Path of oxygen to cells — The rate-limiting step for oxygen moving from a gas bubble to a cell in a bioreactor is typically diffusion across which zone?

Introduction:
Oxygen transfer to microorganisms involves sequential resistances: gas-phase transport, crossing the interface, diffusion through the liquid film, and finally transport to and into the cell. In most aerated, agitated systems, the dominant resistance lies on the liquid side. This question pinpoints the usual rate-limiting step.

Given Data / Assumptions:

• Aerated stirred tank with dispersed bubbles and adequate agitation.
• No extreme gas-phase limitations (small bubbles, low gas-phase mass transfer resistance).
• Cells are much smaller than bubbles; bulk liquid is well mixed.

Concept / Approach:
For sparged systems, the liquid-side film resistance around each bubble typically dominates overall O2 transfer. Hence, k_La focuses on the liquid-film coefficient k_L and interfacial area a. Increasing agitation reduces film thickness and increases a via bubble breakup, improving transfer. Gas-phase resistance is usually minor for oxygen in air at typical scales.

Step-by-Step Solution:
Consider series resistances: gas-phase, interface, liquid film, bulk transport.Bulk liquid is mixed rapidly; concentration gradients exist mainly in the thin liquid film.Therefore, diffusion across the liquid boundary layer near bubbles is rate limiting.

Verification / Alternative check:
Increasing agitation (raising k_La) boosts oxygen transfer primarily by thinning the liquid film and increasing interfacial area, consistent with liquid-side control.

Why Other Options Are Wrong:

• (a) The interface itself is not an independent barrier in most cases.
• (c) Bulk liquid is considered well mixed in design models.
• (d) Gas-phase resistance is small for oxygen except with very large bubbles or stagnant gas films.
• (e) Cell membrane transport can matter but is not universally rate limiting in well-aerated broths.

Common Pitfalls:
Assuming gas-phase control without evidence; neglecting effects of surfactants or viscosity that modify film thickness and interfacial behavior.

Final Answer:
The liquid boundary layer (film) surrounding the bubble