Pervaporation sorption coefficient

The selectivity (amcm) of pervaporation membranes critically affects the overall separation obtained and depends on the membrane material. Therefore, membrane materials are tailored for particular separation problems. As with other solution-diffusion membranes, the permeability of a component is the product of the membrane sorption coefficient and the diffusion coefficient (mobility). The membrane selectivity term amem in Equation (9.11) can be written as... 

The solution-difTusion model is valid only in strictly ideal systems, namely when dealing with solutions of infinite dilution. As soon as one departs from such ideal solutions, it becomes to some extent subjective what can still be considered as almost ideal and highly dilute . For the pervaporation of isobutyl alcohol, for example, a feed concentration of 50 mg kg would lead to a membrane surface concentration of 50 mg kg (according to the sorption coefficient listed in Table 3.6-2). For the same feed concentration, ethyl hexanoate would yield a membrane surface concentration about 240 times higher, namely 12 g kg which may not be considered ideal anymore. The stronger the (desired) solute-polymer affinity, the more pronounced can be the non-ideal phenomena, with the most relevant being discussed below. 

In pervaporation, as the feed fluid is a liquid, a thin, stagnant boundary layer always exists over the membrane surface in which the solute transport is diffusive (Fig. 3.6-11). The thickness of this boundary layer (stagnant liquid film) can be calculated from well-established boundary layer equations (for critical reviews on the use of the most common correlations see, for example, Gekas and Hallstrom, 1987 and Cussler, 1997). If the flux of a solute i across the concentration boundary layer toward the membrane is lower than the maximum (for the respective solute bulk feed concentration) attainable solute flux across the membrane, then solute i will be depleted in the boundary layer over the membrane upstream surface. As a consequence, the concentration of i in the membrane upstream surface will also be lower (assuming a constant sorption coefficient), the concentration gradient over the membrane will decrease and hence so will the trans-membrane flux. 

From Fig. 19.3a-c, and as opposed to purely sorption controlled processes, it can be seen that during pervaporation both sorption and diffusion control the process performance because the membrane is a transport barrier. As a consequence, the flux 7i of solute i across the membrane is expressed as the product of both the sorption (partition) coefficient S, and the membrane diffusion coefficient Di, the so-called membrane permeability U, divided by the membrane thickness f and times the driving force, which maybe expressed as a gradient of partial pressures in place of chemical potentials [6] ... 

Sorption data were used to obtain values for A" L. As pointed out by Paul and Paciotti, the data in Figure 2.17 show that reverse osmosis and pervaporation obey one unique transport equation—Fick s law. In other words, transport follows the solution-diffusion model. The slope of the curve decreases at the higher concentration differences, that is, at smaller values for c,eimi because of decreases in the diffusion coefficient, as the swelling of the membrane decreases. 

For illustration, rubbery polymeric membranes, whose polymeric network is sufficiently elastic and mobile to allow comparatively large organic compounds to diffuse through it (Table 3.6-2), are in general used for the recovery of organic compounds from aqueous solutions. Because of its small size, the bulk solvent, water, unfortunately diffuses through the membrane even better. This is why in organo-philic pervaporation the selectivity is mainly achieved and determined by the ratio of the solubility coefficients (sorption selectivity. Table 3.6-2). Membrane selectivity, as defined in Eq. (7), is an intrinsic parameter and can differ from the overall process selectivity, as wiU be shown later. 

The concentration in the membrane depends on the outside activity and the sorption or partition coefficient of the species, the mobifity on the nature of the membrane. The driving force for a component is a function of the process parameters, e.g. temperature, pressure, and concentration. In a pervaporation process usually the minor component is removed from a mixture. For the retained major component the driving force will always be higher than for the transported one. The selectivity of the membrane is then determined by the differences in the product of mobility and concentration and not by a difference in the driving force. 

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