Membrane pore radius

Microporous membranes (pore radius less than 10 A) are ideal materials to be used as separators in membrane reactor processes. Microporous membranes also combine the high selectivities to certain components with high permeation rates. The high selectivities mean that maximum conversions (and thus equilibria shifts) higher than those achieved by porous membranes can be attained, while the high permeation rates allow for high reaction rates... 

Figure 2.36 shows the effect of the ratio r/k on the relative proportions of Knudsen to Poiseuille flow in a cylindrical capillary [57], When r/k is greater than one, Poiseuille flow predominates. Because the mean free path of gases at atmospheric pressure is in the range of 500-2000 A, for Knudsen flow to predominate and a separation to be obtained, the membrane pore radius must be less than 500 A. 

These constants are best determined experimentally as the membrane stmcture is very complex and difficult to characterize, which makes the direct calculation impossible. However, estimates of the constants can be obtained from the membrane pore radius r, tortuosity t, and porosity s by assuming that the membrane contains uniform cylindrical pores and can be given as [39,43,59]... 

APc depends on the liquid surface tension, y, the liquid-solid (membrane) contact angle, 0 (greater than 90° for hydrophobic membranes), the membrane pore radius, r, and the pore geometry co-efficient, B, in accordance with the Laplace equation [Eq. (1)]. B has a value of 1 for cylindrical pores. The higher the liquid surface tension, the larger the contact angle, and the smaller the pore radius, the greater the pressure required for pore intrusion by the liquid. 

Figure 9. Effect of pressure on the (PR)/(PWP) ratio and solute separation of glucose and an imaginary solute. Membrane material, CA (E-398) membrane pore radius = 7.36 A feed flow rate = 400 cm /min feed concentration — 1 mol/m. ...

Equation (16b) describes the effect of membrane pore radius distribution on solute rejection. In the absence of available exper-... 

Schultz and Asunmaa (40) have suggested that there exists a salt-free 22 A thick liquid-crystalline hydration sheath lining the pores of both cellulose acetate and porous glass membranes, while Ohya, 1 have recently shown that salt rejection improves significantly with a decrease in membrane pore radius below 20-22... 

Knudsen diffusion and separation is based on the large difference between the mean free paths of the molecules and the membrane pore radius. The separation factor from Knudsen diffusion is the inverse square root ratio of two molecular weights, assuming the gas mixture consists of only two types of molecules. The process is limited to systems with large values for the molecular weight ratio, such as that found in H2 separation, and is commercially less attractive because of low selectivity. 

Where R is the membrane pore radius, directly measured by microscopy h, the thickness, which, in this case, is also the pore length W, the weight and N, the pore density... 

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