · 2016: 7 · 2015: 1 · 2014: 6 · 2013: 5 · 2012: 3
- FWCI
- 1.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Industrial & Engineering Chemistry Research (publishedVersion)
- Funders
- Deutsche Forschungsgemeinschaft
- Topics
- Physical Sciences › Engineering › Biomedical Engineering › Fluid Dynamics and Mixing
- Physical Sciences › Engineering › Computational Mechanics › Granular flow and fluidized beds
- Physical Sciences › Engineering › Ocean Engineering › Particle Dynamics in Fluid Flows
- Keywords
- microbial population dynamics, stirred tank bioreactor, non-ideal mixing, Euler-Lagrange method, heterogeneous cell populations, turbulent flow field, fractional step method, population balance equation, single-cell trajectory
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
