Knudsen permeabilities

The Knudsen permeability of a porous system of unit area and thickness is 8 2RT... 

A few publications have reported the permeation of capillary condensate in mesoporous materials. Caiman and Raal [14], measured permeability of CFiCb in Linde silica porous plugs at 240 and 251.5 K. Lee and Hwang [15], measured freon and water vapor permeabilities on vycor membranes. These permeabilities were found to exhibit maxima at relative pressures around 0.6-0.8, with values 20-50 times the Knudsen permeability. Ulhom et al. [16], reported a similar behavior for propylene at 263K in y-alumina membranes. Sperry et al. [17] demonstrated the ability of mesoporous y-alumina membranes in methanol separation at 473 K, provided the applied pressure... 

Let us now turn attention to situations in which the flux equations can be replaced by simpler limiting forms. Consider first the limiting case of dilute solutions where one species, present in considerable excess, is regarded as a solvent and the remaining species as solutes. This is the simplest Limiting case, since it does not involve any examination of the relative behavior of the permeability and the bulk and Knudsen diffusion coefficients. 

Classical commercial ceramic porous materials, as those obtained via sol-gel processes, generally have adequate permeabilities but could present some drawbacks They indeed have a limited thermal stability and are generally not permselective enough their pores are in the mesoporous range and maximum separation factors correspond to Knudsen diffusion mechanisms. 

In Figure 2 we presented the permeability coefficient K of oxygen as a function of the mean gas pressure experimentally obtained for a sample of porous material from acetylene black modified with 35% PTFE. The experimental linear dependence is obtained. The intercept with the abscissa corresponds to the Knudsen term DiK. The value obtained is 2,89.1 O 2 cm2/s. The slope of the straight line is small, so that the ratio K,/ Dik at mean gas pressure 1 atm. is small ( 0.1) which means that the gas flow is predominantly achieved by Knudsen diffusion and the viscous flow is quite negligible. At normal conditions (1 atm, 25°C) the mean free path of the air molecules (X a 100 nm) is greater than the mean pore radii in the hydrophobic material (r 20 nm), so that the condition (X r) for the Knudsen-diffusion mechanism of gas transport is fulfilled. 

In Figure 3, we have presented the experimentally obtained reciprocal values of (Di )t.ff of oxygen in a sample of the nano-porous hydrophobic material as a function of the total pressure P of gas mixture (02-N2) when the oxygen concentration in the mixture is 21%. From the intercept of the straight line with the ordinate the value of the Knudsen diffusion coefficient can be also determined. It must be underlined that the value of Knudsen diffusion coefficient obtained by these diffusion measurements (2,86.10"2 cm2/s) is in very good coincidence with the value obtained by the gas permeability measurements. 

Mitrovic and Knezic (1979) also prepared ultrafiltration and reverse osmosis membranes by this technique. Their membranes were etched in 5% oxalic acid. The membranes had pores of the order of 100 nm, but only about 1.5 nm in the residual barrier layer (layer AB in Figure 2.15). The pores in the barrier layer were unstable in water and the permeability decreased during the experiments. Complete dehydration of alumina or phase transformation to a-alumina was necessary to stabilize the pore structure. The resulting membranes were found unsuitable for reverse osmosis but suitable for ultrafiltration after removing the barrier layer. Beside reverse osmosis and ultrafiltration measurements, some gas permeability data have also been reported on this type of membranes (Itaya et al. 1984). The water flux through a 50/im thick membrane is about 0.2mL/cm -h with a N2 flow about 6cmVcm -min-bar. The gas transport through the membrane was due to Knudsen diffusion mechanism, which is inversely proportional to the square root of molecular mass. 

There are few studies in literature reporting pure gas permeabilities as well as separation factors of mixtures. Vuren et al. (1987) reported Knudsen diffusion behavior of pure gases for y-alumina membranes with a mean pore radius of 1.2 nm. Separation experiments with a 1 1 H2/N2 mixture showed, that the theoretical Knudsen separation factor [of 3.7, Equation 6.4)j for this mixture could be obtained (Keizer et al. 1988 see also Figure 6.2). In Figure 6.2, the effect of process parameters is also demonstrated. The separation factor is a function of the pressure ratio over the membrane, which is the ratio of the pressure on the permeate-side to that on the feed-side. For pressure ratios approaching unity, which means the pressure on both sides of the... 

Du 1986). This reflects the importance of smaU pores in order to apply effectively capillary condensation as a separation mechanism. Uhlhom (1990) demonstrated the effect of multilayer diffusion of propylene through a modified y-alumina membrane at 0°C. The separation factor for the N2/CjHg mixture was 27, where propylene is the preferentially permeating component, while the permeability increased to 7 times the Knudsen diffusion permeability. Although this mechanism appears to be very effective because of a high separation factor and a high permeability, it is limited by the obvious need for a condensable component. This in turn restricts the applicability range, due to limits set by temperature and pressure, needed for formation of multilayers or capillary condensation. 

In all cases studied, the membrane reactor offered a lower yield of formaldehyde than a plug flow reactor if all species were constrained to Knudsen diffusivities. Thus the conclusion reached by Agarwalla and Lund for a series reaction network appears to be true for series-parallel networks, too. That is, the membrane reactor will outperform a plug flow reactor only when the membrane offers enhanced permeability of the desired intermediate product. Therefore, the relative permeability of HCHO was varied to determine how much enhancement of permeability is needed. From Figure 2 it is evident that a large permselectivity is not needed, usually on the order of two to four times as permeable as the methane. An asymptotically approached upper limit of... 

It follows from Equation (2.107) that the permeability of a gas (/) through a Knudsen diffusion membrane is proportional to 1 The selectivity of this... 

The free parameters of this model are the ratio of porosity to tortuosity, e/r, the binary molecular diffusivities, D-j, the Knudsen coefficient, Ko (which determines specific effective Knudsen diffusivities, D j) and the permeability constant, Bo. 

As far as gas separations are concerned, and if only Knudsen processes occur, the effective separation factor (as experimentally measured) is equal to the theoretical permselectivity (ratio of the permeabilities of the pure gases). When processes involving interactions with the surface are important, separation factors generally differ from pcrmaselectivities. For example, if capillary... 

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