Introduction
This quiz collection focuses on diffusional resistance in oxygen transfer, a key topic in bioprocess engineering relevant to M.Pharm students dealing with aerobic fermentations, cell cultures and immobilized systems. The questions emphasize mechanisms of mass transfer limitation — external film resistance, internal diffusion within pellets, biofilms and cell aggregates — and how these influence kLa, oxygen uptake rates and reactor performance. You will encounter concepts such as two‑film theory, effective diffusivity, Thiele modulus, effectiveness factor, and practical measures to diagnose and mitigate oxygen transfer resistance during scale‑up and process optimization. The set balances conceptual depth and applied problem awareness to prepare you for exams and research challenges.
Q1. Which statement best describes external diffusional resistance in oxygen transfer in a stirred tank?
- It arises from oxygen concentration gradients within microbial cell cytoplasm.
- It is due to the boundary layer around gas bubbles or particles limiting transfer from bulk liquid to surfaces.
- It is caused exclusively by chemical reaction kinetics inside cells.
- It refers to oxygen transfer resistance across membrane walls of sealed reactors.
Correct Answer: It is due to the boundary layer around gas bubbles or particles limiting transfer from bulk liquid to surfaces.
Q2. In the two‑film theory, which parameter mainly quantifies the resistance on the liquid side?
- Interfacial surface tension
- Liquid‑side mass transfer coefficient (kL)
- Gas‑side diffusion coefficient
- Bubble rise velocity
Correct Answer: Liquid‑side mass transfer coefficient (kL)
Q3. How does decreasing bubble diameter typically affect oxygen mass transfer in an aerated bioreactor?
- Decreases interfacial area and reduces kLa
- Increases interfacial area and typically increases kLa
- Has no impact on oxygen transfer because kLa is independent of bubble size
- Only affects gas‑side resistance, not liquid‑side resistance
Correct Answer: Increases interfacial area and typically increases kLa
Q4. What is the Thiele modulus used to evaluate in porous catalytic pellets or cell aggregates?
- The ratio of external film resistance to gas‑side resistance
- The ratio of reaction rate to internal diffusion rate within the particle
- The equilibrium solubility of oxygen in the pellet
- The bubble coalescence rate in aeration systems
Correct Answer: The ratio of reaction rate to internal diffusion rate within the particle
Q5. Which outcome indicates significant internal diffusional limitation inside immobilized cell beads?
- Uniform concentration profile across the bead
- Lower observed specific growth rate than predicted from bulk oxygen concentration
- Increased oxygen solubility in the bulk liquid
- Higher kLa measured by dynamic gassing‑out method
Correct Answer: Lower observed specific growth rate than predicted from bulk oxygen concentration
Q6. The effectiveness factor (η) in porous particles is defined as which of the following?
- The ratio of external to internal mass transfer coefficients
- The ratio of actual overall reaction rate to the rate if the entire particle were at bulk concentration
- The ratio of bubble surface area to particle surface area
- The fraction of oxygen consumed in the gas phase
Correct Answer: The ratio of actual overall reaction rate to the rate if the entire particle were at bulk concentration
Q7. Which parameter combination is most useful to predict liquid‑side mass transfer coefficient (kL) in stirred tanks?
- Reynolds (Re) and Schmidt (Sc) numbers
- Thiele modulus and effectiveness factor
- Henry’s constant and reaction order
- Biochemical oxygen demand (BOD) and COD
Correct Answer: Reynolds (Re) and Schmidt (Sc) numbers
Q8. What is the practical effect of a high cell density culture on oxygen transfer?
- Decreases oxygen uptake rate and increases dissolved oxygen
- Increases oxygen uptake rate and may create severe diffusional resistance leading to oxygen limitation
- No effect; oxygen transfer depends only on aeration rate
- Always improves kLa by enhancing mixing
Correct Answer: Increases oxygen uptake rate and may create severe diffusional resistance leading to oxygen limitation
Q9. Which experimental method is commonly used to measure kLa in a bioreactor and can indicate transfer resistance?
- Batch growth rate measurement
- Dynamic gassing‑out method (sodium sulphite or gas‑stripping dynamic method)
- Optical density at 600 nm
- pH titration curve
Correct Answer: Dynamic gassing‑out method (sodium sulphite or gas‑stripping dynamic method)
Q10. Which dimensionless number relates convective mass transport to diffusive transport and is important when considering bubble‑induced mixing?
- Thiele modulus (ϕ)
- Damköhler number (Da)
- Peclet number (Pe)
- Henry number (He)
Correct Answer: Peclet number (Pe)
Q11. In oxygen transfer analysis, what does a Damköhler number (Da) much greater than one indicate?
- Reaction is much slower than mass transfer; system is reaction‑limited
- Reaction is much faster than mass transfer; system is mass transfer limited
- System is at chemical equilibrium
- External film resistance is negligible
Correct Answer: Reaction is much faster than mass transfer; system is mass transfer limited
Q12. How does increasing agitation speed typically influence internal versus external diffusional resistances?
- Primarily reduces external film resistance by thinning boundary layers; internal resistance within aggregates remains largely unchanged
- Only reduces internal resistance inside cells
- Increases both internal and external resistances
- Has no effect on either resistance
Correct Answer: Primarily reduces external film resistance by thinning boundary layers; internal resistance within aggregates remains largely unchanged
Q13. Which factor most reduces internal diffusivity of oxygen inside microbial flocs or pellets?
- High porosity
- Dense biomass packing and extracellular polymeric substances (EPS)
- Small pellet diameter
- Low oxygen consumption rate
Correct Answer: Dense biomass packing and extracellular polymeric substances (EPS)
Q14. What role does the effective diffusivity (De) play in modeling oxygen transfer into porous particles?
- De equals the bulk diffusion coefficient and ignores structure
- De accounts for tortuosity and porosity, reducing bulk diffusivity to represent transport within the porous medium
- De increases with increased biomass density
- De is irrelevant if external film resistance dominates
Correct Answer: De accounts for tortuosity and porosity, reducing bulk diffusivity to represent transport within the porous medium
Q15. Which change is most effective at mitigating internal diffusional limitations in immobilized cell beads?
- Increasing bead diameter
- Reducing bead diameter or increasing bead porosity
- Lowering aeration rate
- Decreasing temperature to increase oxygen solubility
Correct Answer: Reducing bead diameter or increasing bead porosity
Q16. Why is the measurement of dissolved oxygen microprofiles inside biofilms useful?
- To estimate bulk liquid oxygen solubility only
- To identify the spatial extent of oxygen penetration and locate internal diffusion limitation zones
- To measure gas‑phase oxygen concentration
- To calibrate pH probes
Correct Answer: To identify the spatial extent of oxygen penetration and locate internal diffusion limitation zones
Q17. Which modeling approach explicitly couples reaction kinetics with diffusion to predict concentration profiles inside pellets?
- Plug flow reactor model
- Reaction‑diffusion model (solving Fick’s law with reaction term)
- Two‑film theory without internal terms
- Ideal stirred tank model with infinite internal mixing
Correct Answer: Reaction‑diffusion model (solving Fick’s law with reaction term)
Q18. How does oxygen solubility influence the severity of diffusional resistance for a given kLa and oxygen uptake rate?
- Higher oxygen solubility increases driving force and can lessen the impact of diffusional resistance
- Solubility has no effect on diffusional resistance
- Higher solubility always increases internal diffusion resistance
- Lower solubility improves oxygen penetration into pellets
Correct Answer: Higher oxygen solubility increases driving force and can lessen the impact of diffusional resistance
Q19. Which strategy can be used during scale‑up to avoid oxygen limitation caused by diffusional resistance?
- Reducing agitation power per volume without changing aeration
- Increasing both aeration rate and agitation to maintain similar kLa and shear conditions, or using oxygen enrichment
- Always decreasing cell density to negligible levels
- Eliminating spargers to reduce bubble formation
Correct Answer: Increasing both aeration rate and agitation to maintain similar kLa and shear conditions, or using oxygen enrichment
Q20. Which observation during a bioprocess suggests that oxygen transfer resistance has shifted from external to internal control as biomass increases?
- kLa measured by dynamic method decreases with time while external mixing conditions remain constant
- Local dissolved oxygen gradients appear inside pellets or flocs, with low oxygen at core despite adequate bulk DO
- Bulk dissolved oxygen drops uniformly but no intra‑aggregate gradients are seen
- Oxygen transfer coefficient kLa increases dramatically with biomass
Correct Answer: Local dissolved oxygen gradients appear inside pellets or flocs, with low oxygen at core despite adequate bulk DO
