Penetration theory of gas

The classic penetration theory of gas-liquid mass transfer across a stationary interface (i.e., n = 0, k = 1) reveals /i dependence for the total number of moles of O2 that has been transported into the quiescent liquid. In general, the functional dependence of [moles(f)]A on time scales as /(2 /3)+i/2 -phe volume of the bubble must increase according to t, or its radius must increase as fC" to realize a linear increase in [moles(f)]A vs. time throughout the duration of the process. 

The above is the stationary two-film theory. Later developments recognized that a real process has some means of continuous agitation or renewal of the liquid surface in contact with the gas. The so-called penetration theory of gas absorption, therefore, considers the transient diffusion of a dissolved gas into a stationary liquid phase away from an interface at constant concentration. The difference between this approach and the steady-state two-film theory is that one assumes the periodic replacement of the liquid surface layer. There is no steady state, and the standard equations of diffusion hold ... 

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