130. A concentrated feed of substrate is added at a constant rate in a fed- batch reactor. If all the
substrate is utilized, the specific growth rate (𝜇) pattern will be:
A. Exponential growth with constant 𝜇
B. Exponential growth with increasing 𝜇
C. Growth with decreasing 𝜇
D. Growth with fluctuating 𝜇

Correct Answer:

C. Growth with decreasing 𝜇

Detailed Explanation:

In a fed-batch reactor, a concentrated substrate is added at a constant rate, while the culture volume gradually increases. Because the substrate is immediately consumed, the substrate concentration stays low, preventing substrate inhibition but also limiting the specific growth rate.

Key Points:

• Specific growth rate (μ) depends on substrate concentration via Monod kinetics:

  μ=μmax⋅SKs+S\mu = \mu_{\text{max}} \cdot \frac{S}{K_s + S}μ=μmax​⋅Ks​+SS​

  where:

  • $\mu$ = specific growth rate

  • μmax\mu_{\text{max}}μmax​ = maximum growth rate

  • $S$ = substrate concentration

  • KsK_sKs​ = half-saturation constant

• Since substrate is being added slowly and is consumed immediately, the actual substrate concentration remains low.

• As the biomass increases, more substrate is required to maintain the same μ, but the constant feed rate cannot match this increasing demand.

• Hence, μ decreases over time as substrate availability per biomass decreases.

Conclusion:

In this fed-batch setup, the specific growth rate decreases over time because the substrate is limiting, and demand rises with increasing biomass. Thus, the correct answer is:

C. Growth with decreasing 𝜇.