Pervaporation diffusion coefficient

The composition at the permeate-phase interface depends on the partial pressure and saturation vapour pressure of the component. Solvent composition within the membrane may vary considerably between the feed and permeate sides interface in pervaporation. By lowering the pressure at the permeate side, very low concentrations can be achieved while the solvent concentration on the feed-side can be up to 90 per cent by mass. Thus, in contrast to reverse osmosis, where such differences are not observed in practice, the modelling of material transport in pervaporation must take into account the concentration dependence of the diffusion coefficients. 

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. 

Figure 4.11 shows that ultrafiltration and pervaporation for the removal of organic solutes from water are both seriously affected by concentration polarization. In ultrafiltration, the low diffusion coefficient of macromolecules produces a concentration of retained solutes 70 times the bulk solution volume at the membrane surface. At these high concentrations, macromolecules precipitate, forming a gel layer at the membrane surface and reducing flux. The effect of this gel layer on ultrafiltration membrane performance is discussed in Chapter 6. 

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... 

Separation from mixtures is achieved because the membrane transports one component more readily than the others, even if the driving forces are equal. The effectiveness of pervaporation is measured by two parameters, namely flux, which determines the rate of permeation and selectivity, which measures the separation efficiency of the membrane (controlled by the intrinsic properties of the polymer used to construct it). The coupling of fluxes affecting the permeability of a mixture component can be divided into two parts, namely a thermodynamic part expressed as solubility, and a kinetic part expressed as diffusivity. In the thermodynamic part, the concentration change of one component in the membrane due to the presence of another is caused by mutual interactions between the permeates in the membrane in addition to interactions between the individual components and the membrane material. On the other hand, kinetic coupling arises from the dependence of the concentration on the diffusion coefficients of the permeates in the polymers [155]. 

Similar behavior is observed for the diffusion coefficient. Calculation of flux and selectivity for a membrane even for a simple binary mixture from singlecomponent data therefore requires measurements of solubility and diffusion for both components over the whole range of composition and of temperature of the mixture with high accuracy. For any practical application and engineering design of a pervaporation plant such an approach is not realistic. 

Vapor permeation differs from pervaporation, as stated above, insofar as the feed mixture to be separated is supplied as a vapor. At least the more-permeable component is kept as close to saturation conditions as possible. Thermodynamically there is no difference between a liquid and ifs equilibrium vapor, the partial vapor pressure and thus the driving force for the transport through the membrane are identical and the same solution-diffusion mechanism is valid. However, the density of the vaporous feed and thus the concentration of molecules per volume is lower by two to three orders of magnitude than that of the liquid. As a consequence the membrane is usually less swollen than when in contact with a liquid feed. As the feed mixture getting in contact with the membrane is already in the vapor phase no phase change occurs across the membrane and thus no temperature polarization will be observed. Concentration polarization, however, is still an issue. Although the diffusion coefficient is much higher in a vapor than in a liquid, this is at least partially outbalanced by the lower density of the vapor, and therefore concentration polarization effects may be observed at all concentrations of the component to be removed. Minimum... 

The flux in pervaporation can be described by Pick s law. Derive for a component the concentration in the membrane as a function of the distance (i.e. the concentration profile) in a steady-state process for a system with a constant difiusion coefficient and with an exponential diffusion coefficient and draw these concentration profiles. Derive an equarion for the concentration dependent diffusion coefficient as a function of the distance in the membrane and draw this diffusion profile. 

An overview of mass transfer correlalion.s in membrane processes can be found in ref. J In microflltration and ulirailllration. the diffusion coefficients of the retained macromolecuies, or suspended panicles are small relative to those which apply to the retained components in reverse osmosis, gas separation and pervaporation. In addition, the fluxes in microflltration and ultrafiltration are large relative to those in pervaporation and gas separation. Hence, the consequences of concentradon polarisation in the case of microfiltradon and ultrafiltration are very severe. The consequences of fouling will be discussed later. 

Profiles in which this latter profile can be found are electrodialysis, per/aporation, gas separation, dialysis, diffusion dialysis, facilitated transport or carrier mediated transport and membrane contactors. The extent of the boundary layer resistance varies from process to process and even for a specific process it is quite a lot dependent on application. Table Vn.2 summarises the causes and consequences of concentration polarisation in various membrane processes. The effect of concentration polarisation is very severe in microfiltration and ultrafiltration both because the fluxes (J) are high and the mass transfer coefficients k (= EV8) are low as a result of the low diffusion coefficients of macromolecuiar solutes and of small particles, colloids and emulsions. Thus, the diffusion coefficients of macromolecules are of the order of lO ° to 10 m /s or less. The effect is less severe in reverse osmosis both because the flux is lower and the mass transfer coefficient is higher. The diffusion coefficients of low molecular weight solutes are roughly of the order of 10 m /s. In gas separation and pervaporation the effect of concentration polarisation is low or can be neglected. The flux is low and the mass transfer coefficient high in gas separation (the diffusion coefficients of gas molecules are of the... 

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. 

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. 

Reverse osmosis and pervaporation are able to separate molecules of similar size, such as sodium chloride and water. In such cases, the affinity between the membrane and the target component is important, as the speed of permeation through the membrane. Components that have a greater affinity for the membrane material dissolve in the membrane more easily than other components, cansing the manbrane material acts as an extraction phase. Differences in diffnsion coefficients of components throngh the membrane allow the separation. According to the theory of solution diffusion, solubility and diffusivity together will control the manbrane selectivity. The mechanism by which NF membranes act is... 

For water permeation, the measurements were carried out by using a pervaporation method. This differential permeation method allow to obtain the diffusion and permeability coefficients by taking into account the exposed area of the film and the vapor pressure difference across the two sides of the film. 

This shows that pervaporation depends on two sources of selectivity. The first source, given in the square brackets, is the relative permeability across the membrane. As expected, this relative permeability is the product of diffusion and partition coefficients. Second, the selectivity of the pervaporation is influenced by the relative volatility given in the braces. This volatility, a thermodynamic factor, is independent of any dynamic concerns. This combination of dynamic and equilibrium factors explains why the less volatile species may be concentrated in the permeate stream of a pervaporation process. 

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