Multilayered, Asymmetric Supported Systems

The use of supports in asymmetric, supported membranes introduces a number of complications in the interpretation of permeation and separation data as well as in the optimalisation of membrane systems. If the flow resistance of the support is not negligible, there is a pressure drop across the support. This implies that the pressure and so the occupancy at the interface of separation layer and support is different from the (directly accessible) pressure at the support surface, usually the permeate side. Consequently, the driving force for permeation through the separation layer is different from the total driving force across the membrane system. In cases where one wants to calculate or compare transport properties of the separation layer material, it is necessary to correct for this effect (for illustration see below). 

Expressions to calculate the pressure Pint at the interface of top layer and substrate and thus to calculate the pressure drop across the top layer only are originally derived by Uhlhorn et al. [21] and further developed and used by Lin et al. [103,104] and de Lange et al. [59,60]. More recently Uchytil [102] used and refined this method for different cases. De Lange [60] gives an illustration of the 

A similar expression to Eq. (9.68) usually fits very well the behaviour of the membrane support + top layer) so  

The values of gs and Ps are calculated from measured permeation data for non-adsorbable gases (He, Ar, H2) using Eq. (9.68a). The permeation or permeability properties of the top layer are calculated now by subtracting the permeation data of the support only from the measured permeation data of the membrane using the series model. Note that Ph (high pressure) and Pi are measured at the interfaces of gas/top layer and gas (permeate side)/support respectively. 

The theoretical validity of Eq. (9.68b) is discussed by Lin et al. [104] and it is shown that this equation is a special simplified case of a more general, but very complicated expression which strictly holds for the case that Pm/gm = Ps/ s-Uchytill [102] also devotes an extended discussion to this problem. T5q ical examples of the value of Pi and of the magnitude of the corrections are given in the cited literature. 

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