N

Porous membrane

Boundary layer wv

Porous membrane

Knudsen-molecule diffusion transition

Knudsen-molecule diffusion transition

Fig. 12. Schematic representation of mass transfer in MD.

For another case, if a solution, which contains one non-volatile component and at least one volatile component, is used as the feed in MD, then within the mixture the mass transfer resistance to volatile component exists. Due to this resistance, the evaporation of volatile component at the membrane surface will result in its depletion and/or the buildup of the non-volatile component near the membrane surface. The region near the membrane surface, where the concentration profile of volatile and non-volatile components is established, is called concentration boundary layer. As shown in Fig. 10, the thickness of concentration boundary layer is 8 c (m). In this layer the concentration of non-volatile component increases from cb to CB,m (kmol m"), while that of volatile component decreases from ca to CA,m (kmol m"). The depletion or buildup of components in the concentration boundary layer due to the mass transfer resistance is referred to as concentration polarization. For a given bulk concentration, the presence of concentration boundary layer reduces the driving force for the volatile component to pass through the membrane, and thus decreases the transmembrane mass flux.

According to the theory of mass transfer in boundary layer, a mass balance in the feed side boundary layer yields to the relationship of the concentration of non-volatile component at the membrane surface and at feed bulk:

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