Why does a large D wash the culture out?

Cells grow at most at μ(S0)<μmax. If the vessel is flushed faster than that, X′ stays negative and biomass is carried out faster than it is produced.

Is this the same as logistic growth in a flask?

No. A closed batch culture has no inflow/outflow and approaches a carrying capacity set by the initial nutrient. A chemostat is an open system whose steady state is set by D and S0.

What is productivity DX?

It is the biomass harvested per unit time in the outflow. Raising D increases throughput but lowers residual X; the product DX typically peaks at an intermediate dilution below washout.

Chemostat Microbial Growth

Q: Is this the same as logistic growth in a flask?

No. A closed batch culture has no inflow/outflow and approaches a carrying capacity set by the initial nutrient. A chemostat is an open system whose steady state is set by D and S0.

Q: What is productivity DX?

It is the biomass harvested per unit time in the outflow. Raising D increases throughput but lowers residual X; the product DX typically peaks at an intermediate dilution below washout.

Continuous culture: Monod μ(S), dilution D, washout threshold, yield, and productivity DX versus D.

Raise D past Dw and the culture washes out: X decays to 0 while S returns to the feed S0. The gold dot on P(D) is the steady productivity maximum; the cyan square is the live harvest DX.

About this model

A well-mixed chemostat has dilution rate D, feed substrate S0, biomass X, and yield Y. Substrate and cells obey S′=D(S0−S)−μ(S)X/Y and X′=(μ(S)−D)X with Monod growth μ(S)=μmax S/(Ks+S). Washout occurs when D exceeds μ(S0)=μmax S0/(Ks+S0). Below that threshold the unique positive steady state is S*=D Ks/(μmax−D) and X*=Y(S0−S*). Productivity DX as a function of D has an interior maximum before washout.

Who it's for: Microbial ecology, bioprocess engineering, and mathematical biology courses on continuous culture.

Key terms

Chemostat
Monod kinetics
Dilution rate
Washout
Yield
Productivity
Steady state

How it works

Well-mixed chemostat with Monod growth μ(S)=μmax S/(Ks+S). Dilution D washes cells out when D ≥ Dw=μ(S0). Below washout, S*=D Ks/(μmax−D) and X*=Y(S0−S*). Productivity DX vs D has a marked interior maximum.

Key equations

S' = D (S0 − S) − μ(S) X / Y X' = (μ(S) − D) X

μ(S) = μmax S / (Ks + S)

D_w = μ(S0) = μmax S0 / (Ks + S0); if D ≥ D_w then X* = 0, S* = S0

If D < D_w and μmax > D: S* = D Ks / (μmax − D), X* = Y (S0 − S*)

Frequently asked questions

Why does a large D wash the culture out?: Cells grow at most at μ(S0)<μmax. If the vessel is flushed faster than that, X′ stays negative and biomass is carried out faster than it is produced.
Is this the same as logistic growth in a flask?: No. A closed batch culture has no inflow/outflow and approaches a carrying capacity set by the initial nutrient. A chemostat is an open system whose steady state is set by D and S0.
What is productivity DX?: It is the biomass harvested per unit time in the outflow. Raising D increases throughput but lowers residual X; the product DX typically peaks at an intermediate dilution below washout.

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Key equations

Frequently asked questions