Transport of liquid mixtures

The transport of liquid mixtures through a polymeric membrane is generally much more complex than that of a single liquid. For a binar liquid mixture, fee flux can also be described in terms of the solubility and the diffusivity, such that they may influence each other strongly. 

Two phenomena must be distinguished in multi-component transpon i) flow coupling and ii) thermodynamic interaction. Flow coupling may be described via nonequilibrium thermodynamics (see earlier in this chapter), the following equations being obtained for a binajy liquid mixture  

The first term on fee right-hand side of eq. VI - 15 describes the flux of component i due to its own gradient while the second term describes fee flux of component i due to the gradient of component j. This second term also represents the coupling effect. If no coupling occurs (L, j = Ljj = 0), the flux equations reduce to simple linear relationships. 

These linear relationships assume that the components permeate through the membrane independently of each,other. This s, not generally the. case as can jbe/s mp y demoriWated by Coinparing die pure component data with those of ithe mixture/ ft is i yen possible for a component with a very low permeability, e.g. water in polysulfone shows a much higher permeability in the presence of a Second component, e.g. ethanol. This second component has a much higher affinity towards the polymer and consequently a higher (overall) solubility is obtained which allows water peimeadon. 

Coupling phenomena are difficult to describe, predict or even to measure quantitatively. However, when thermodynamic interactions (or preferential sorption) are considered in relation to selective transport, it is possible to obtain indirect information about flow coupling. 

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