Membrane transport coefficients

The intestinal permeability (Peff) is a major determinant of fraction drug absorbed, and quantitatively represents the principal membrane transport coefficient of the... 

A new type of configuration, the flowing liquid membrane (FLM) was studied by Teramoto et al. [20]. In this case, the membrane liquid phase is in motion as the feed and strip phase. In this type of system a plate-and-frame and spiral-wound configuration with flat membrane was used. The scheme of the FLM configuration is drawn in Fig. 7.3A. The hquid phase flows (FLM) between two hydrophobic microporous membranes. The two membranes separate the hquid membrane phase from feed and strip phases. In Fig. 7.3B, it is reported the classical plate-and-frame module employed for the separation of ethylene from ethane [20]. The liquid membrane convection increased the membrane transport coefficient in gas separation. However, the membrane surface packing density (membrane surface area/ equipment volume) is much lower in spiral-wound system than in hollow fiber. 

The membrane transport coefficients may be measured based on the equations and... 

Shah et al. [51] demonstrated the use of a donor-receptor compartment apparatus separated by a cell monolayer to estimate membrane transport parameters. Permeability coefficients, P, were calculated as... 

The side-by-side diffusion cell has also been calibrated for drug delivery mass transport studies using polymeric membranes [12], The mass transport coefficient, D/h, was evaluated with diffusion data for benzoic acid in aqueous solutions of polyethylene glycol 400 at 37°C. By varying the polyethylene glycol 400 content incrementally from 0 to 40%, the kinematic viscosity of the diffusion medium, saturation solubility for benzoic acid, and diffusivity of benzoic acid could be varied. The resulting mass transport coefficients, D/h, were correlated with the Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc) according to the relationships... 

In whole tissue or cell monolayer experiments, transcellular membrane resistance (Rm = Pm1) lumps mucosal to serosal compartment elements in series with aqueous resistance (R = P ). The operational definition of Lm depends on the experimental procedure for solute transport measurement (see Section VII), but its magnitude can be considered relatively constant within any given experimental system. Since the Kp range dwarfs the range of Dm, solute differences in partition coefficient dominate solute differences in transcellular membrane transport. The lumped precellular resistance and lumped membrane resistance add in series to define an effective resistance to solute transport ... 

Two distinguishing features of gastrointestinal active and facilitated transport processes are that they are capacity-limited and inhibitable. Passive transcellular solute flux is proportional to mucosal solute concentration (C), where the proportionality constant is the ratio of the product of membrane diffusion coefficient (Dm) and distribution coefficient (Kd) to the length of the transcellular pathway (Lm). 

When it comes to the equilibration of water concentration gradients, the relevant transport coefficient is the chemical diffusion coefficient, Dwp. This parameter is related to the self-diffusion coefficient by the thermodynamic factor (see above) if the elementary transport mechanism is assumed to be the same. The hydration isotherm (see Figure 8) directly provides the driving force for chemical water diffusion. Under fuel-cell conditions, i.e., high degrees of hydration, the concentration of water in the membrane may change with only a small variation of the chemical potential of water. In the two-phase region (i.e., water contents of >14 water molecules... 

Figure 18 shows the temperature dependence of the proton conductivity of Nafion and one variety of a sulfonated poly(arylene ether ketone) (unpublished data from the laboratory of one of the authors). The transport properties of the two materials are typical for these classes of membrane materials, based on perfluorinated and hydrocarbon polymers. This is clear from a compilation of Do, Ch 20, and q data for a variety of membrane materials, including Dow membranes of different equivalent weights, Nafion/Si02 composites ° ° (including unpublished data from the laboratory of one of the authors), cross-linked poly ary lenes, and sulfonated poly-(phenoxyphosphazenes) (Figure 19). The data points all center around the curves for Nafion and S—PEK, indicating essentially universal transport behavior for the two classes of membrane materials (only for S—POP are the transport coefficients somewhat lower, suggesting a more reduced percolation in this particular material). This correlation is also true for the electro-osmotic drag coefficients 7 20 and Amcoh...

Figure 19. Transport coefficients of diverse membranes based on perfluorinated polymers and Nafion/...

Instead of the dilute solution approach above, concentrated solution theory can also be used to model liquid-equilibrated membranes. As done by Weber and Newman, the equations for concentrated solution theory are the same for both the one-phase and two-phase cases (eqs 32 and 33) except that chemical potential is replaced by hydraulic pressure and the transport coefficient is related to the permeability through comparison to Darcy s law. Thus, eq 33 becomes... 

Figure 18. Profile of the net water transport coefficient through the membrane in the midchannel cross-section of a 36-channel fuel cell at 1/ceii = 0.65V and /avg = 0.91 A/cm. ...

Figure 13.9. Membrane permeability coefficience of solutes. Solute permeabilities across typical lipid bilayers of liposomes or lipid vesicles are presented as their respective coefficients in cm/s. In the absence of other transport processes, it would require 10 s to move Na+ across 1 cm distance. When there is a concentration difference across a membrane, multiplying the concentration difference (mole/ml equivalent to mole/cm ) by the permeability coefficient (cm/s) allows estimation of flow rate (mole/s-cm ). For example, a concentration difference of 1Q- mole/cm Na (or 1 x 10" M Na ) would provide a flow of 10 mole/cm x 10" cm/s = IQ- mole/s through 1 cm or 0.006 mole/s through 1 pm of a membrane bilayer.

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] ... 

In practice we measure changes in pressure and salt concentration, rather than chemical potential, and it can be helpful to think of transport coefficients in terms of Darcy flow and diffusion. We define xs = ns/(nw + ns), where nw, ns are the number of moles of water and salt, and write the change in chemical potential of salt across the membrane as... 

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