Question

In a bioreactor, what is the term used to describe the resistance to mass transfer across the gas-liquid interface?

• A. Interfacial tension
• B. Gas holdup
• C. Mass transfer coefficient
• D. Film thickness

Hint:

• Two-Film Theory Assumes stagnant films on gas and liquid sides of the interface, where mass transfer occurs by molecular diffusion.
• Resistance to mass transfer is primarily within these films.
• Factors affecting film thickness (and thus \(k_L\)): Agitation, turbulence, fluid properties.
• Overall Volumetric Mass Transfer Coefficient (\(k_L a\)): Combines liquid-side coefficient (\(k_L\)) and interfacial area per unit volume (\(a\)). Higher \(k_L a\) means better mass transfer (lower resistance).

Answer 1

The Correct Option is D

Mass transfer across a gas-liquid interface (e.g., oxygen transfer from air bubbles to the liquid medium in an aerobic bioreactor) is often described by the two-film theory. This theory postulates the existence of stagnant or slow-moving films on either side of the interface (a gas film and a liquid film) through which the solute must diffuse. The resistance to mass transfer is considered to reside primarily within these films.

• The thickness of these hypothetical films influences the resistance. A thicker film means a longer diffusion path and thus higher resistance to mass transfer.
• The overall mass transfer rate is often characterized by a volumetric mass transfer coefficient (\(k_L a\)), where \(k_L\) is the liquid-side mass transfer coefficient and \(a\) is the interfacial area per unit volume.
• The reciprocal of the mass transfer coefficient (\(1/k_L\)) can be considered a measure of the resistance in the liquid film. Similarly for the gas film (\(1/k_G\)).

Let's analyze the options: (a) Interfacial tension: A property of the interface between two immiscible phases (like gas and liquid). It affects bubble size and interfacial area, but it is not directly "the resistance" itself, though it influences \(a\). (b) Gas holdup: The volume fraction of gas in the gas-liquid dispersion. It relates to interfacial area \(a\), but is not the resistance. (c) Mass transfer coefficient (\(k_L\) or \(k_L a\)): This coefficient quantifies the *rate* of mass transfer, not the resistance itself. Resistance is inversely proportional to the coefficient (e.g., \(1/k_L\)). (d) Film thickness: According to the two-film theory, the primary resistance to mass transfer lies within thin stagnant films at the gas-liquid interface. The thickness of these films directly contributes to the diffusional resistance. (Resistance \(\propto\) thickness / diffusivity). Therefore, "film thickness" is the term most directly related to the concept of resistance to mass transfer across the interface according to the film theory. A greater film thickness implies greater resistance. While \(1/k_L a\) is the overall volumetric mass transfer resistance, "film thickness" is a more fundamental concept from the theory explaining this resistance. \[ \boxed{\text{Film thickness}} \]