Step 1: Understanding kLa
The term \( k_La \) refers to the volumetric mass transfer coefficient, which measures the rate of oxygen transfer into the liquid phase from the gas phase in a bioreactor.
Step 2: Evaluating the Options
- Liquid-liquid mass transfer coefficient: Involves transfer between two liquids, not relevant to \( k_La \).
- Distribution of gas bubble size: Related to aeration but does not define \( k_La \).
- Volumetric oxygen mass transfer coefficient: Correct, as \( k_La \) represents oxygen transfer efficiency.
- Dankwerts gas-liquid interfacial energy coefficient: Relates to the interfacial area, not directly to \( k_La \).
Step 3: Conclusion
The correct answer is the volumetric oxygen mass transfer coefficient.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.