Permeability mass transfer expression

For each compound, a classical permeability mass transfer expression, which makes use of the compound permeability in the membrane material, P, is written ... 

Permeability A rate of mass transfer, usually expressed per unit surface area. For Fickian diffusion in a membrane, the permeability is proportional to the diffusion coefficient and inversely proportional to the membrane thickness. 

The lattice model of mass transfer gives self-consistent expressions for sorption isotherms and permeability coefficients for microheterogeneous membranes of variable thickness at an arbitrary degree of filling. The parameters of the lattice model can be related to the molecular structure of a matrix and to the parameters of the interaction between diffusant and matrix [191]. The lattice model can serve as a basis to construct phenomenological models, which are capable of describing the features of a molecular system diffusant-membrane matrix . 

Consider a solid plane wall (medium B) of area A, thickness L, and density p. The wall is subjected on both sides to different concentrations of a species A to which it is permeable. The boundary surfaces at.t = 0 and x - L are located within the solid adjacent to the interfaces, and the mass fractions of A at those surfaces are maintained at and 2. respectively, at all times (Fig. 14-19). The mass fraction of species A in the wall varies in the. v-direction only and can be expressed as >v (.t). Therefore, mass transfer through the wall in this case can be modeled as steady and one-dimensional. Here we determine the rate of mass diffusion of species A through the wall using a similar approach to that used in Chapter 3 for heat conduction. 

The ASTM standards adopt definitions that are consistent w ith the equivalent definitions for gas transmission. Water vapor transmission rate is the mass transfer rate of water vapor per unit area (g nr 24h). Permeance is the ratio of the water vapor transmission rate to the difference in vapor pressure between the surfaces of the test piece measured in mm of mercury this unit is known as the metric perm (g nr 24h mmHg). This is equivalent to the gas transmission rate. Permeability is the product of the permeance and the thickness of the test piece, assuming that the permeance is inversely proportional to thickness for homogeneous materials this unit is known as the perm-centimetre (g cm nr 24h mmHg). Since the adoption of SI units, the water vapor permeability may also be expressed in the units of microgram meter per newton hour (pgm N h or pgm m Pa h ). 

Here, kQ is the mass transfer coefficient describing the diffusion resistance and H represents the membrane permeability. Following [129], an expression can be derived relating the film effectiveness factor to these two dimensionless variables. High values of O indicate high mass transfer resistance of the film compared to the membrane and thus strong concentration polarization. 

There has been significant progress made recently in the fabrication of FO membranes. While these were not specifically tested for PRO operation (e.g. permeation rates under pressurized conditions), their estimated potential performance may be calculated based on the experimentally determined characteristics, namely, the water and salt permeabilities of the filtering layer and the mass transfer resistance of the support to diffusive transport. Membrane permeability is expressed in m/s-Pa and measures the water volume flow rate permeated across a membrane area unit under a 1 Pa osmotic pressure difference between the membrane sides. High values of water permeability denote the membrane capability of avoiding resistance to water flux. 

Expression 2.14f and Expression 2.14g are used particularly for the determination of the mass transfer coefficient, assuming that values of K and Q have been determined independently. This can be done in the usual fashion by making a semilog plot of the concentration fraction in Equation 2.14e against the reciprocal 1/Q, i.e., by rurming a series of experiments at different volumetric flow rates Q. For clearance experiments, Cb is set equal to zero. The slope of the plot then yields the product k Ji. Because detailed anatomical information for the determination of the interfacial area A is rarely available, we must be content to deal with the product k itself. That quantity, however, is still highly useful because it provides a measure of the overall permeability of the tissue-capillary interface. 

The product, DimKim, is a permeability coefficient of solute i through the membrane of thickness Sm- The product Di Ki /d ) has been called the solute transport parameter in reverse osmosis literature (Sourirajan, 1970). Expression (3.4.59) is an integrated flux expression for solute transport through a reverse osmosis membrane in terms of the differences in concentrations of the external solutions and a mass-transfer coefficient-like quantity DiinXim/ m). 

We can use Faxen s expression (3.1.112e) for GDr Ti,Tp) as long as (ri/fp) < 0.5. Further, Kt may be obtained from relation (3.3.88a). The membrane mass-transfer coefficient and the permeability coefficient in the case of hindered ditfiision and geometrical partitioning are defined as follows ... 

Direct-Contact Membrane Distillation Configuration If the mean free path of the transported molecules is large in comparison with the membrane pore size (i.e., Kn > 1 or dp < X.,)> the molecule-pore wall collisions are dominant over the molecule-molecule collisions, and the Knudsen type of flow is responsible for mass transfer through the membrane pore. In this case the permeability through each pore in the Knudsen region was expressed as follows (Matsuura, 1994 Khayet et al., 2004a) ... 

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