Microporous membranes porous wall

In the analysis of fluid flow in microporous membrane tubes and channels, it is tacitly assumed that the no-shp boundary condition that characterises flows with sohd bounding walls is apphcable. This postulate is incorrect because the surface velocity at a porous waU is in fact not zero but proportional to the shear rate at the permeable boundary, i.e. 

Microporous membranes have larger specific surface than plain (non porous) membrane. Assuming that micropores are cylindrical it is possible to calculate a rough approximation of the gain in the active surface. In fact, the total surface is greater than calculated because the walls of the pores are not smooth. The total surface depends on the number of pores per square centimeter, the pores diameter and the thickness of the membrane. It can be expressed as ... 

If the membrane happens to be porous (or microporous) and uncharged, the nature of the liquid-membrane equilibrium will be determined by the relative size of the solute molecules with respect to the pore dimensions in the absence of any specific solute-pore wall interaction. Similar considerations are also valid for liquid-porous sorbent equilibria. If the solute dimensions are at least two orders of magnitude smaller, then the solute concentration in the solution in the pore should be essentially equal to that in the external solution. However, the solute concentration in the porous membrane/porous sorbent/gel will be less than that in the external solution due to the porosity effect. Assuming that the solute exists only in the pores of the memhrane/porous sorbent with a porosity e , the value of kirn should be equal to the membrane or sorbent porosity e if the solute characteristic dimensions are at least two orders of magnitude smaller than the radius of the pore. 

When the catalyst is immobilized within the pores of an inert membrane (Figure 25.13b), the catalytic and separation functions are engineered in a very compact fashion. In classical reactors, the reaction conversion is often limited by the diffusion of reactants into the pores of the catalyst or catalyst carrier pellets. If the catalyst is inside the pores of the membrane, the combination of the open pore path and transmembrane pressure provides easier access for the reactants to the catalyst. Two contactor configurations—forced-flow mode or opposing reactant mode—can be used with these catalytic membranes, which do not necessarily need to be permselective. It is estimated that a membrane catalyst could be 10 times more active than in the form of pellets, provided that the membrane thickness and porous texture, as well as the quantity and location of the catalyst in the membrane, are adapted to the kinetics of the reaction. For biphasic applications (gas/catalyst), the porous texture of the membrane must favor gas-wall (catalyst) interactions to ensure a maximum contact of the reactant with the catalyst surface. In the case of catalytic consecutive-parallel reaction systems, such as the selective oxidation of hydrocarbons, the gas-gas molecular interactions must be limited because they are nonselective and lead to a total oxidation of reactants and products. For these reasons, small-pore mesoporous or microporous... 

Transfer mechanisms involved in SC CO2 permeation through such porous membranes can be convection (Poiseuille law), diffusion (Knudsen flow), and surface membrane interaction by adsorption, capillary condensation, etc. [11]. Mechanisms have been specifically investigated for nanofiltration and zeolite membranes. With a nanofilter presenting a pore diameter of about 1 nm, Sarrade [11] mentioned a Poiseuille flow associated with an irreversible CO2 adsorption on the micropore wall. Transfer... 

Fig. 12.12. Influence of zeta-potential (Stem-layer thickness 1) and Streaming-potential (electrokinematic flow) on ion rejection and volume flux for porous ceramic membranes exhibiting negatively charged pore walls. Cases of micropores (nanofiltration), mesopores (ultrafiltration) and macropores...

A microporous hollow fiber supported liquid membrane (HFSLM) module consists of a bundle of porous hollow fibers with thin walls which can be wetted by the membrane liquid. Initial studies of hollow fibers were made with a single fiber and the aqueous feed and strip solutions were passed through the lumen and over the shell side of the hollow fiber (29). This was followed by a hollow fiber module containing a bundle of fibers in which organic and feed phases were passed through... 

A very common column configuration in elution chromatography is simply a tuhular column packed with porous particles, the packings, with or without a bonded liquid phase on the particle surfiices. Other column configurations include capillary columns or open tubular columns, in which a thin hquid film of adsorbents has been applied (or bonded) to the internal surface of the capillaries. A potential variation of this is the microporous hollow fiber membrane based column, wherein the stationary phase is heid in the pores of fiber wall and the eluent is passed through the bore of the fiber (Ding et al., 1989). 

Table 2.7 summarizes some of the dehydrogenation reactions studied in the literature using porous MRs. As can be seen, the membranes for dehydrogenation reactions are primarily microporous silica due to it high hydrogen perm-selectivity. Meso- or macroporous membranes are not suitable for dehydrogenation reactions because their low perm-selectivity may lead to much loss of the reactants. The catalysts for dehydrogenation may be packed in the reactor or loaded inside the membrane wall. All the studies demonstrate enhanced conversions or even beyond-equilibrium values. 

The different situations that can be encountered analysing the permeation of molecules through a porous membrane are reported below. When the pore diameter of a porous solid is in the macropore range, collisions between the molecules will occur much more frequently than collisions with the wall. In this case molecular diffusion is the dominant mechanism. As the size of the pores decreases (mesoporous solid), the number of collisions with the wall increases and can become more frequent and important than the molecule-molecule colUsions. At this point, Knudsen diffusion takes over. When the pore diameter becomes comparable to the size of the molecules (microporous solid), the molecules continuously collide with the walls. When this happens, diffusion behaves as an activated process and the term configurational regime is used to describe it. 

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