Membranes Random packings

Amorphous silicas play an important role in many different fields, since siliceous materials are used as adsorbents, catalysts, nanomaterial supports, chromatographic stationary phases, in ultrafiltration membrane synthesis, and other large-surface, and porosity-related applications [16,150-156], The common factor linking the different forms of silica are the tetrahedral silicon-oxygen blocks if the tetrahedra are randomly packed, with a nonperiodic structure, various forms of amorphous silica result [16]. This random association of tetrahedra shapes the complexity of the nanoscale and mesoscale morphologies of amorphous silica pore systems. Any porous medium can be described as a three-dimensional arrangement of matter and empty space where matter and empty space are divided by an interface, which in the case of amorphous silica have a virtually unlimited complexity [158],... 

The regular structure of the arranged catalysts prevents the formation of the random maldistributions characteristic of beds of randomly packed particles. This reduces the probability of the occurrence of hot spots resulting from flow maldistributions. Scale-up of monolithic and membrane reactors can be expected to be straightforward, since the conditions within the individual channels are scale invariant. 

A defect in a porous layer on a porous support is a microstructural or textural feature which hampers application of a defect-free functional membrane layer. Defects are cracks or micro-cracks in the substrate layer, irregularities in surface roughness, pinholes or voids percolating the layer or large percolating pores as a result of the particle packing process. These last defects are not really defects because they are an unavoidable result of the particle size distribution in the dispersion and random packing. 

Mass transfer in fiber bundles is a problem of great practical importance for membrane separation processes. Such processes commonly utilize a bundle of randomly packed hollow fibers enclosed in a case to contact two process streams. Ports on the case permit one to introduce and remove streams from the space inside the fibers, the lumen, and the space outside the fibers, the shell. Figure 2.6 illustrates the construction of a typical hollow-fiber membrane module (Bao et al., 1999). 

L. Bao and G.G. Lipscomb, Mass transfer in axial flows through randomly packed fiber bundles, in New Insights into Membrane Science and Technology, D. Bhattacharyya and D.A. Butterfield, Eds., Elsevier, 2003. 

Figs. 4.37 and 4.38 show the time-averaged solids holdup distribution with gas extracted or added via the membranes at different positions. Fig. 4.37 clearly shows the effect of gas extraction causing the formation of very densified zones close to membrane walls. Here, the solids holdup can reach values up to the value of a random packed bed with monodisperse particles of the same type. However, analogous to the experimental results presented in Section 2.3.3.2, the term stagnant is not accurate since some movement of the particles is stiU detected, and hence densified zones is a more appropriate term. Even though particles close to membrane walls are... 

For the cases with gas permeation imposed via membranes built in the front and back walls, similar but much less pronounced phenomena can also be observed in Fig. 4.38 for the soHds holdup distribution, i.e., relative densified zones for the cases with gas extraction and relatively lower solids holdup close to the membrane walls for the cases with gas addition, especially for the cases with a high gas permeation ratio of 40%. Note that the very densified zones close to membrane walls, where the values of solids holdup are close to the value of a random packed bed with monodisperse particles of the same type, can be seen in the 140% — 40% (A) case but not in the 120% — 20% (B) case in Fig. 4.38. Close comparison of the sohds holdup distribution for the 140% — 40% (A) and 120% — 20% (B) cases tells that it is possible to avoid very high solids holdups close to membrane walls by increasing the membrane area. 

Structures at all relevant length scales, as described in Sections 34.2.1-34.2.4, can be classified further into organized and random packing stmetures. For dense materials, structural organization is expressed in the presence (or absence) of a periodic crystal lattice. For microporous materials there is a clear distinction between crystalline zeohtes and amorphous sihea with a very short range order. Zeohte membranes may consist of a three-dimensional mosaic of crystaUites that may be either randomly orientated with respect to each other or possess a certain preferred orientation or texture (Lai et al., 2003). The polycrystaUine nature of and presence of texture in zeohte membranes can have important consequences for flux and separation behavior. 

One can apply the MC technique to the same molecular model, as explored in MD. One can use the same box and the same molecules that experience exactly the same potentials, and therefore the results are equally exact for equilibrium membranes. However, MC examples of this type are very rare. One of the reasons for this is that there is no commercial package available in which an MC strategy is combined with sufficient chemistry know-how and tuned force fields. Unlike the MD approach, where the phase-space trajectory is fixed by the equations of motion of the molecules, the optimal walkthrough phase space in an MC run may depend strongly on the system characteristics. In particular, for densely packed layers, it may be very inefficient to withdraw a molecule randomly and to let it reappear somewhere else in... 

For the description of this flow, the Carman-Kozeny expression [16] can be applied, since the Hagen-Poiseuille equation is not valid, given that usually inorganic macroporous and mesoporous membranes are prepared by the sinterization of packed quasispherical particles, which develop a random pore structure [19]. In this case, the Carman-Kozeny factor for a membrane formulated with pressed spherical particles is [74]... 

Figure 9.3. Electron microscopy and electron crystallography of the nicotinic acetylcholine receptor (NAR). a NAR channels in liposome membranes. On the left, they are mostly randomly oriented (but some form a more regular pattern). On the right, a regularly packed two-dimensional crystal has formed. Such samples can be used to obtain a three-dimensional structure at low resolution by electron crystallography, b Electron crystallographic structure, represented as density contour maps. Left Top view. Middle, right Side view. The bilayer and the portions of the receptor protruding from it into both directions are visible. The arrow in the right frame points to the acetylcholine binding site.

Iversen et al. [6] found that for a polymer strucmre similar to the interstices between closely packed spheres (phase inversion membrane), Equation 38.4 is able to well describe the tortuosity-porosity relationship whereas for a polymer structure similar to random spheres or clusters (stretched membrane), Equation 38.5 has to be used. 

Pilot plant smdied have also been performed by Larsen et al. [37], who obtained stable operation and more than 95% SO2 removal from flue gas streams with a gas-side pressure drop of less than 1000 Pa. The importance of the membrane structure on the SO2 removal has been studied by Iversen et al. [6], who calculated the influence of the membrane resistance on the estimated membrane area required for 95% SO2 removal from a coal-fired power plant. Authors performed experiments on different hydrophobic membranes with sodium sulfite as absorbent to measure the SO2 flux and the overall mass-transfer coefficient. The gas mixture contained 1000 ppm of SO2 in N2. For the same thickness, porosity, and pore size, membranes with a structure similar to random spheres (typical of stretched membranes) showed a better performance than those with a closely packed spheres stmcture. 

Systems used in practice have a spongy structure (porous glass or carbon) or have the structure common in ceramic membranes. The latter have an interconnected, tortuous and randomly oriented pore network with constrictions and dead ends (Fig. 9.1) and are formed by packing of particles. 

Figure 12.32 The phase-transition, or melting, temperature (T ) for a phospholipid membrane. As the temperature is raised, the phospholi membrane changes from a packed, ordered state to a more random one.

A packed bed membrane reactor is an assembly of usually uniformly sized catalytic particles, which are randomly arranged and firmly held in position within a vessel or tube. A permeable membrane (generally tubular) is immersed within the particles or represents the tube wall of the fixed bed. The PBMR could look, for example, like a tube-in-shell or a multi-tubular reactor. Zooming in on the reaction zone the different phenomena occurring in the reactor can be described as follows ... 

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