Chemostat Calculator
A 2 L chemostat fed at 0.5 L/h (D = 0.25 per hour) settles at 4.9 g/L of biomass with 0.2 g/L of substrate left.
4.9 g/L
- Dilution rate D = F/V
- 0.25 per h
- Residual substrate S = KsD/(μmax − D)
- 0.2 g/L
- Biomass productivity DX
- 1.225 g/(L·h)
- Critical (washout) dilution rate
- 0.4901960784 per h
- Dilution rate for maximum productivity
- 0.4299859958 per h
Step-by-step solution
- D = F ÷ V = 0.25 per h (at steady state μ = D)
- S = Ks D ÷ (μmax − D) = 0.2 g/L
- X = Y(S₀ − S) = 4.9 g/L
Chemostat Formula
D = F/V = μ, S = Ks D/(μmax − D), X = Y(S₀ − S)
washout above D_crit = μmax S₀/(Ks + S₀); productivity DX
Worked Example
A 2 L chemostat fed 0.5 L/h with 10 g/L substrate, μmax 0.5 per h, Ks 0.2 g/L, Y = 0.5:
- D = F ÷ V = 0.25 per h (at steady state μ = D)
- S = Ks D ÷ (μmax − D) = 0.2 g/L
- X = Y(S₀ − S) = 4.9 g/L
Residual substrate S = KsD/(μmax − D): 0.2 g/L · Biomass productivity DX: 1.225 g/(L·h) · Critical (washout) dilution rate: 0.4901960784 per h · Dilution rate for maximum productivity: 0.4299859958 per h
GATE tip
The chemostat is a CSTR: τ = 1/D. Compare its productivity DX with a batch reactor’s, which must include the turnaround time between batches.
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Frequently asked questions
What is washout?
If the dilution rate exceeds the maximum growth rate the cells can reach at the feed concentration, they are flushed out faster than they divide and the culture is lost.
Where is productivity highest?
Just below washout, at D_opt = μmax(1 − √(Ks/(Ks + S₀))); operating there is risky, so plants run a little lower.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Chemostat Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/chemostat-calculator/
IEEE
Scientific Converters, "Chemostat Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/chemostat-calculator/