In aerobic, gas-sparged bioreactors, how does the power required by a rotating impeller at a given speed typically compare with the power in the same liquid without gas (ungassed), and what is the process reason for this difference?

Introduction / Context:
Power input in stirred, gas-sparged bioreactors is a key design and scale-up variable affecting mixing, oxygen transfer, shear, and heat removal. This question checks whether you know the usual qualitative effect of aeration on impeller power draw when speed is held constant.

Given Data / Assumptions:

• Same impeller speed in both cases (gassed vs. ungassed).
• Same impeller and tank geometry; Newtonian broth assumed for simplicity.
• Operation below flooding; normal aeration rates for fermentation.

Concept / Approach:
Introducing gas reduces the effective density and continuity of the liquid around the blades, causing slip and blade ventilation. As a result, the impeller power number in the gassed state (P_g) is lower than the ungassed value (P_u) at the same rotational speed. This is widely observed for radial and axial impellers before flooding. Therefore, at constant rpm, P_g < P_u in most practical regimes.

Step-by-Step Solution:

Verification / Alternative check:
Engineering correlations and shop tests show power reduction factors (P_g/P_u) commonly in the range 0.3–0.8 depending on gas rate, impeller type, submergence, and scale—consistent with “lesser.”

Why Other Options Are Wrong:

• Higher: occurs only in rare, geometry-specific edge cases; not typical.
• Same: contradicts standard two-phase power correlations.
• “May be lesser or higher…”: too noncommittal; the usual trend is lower.
• “Negligible…”: power remains a major design load.

Common Pitfalls:
Confusing constant power with constant tip speed; or assuming increased oxygen transfer must mean increased power draw.

Final Answer:
Lesser.