Diffusion through a flat membrane

One-dimensional diffusion through a flat membrane will be treated in the following discussion. The effects of membrane asymmetry will be neglected since the process of permselection occurs in the thin dense layer of effective thickness, Z, at the membrane surface. In such a case, the expression for the local flux of a penetrant at any point in the dense layer can be written as shown in Equation 1 C14) ... 

Simple diffusion from a flat surface through an unstirred layer 0.025 cm thick would result in a solute permeability 20-10 cm/s. Thus, the value of computed for this model, 5.5-10 cm/s, signifies that solute transport into an interspace bounded by a basement membrane retards its diffusion from the region adjacent to the cell membrane by a factor of four. The permeability can also be translated into an electrical resistance, R, by use of the formula... 

The third main class of separation methods, the use of micro-porous and non-porous membranes as semi-permeable barriers (see Figure 2c) is rapidly gaining popularity in industrial separation processes for application to difficult and highly selective separations. Membranes are usually fabricated from natural fibres, synthetic polymers, ceramics or metals, but they may also consist of liquid films. Solid membranes are fabricated into flat sheets, tubes, hollow fibres or spiral-wound sheets. For the micro-porous membranes, separation is effected by differing rates of diffusion through the pores, while for non-porous membranes, separation occurs because of differences in both the solubility in the membrane and the rate of diffusion through the membrane. Table 2 is a compilation of the more common industrial separation operations based on the use of a barrier. A more comprehensive table is given by Seader and Henley.1... 

According to assumptions and concentration profiles, illustrated in Fig. 2.1 A, solute being extracted through a hydrophobic flat membrane can be described by the solute flux from the bulk aqueous phase to the bulk organic phase in terms of individual mass-transfer coefficients at steady state and additivity of a one-dimensional series of diffusion resistances. Overall mass-transfer coefficient, Ap/p ... 

Zaspalis conducted a theoretical study of an asymmetric membrane with a thin, small-pore toplayer on a large-pore support, in both flat and tubular geometries for the simple isothermal reaction A - B. The best conversion was in the case where all of the catalyst was near the outer surface of the toplayer, on the reactant side. In fact, for this reaction, reactant loss meant that the membrane reactor did worse than the fixed bed reactor. He also claimed that the optimal distribution is a delta function, for both geometries, for all possible kinetics, when diffusion of a reactant occurs from one side only. For segregated reactants, for the reaction A + B - C as illustrated in Figure 22, the optimal location of the catalyst was at the toplayer/support interface, assuming that diffusion was the only transport mechanism through the support. 

Suppose a solution flows through a channel between two flat membranes placed in parallel. Assume that the membrane width is much larger than the distance between the two membranes. The solution permeates both the upper and the lower membranes (Figure 8.1). The solution flow is therefore considered to be restricted to x-y directions on Figure 8.1 and to be symmetric on both sides of the center line. Assume also that the solution flow is laminar, and the effect of the convective flow can be neglected. Furthermore, the diffusion constant of the solute. Dab (m /s), is assumed to be independent of the solute concentration, and the solute concentration at the channel inlet is assumed to be cj (mol/m ) over the entire cross-section of the channel inlet. The mass balance of the solute can then be established as follows. Considering a square-shaped area of dxdy as shown in Figure 8.2, which has a 1 — m depth in the z direction. 

Once the formulation is established, asymmetric membranes can be cast as flat sheets or spun (extruded through a spinneret) into fiber form, followed either by an evaporation step or directly submerged into the quench bath. In this quenching process, the nonsolvent penetrates the membrane and the solvent diffuses out into the quench bath. The entering nonsolvent causes the phase separation of the membrane with the porosity being formed by the domains of polymer lean phase, which are washed out of the final membrane structure. For mixed-matrix membranes, it is believed that defects (sieve-in-cage) can form due to the nucleation of nonsolvent-polymer lean phase around the DP during the phase separation. One successful... 

As expected, glucose was freely permeable through the membranes while insulin was somewhat less permeable and albumin was impermeable. The membranes exhibited superior permeability characteristics. Membranes with higher Mc,hydrophiiic were more permeable to insulin. In comparison, the diffusion coefficients of glucose and insulin through membranes prepared with poly(hydroxyethyhnethacrylate) as the hydrophilic segment were only 0.042 and 0.009 X 10 (cm /sec) respectively (15). Earlier diffusion studies performed with different MA-PEB-MA membranes formed into flat membranes (15,18) gave very similar results as described herein for tubules. Our results for insulin permeability and diffusion indicate that the membranes and the tubules are satisfactory for use in an artificial pancreas biodevice. On the basis of these results the A-10-40 network was chosen for further in vitro and in vivo experiments. 

From studies of lipid-water mixtures and isolated membranes the general functional features of the bilayer are known barrier properties, lateral diffusion, acyl chain disorder and protein association. To vmderstand the mechanisms behind a wide spectrum of membrane functions, a detailed picture at the level of local curvature is needed. Examples are fusion processes, cooperativity in receptor/ligand binding or transport through the bilayer of the proteins that are constantly synthesised for export from the endoplasmic reticulum. Some preliminary discussions of the possibilities of curved, rather than flat, membremes follow. 

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