Growth and Oxygen

Inspect a culture over time and compare nutrient feeding with improved oxygen transfer.

Starting culture

Intervention at 6 hours

Fixed-volume aerobic culture · illustrative

0.00 h

Oxygen transfer: kLa = 80 h⁻¹

Nutrient pulse: none

Gas supplies dissolved oxygen; feeding supplies nutrient. The vessel drawing shows connections, not measured flow or volume changes.

Solid: selected run. Dashed: no intervention. Dotted line: 6-hour intervention time.

Inspect time: 0.00 h

Both support growth

Biomass: 0.120 g/L
Nutrient: 0.500 g/L
Oxygen: 100.0%

12-hour outcome

Nutrient runs out while oxygen remains available.

At 12 h: 0.370 g/L biomass; no-intervention comparison: 0.370 g/L.

Model and balance notes

μ = μmax × S/(Ks + S) × O/(Ko + O). Oxygen enters at kLa(O* − O); growth consumes nutrient and oxygen at fixed yields. μmax 0.5 h⁻¹; Ks 0.08 g/L; Ko 0.2 mg/L; O* 8 mg/L; biomass/nutrient yield 0.5 g/g; biomass/oxygen yield 0.8 g/g.

Initial biomass 0.12 g/L. Restricted kLa 8 h⁻¹; strong kLa 80 h⁻¹. Extra aeration raises these to 80 or 160 h⁻¹ respectively. The concentrated nutrient pulse adds 1.5 g/L with negligible volume. Temperature, pH, death, maintenance, product formation, inhibition and adaptation are omitted. Parameters illustrate mechanisms; no organism or reactor is calibrated.

Bookkeeping uses S + (X − X₀)/Yxs = S₀ + nutrient added and O + (X − X₀)/Yxo = O₀ + oxygen transferred. These are yield-based nutrient and oxygen balances, not a complete elemental-carbon model.

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Quick reference

Growth has requirements

In this teaching model, specific growth rate depends on both nutrient and dissolved oxygen. Each requirement contributes a saturating Monod term. When one factor becomes small, abundant supply of the other cannot restore the maximum growth rate. No particular organism is fitted.

Gas transfer competes with uptake

Oxygen enters the liquid at kLa times the difference between saturation and the current dissolved concentration. Growing biomass consumes oxygen. Increasing kLa can help an oxygen-limited culture, while adding nutrient alone may leave the oxygen bottleneck in place. The transfer coefficient is a model input, not a direct setting for an uncharacterised real reactor.

Compare a cause with its control

The dashed run keeps the same starting conditions without the 6-hour intervention. A nutrient pulse increases the nutrient inventory; extra aeration changes oxygen transfer. Volume is held constant and the concentrated pulse is assumed to have negligible volume. Fixed yields account for nutrient and oxygen use; maintenance, inhibition, cell death and adaptation are omitted.

Check your understanding Optional

Nutrient remains abundant, but dissolved oxygen is very low. Which change directly addresses the current bottleneck in this model?

Increase oxygen transfer into the liquid.Add more of the already abundant nutrient.Treat the biomass plateau as proof that cells have died.

At the bench

Explore the fuller bioreactor models, parameter provenance and feed strategies after learning to distinguish the two limiting supplies.

Open Bioreactor

Sources and model notes

These interactive examples explain selected relationships using the assumptions shown beside their controls. Calculated quantities and illustrative inputs are identified in each tool; use the linked Drybench app to work with your own data.

Monod · The growth of bacterial cultures

Foundational account of growth kinetics. The numerical parameters in this workspace are illustrative and are not fitted to this paper.

Hansen et al. · Oxygen transfer and respiration

Primary experimental study and oxygen-balance formulation illustrating how oxygen transfer, uptake and limitations are connected. This workspace is not a reproduction or validation of the experimental system.