effect on the flow. Currently the number of particles being tracked is in the order of
100,000–1,000,000 particles. This, on the one hand, forces the investigation to adapt
an extra assumption which is to associate a fix biomass to the Eulerian flow field and
consider simulating a quasi-steady state [15]. On the other hand, associating the
biomass with particles might introduce artificial concentration gradients especially in
the spatial locations that are less visited by the limited number of particles. In an
ideal scenario, it is desired to have a large enough set of particles that results in a
statistically stable gradient although if the number of particles is too large, apart from
computational resource limitations, it could be that a cluster of particles will be
present at the same cell where the limited number of cells will have access to the
substrate and the others will face starvation. This is of utmost importance for
coupling consumption to concentrations (two-way coupled metabolism). Among
other things, agglomeration is not considered, and the heterogeneities arising from
such agglomerations can be an interesting question to tackle by assuming the particle
as a swarm center point. Based on the final goal of the simulation, valid assumptions
are to be made so that most of the concerning happenings at reasonable numerical/
computational costs are revealed.
• Kinetic considerations
The choice of proper kinetic models depends on the traits of the microbe.
Particular focus should be given to the timescale of cellular response. Conventional
black-box, nonstructured kinetics typically initiate instantaneous microbial
responses with respect to substrate uptake, growth, etc. However, the consideration
of structured models additionally considering multiple cellular regulation levels
integrates delayed responses, most likely. The latter cause a spatial disconnection
of initiation and cellular response inside the bioreactor [2, 18]. Besides, even the
consideration of proper metabolic models reacting instantaneously on microenvironmental stimuli may be a challenging task. Modeling the cellular behavior by
lumped metabolic pools is considered a reasonable compromise to cope with the
complexity of metabolism [30, 36, 70]. It might be intriguing to employ data science
techniques like reduced order modeling to decide the features that have the most
impact on the behavior in the future. Especially in cases where biomass concentration is low enough to create a large limitation zone but larger enough to increase
oxygen sensitivity and resulting in unwanted overflow metabolism production [71–
73]. One can modify a lumped metabolic model in a way so that it also takes into
account the transient behavior of the population. An abstract illustration of
such models is shown in Fig. 9. Here, oxygen concentrations above three times
the affinity constant of oxygen [74] are assumed to supply enough oxygen to support
the utilization of substrate, which equals to maximum oxygen uptake rate of
the cell (q O 2 ¼ q O 2, max ). In this region overflow metabolism is expected only
when the concentration of the substrate exceeds the respiration capacity
q s  Y O=S > q O 2, max
). This holds true for most of the bioprocesses that operate in
a way that guarantees the oxygen demand (> 30% DO concentration). This assumption requires revisiting once the rheology is changed. With slight adaptions, it can be
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
247
100,000–1,000,000 particles. This, on the one hand, forces the investigation to adapt
an extra assumption which is to associate a fix biomass to the Eulerian flow field and
consider simulating a quasi-steady state [15]. On the other hand, associating the
biomass with particles might introduce artificial concentration gradients especially in
the spatial locations that are less visited by the limited number of particles. In an
ideal scenario, it is desired to have a large enough set of particles that results in a
statistically stable gradient although if the number of particles is too large, apart from
computational resource limitations, it could be that a cluster of particles will be
present at the same cell where the limited number of cells will have access to the
substrate and the others will face starvation. This is of utmost importance for
coupling consumption to concentrations (two-way coupled metabolism). Among
other things, agglomeration is not considered, and the heterogeneities arising from
such agglomerations can be an interesting question to tackle by assuming the particle
as a swarm center point. Based on the final goal of the simulation, valid assumptions
are to be made so that most of the concerning happenings at reasonable numerical/
computational costs are revealed.
• Kinetic considerations
The choice of proper kinetic models depends on the traits of the microbe.
Particular focus should be given to the timescale of cellular response. Conventional
black-box, nonstructured kinetics typically initiate instantaneous microbial
responses with respect to substrate uptake, growth, etc. However, the consideration
of structured models additionally considering multiple cellular regulation levels
integrates delayed responses, most likely. The latter cause a spatial disconnection
of initiation and cellular response inside the bioreactor [2, 18]. Besides, even the
consideration of proper metabolic models reacting instantaneously on microenvironmental stimuli may be a challenging task. Modeling the cellular behavior by
lumped metabolic pools is considered a reasonable compromise to cope with the
complexity of metabolism [30, 36, 70]. It might be intriguing to employ data science
techniques like reduced order modeling to decide the features that have the most
impact on the behavior in the future. Especially in cases where biomass concentration is low enough to create a large limitation zone but larger enough to increase
oxygen sensitivity and resulting in unwanted overflow metabolism production [71–
73]. One can modify a lumped metabolic model in a way so that it also takes into
account the transient behavior of the population. An abstract illustration of
such models is shown in Fig. 9. Here, oxygen concentrations above three times
the affinity constant of oxygen [74] are assumed to supply enough oxygen to support
the utilization of substrate, which equals to maximum oxygen uptake rate of
the cell (q O 2 ¼ q O 2, max ). In this region overflow metabolism is expected only
when the concentration of the substrate exceeds the respiration capacity
q s  Y O=S > q O 2, max
). This holds true for most of the bioprocesses that operate in
a way that guarantees the oxygen demand (> 30% DO concentration). This assumption requires revisiting once the rheology is changed. With slight adaptions, it can be
Euler-Lagrangian Simulations: A Proper Tool for Predicting Cellular Performance. . .
247