Two-Film Overall Mass Transfer Coefficient

Warren Lewis and Walter Whitman proposed the two-film model in 1924, and it has survived a century of better theories because it is simple, it is roughly right, and it makes the correct engineering decision fall out immediately. The picture is this: a stagnant gas film clings to one side of the interface and a stagnant liquid film to the other; the interface itself is at equilibrium and offers no resistance at all; everything that slows the transfer down happens inside the two films. Resistances in series add, and $1/K_{OG} = 1/k_G + m/k_L$ is that addition written out.

The slope $m$ is what makes the sum interesting rather than trivial. It converts a liquid-side resistance into gas-side currency, and it comes from the equilibrium relationship — Henry's law constant for a dilute system. A highly soluble gas has a small $m$, which shrinks the liquid film's contribution to nothing and leaves the gas film in charge. A sparingly soluble gas has a large $m$, which magnifies the liquid film's resistance enormously and leaves the liquid in charge. This is not a subtle weighting; the split is usually 90 to 10 or worse, and the model's real payoff is telling you which side of the interface to spend money on.

Work an example and the point lands. Ammonia in water has a Henry's constant so low that the gas film carries essentially all the resistance: raise the gas velocity, improve the distribution, open up the packing, and the column gets better. Pump more water through it and nothing measurable happens. Oxygen in water is the mirror image — the liquid film holds well over ninety percent of the resistance, and the blower is the wrong thing to upsize. This is why aerators are designed around bubble breakup and surface renewal rather than around air pressure, and why an operator who responds to poor oxygen transfer by turning up the air is usually buying nothing but power.

The model's honest weaknesses are worth knowing. There is no stagnant film — the "film thickness" is a fitted parameter with no independent existence, and film theory predicts $k_c \propto D$ while Higbie's 1935 penetration theory and Danckwerts' 1951 surface-renewal theory both predict $D^{1/2}$. Experiment generally lands between, nearer the square root. The later theories are better physics; the two-film model persists because for design purposes the resistance-addition result is the same, and it is the result that sizes the column.