Interphase mass transfer — Which of the following is NOT one of the three best-known classical theories for gas–liquid interphase mass transfer?

Introduction:
Mass transfer across gas–liquid interfaces is often explained using conceptual models that relate transport resistances and eddy renewal to measurable quantities like k_La. Three classical theories dominate introductory treatments: two-film, penetration, and surface renewal. This question asks you to identify which listed item is not among those foundational theories.

Given Data / Assumptions:

• Focus on conceptual frameworks, not specific empirical correlations.
• Gas–liquid interphase with turbulent liquid-side mixing.
• Standard chemical/biochemical engineering curriculum.

Concept / Approach:
The two-film theory (Whitman) posits stagnant films controlling resistance. The penetration theory (Higbie) considers unsteady diffusion into elements of liquid exposed for short times. The surface renewal theory (Danckwerts) generalizes exposure times via a renewal rate, blending features of the first two. Calderbank and Moo-Young, by contrast, is chiefly associated with empirical correlations linking k_La to power input, gas velocity, and physical properties in agitated vessels—useful, but not a fourth classical “theory”.

Step-by-Step Solution:
List the classical trio: two-film, penetration, surface renewal.Compare to options: Calderbank & Moo-Young provides correlations, not a distinct conceptual theory of interphase transport.Select the outlier: Calderbank and Moo-Young.

Verification / Alternative check:
Standard texts present the three theories together before introducing empirical k_La correlations (Calderbank–Moo-Young, Aiba, Van’t Riet) for design; this separation affirms the correct choice.

Why Other Options Are Wrong:

• Two-film, penetration, and surface renewal are precisely the three classical theories.
• Hybrid/derivative formulations are still rooted in those three.

Common Pitfalls:
Confusing widely used correlations with theoretical frameworks; assuming any famous authorship implies a foundational theory rather than a design correlation.

Final Answer:
Calderbank and Moo-Young theory (empirical correlation family)