Understanding Fermenter Wash Out
Wash out in a continuous stirred tank fermenter signifies a state where the rate at which cells are removed from the reactor exceeds their growth rate. The question specifies this critical condition as the dilution rate ($D$) being equal to the maximum specific growth rate ($\mu_{max}$), i.e., $D = \mu_{max}$.
Impact on Reactor Components
- Biomass Concentration ($X$): When the dilution rate ($D$) equals or exceeds the maximum specific growth rate ($\mu_{max}$), cells are washed out faster than they can reproduce. This leads to the biomass concentration ($X$) in the bioreactor approaching zero.
- Substrate Concentration ($S$): In a wash out state, the limited amount of viable biomass present consumes very little substrate. Consequently, the substrate concentration within the reactor ($S$) tends towards the substrate concentration found in the incoming feed ($S_0$).
- Product Concentration ($P$): Product formation is typically dependent on the metabolic activity of the biomass. As the biomass concentration ($X$) drops to zero during wash out, the metabolic activity responsible for product synthesis also ceases, resulting in the product concentration ($P$) approaching zero.
Conclusion on Wash Out Conditions
Based on the analysis, the state of wash out ($D = \mu_{max}$) is characterized by:
- Biomass ($X$) = 0
- Substrate ($S$) = $S_0$
- Product ($P$) = 0
This corresponds to Option B.
Important Questions from Kinetics of Cell Growth Substrate Utilization and Product Formation
If the rate at which $E. coli$ divides is $0.5 \text{ h}^{-1}$, then its doubling time is _______________ h.
- Which of the following factors can affect the growth of a microbial culture in a batch cultivation process?
Let $y(t)$ be a bacterial population whose growth is given by
$ \frac{dy}{dt} = \lambda(y + 2) $
where $ \lambda $ is the growth rate constant. If $y(0) = 1$ and $y(1) = 4$, then the value of $ \lambda $ is
If the doubling time of a bacterial population is 3 hours, then its average specific growth rate during this period is _________ $h^{-1}$.
(Round off to two decimal places)
- A microorganism is grown in a batch culture using glucose as a carbon source. The apparent growth yield is $0.5 \frac{\text{g biomass}}{\text{g substrate}}$. The initial concentrations of biomass and substrate are $2 \text{ g L}^{-1}$ and $200 \text{ g L}^{-1}$, respectively. Assuming that there is no endogenous metabolism, the maximum biomass concentration that can be achieved is ________ $\text{g L}^{-1}$.
