Membrane penetration theory

For the gas permeation measurements the diffusion coefficient was determined by the well-known time lag procedure, based on the penetration theory. If a penetrant-free membrane is exposed to the penetrant at the feed side at t = 0 and the penetrant concentration is kept very low at the permeate side, then the total amount of penetrant, Q passing through the membrane in time t is given by [37] ... 

One of the most significant contributions of the penetration theory is the prediction that the mass transfer coefficient varies as D. As will be seen in Section 2.4-3, experimental mass transfer coefficients generally are correlated with an exponent on Pab ranging from to. The penetration theory model has also been successfully used to predict the effect of simultaneous chemical reaction on mass transfer in gas absorption and in carrier-facilitated membranes. Stewart solved the penetration theoiy model by taking into account bulk flow at the interface. The results, as in the film theory case, are conveniently expressed as the dependence of the ratio kj/k on the dimensionless total flux, (Nf, + Na)k°. This curve is also shown in Fig. 2.4-2 and generally predicts greater effects of convection than does the film theoiy. 

The current efficiency amounts to ca. 95% again. The reason for losses lies in the fact that the membranes are not completely impermeable for OH- -ions, so that reactions (6) to (8) can take place to a certain amount. Caustic alkali is generated with ca. 33 wt%, in theory it would be free of chloride-ions, but in reality Cl--ions can penetrate the membranes, too, by a certain amount. So, the NaOH generated will contain up to 50 ppm Cl-. 

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