Roundness pore

Each vessel consists of numerous drumshaped vessel members with open ends, stacked one above the other to form a continuous vessel pipeline from root tips to the leaves. The vessels in oaks and some other broad-leaved trees are large enough to be seen with the unaided eye, that is, as round pores at the end surface and as needlelike grooves at the lateral surface (Fig. 28.2).4... 

As described in Sec. 35a, there are still many puzzling aspects of conf nra-tional diffusion that remain to be explained. About the only theoretical infcmna-tion available concerns the motion of spherical particles in liquids through cylindrical pores. Anderson and Quinn [71] have shown that the fective difiiirivity in straight, round pores (tortuosity t = 1.0) is given by ... 

Abstract Recently there has been much interest in the X-ray focusing properties of microch umel plates (MCPs). MCPs with both round and square pores have been shown to focus soft X-rays (Eraser ei al. Nucl.Inst.Meth.A 324 (1993) 404 and Nucl.Inst.Meth.A 334 (1993) 579). In particular, images have been obtained from point sources positioned at the foci of round-pore MCP X-ray lenses for 0.28-17.4 keV X-rays. A Monte Carlo ray trace model has been developed which gives good agreement with experimental images. 

Floe structure changes under different conditions, for example freezing and thawing produced more rounded pores [47]. Floe structure affects settleability and filterability. Some floes settle rapidly and others more slowly. For floes from two different sewage treatment plants, floes with fractal dimensions (determined using a two-point correlation function Section 8.2.4) of 1.9 and 1.8 settled more slowly than floes with fractal dimensions of 2.2 and 2.1 [47]. Differences in fractal dimension reflected different species compositions. Though the fractal dimension values reflect heterogeneity... 

Electron micrographs at very-high magnification by Pankratz reveal two kinds of structures in acid-cleaned silica from a radiolarian. According to Hurd (46b), who prepared the specimens. Figure 7.3 shows silica as 500 A thick lamina separated by open channels. The darker silica appears to consist of aggregated ultimate particles about 200 A in diameter. This would correspond to a specific surface area of 140 m g Figure 7.4 shows an apparently continuous matrix of silica (darker material) Hill of round pores or holes 20-500 A in diameter. 

Figure 7.4. A different area of silica shown in Figure 7.3, where the silica is a continuous matrix full of rounded pores (lighter areas) 20-500 A in diameter. [Courtesy of Hurd and Pan-kratz(46b).], , ...

Fig. 3 Macroporous Si with triangular pore arrangement (a, b) front view images of oxidized initially round pores under (a) optical and (b) electron microscopes, (c) front view of rounded-square-shaped pores after removal of the oxide, scale bar is 10 pm (Astrova et al. 2011) (With kind permission from Springer Science-i-Business Media), (d) broadening of symmetrically modulated pores upon their merging along the square comers, scale bar is 6 pm (Trifonov et al. 2008) (With permission from Elsevier, 2008)...

Fig. 5.26 SEM micrographs of several membrane surfaces reveal a range of pore structures that in turn result in a range of separation applications. An experimental, microporous, polyethylene membrane is shown (A) with elongated, stretched porous regions of various sizes, separated by fibrils, in the draw direction, and unstretched lamellae normal to the draw direction. This surface structure is quite different from three commercial membranes (B-D). One membrane (B) consists of a low density network of rounded pores, many of which are larger than 1 /im across. A nucleopore membrane (C) has more defined pore structure with rounded pores bored through from one side to the other. The morphology in (D) is an open network structure with the polymer in the form of strings of particles.

Fig. 5.35 The surface of a PTFE membrane imaged at 5 kV in an FESEM exhibits a non-imiform series of rounded pores, and a three dimensional nature as the pores extend into the bulk membrane. The surface of the membrane appears wrinkled in texture but imaging at lower magnifications, after high magnification imaging, did not reveal picture frame contrast that would suggest this texture is due to beam damage. (From M. Jamieson, unpublished [162].)...

Stomatal pores Round-pored Long-pored Mostly long-pored... 

Assume that each gram of catalyst contains np straight, round pores of radius r and length Lp. Since Vp is the volume of pores per gram of catalyst,... 

Here, I>A,p(r) is the diffusion coefficient of A in an assembly of straight, round pores that has the same distribution of pore sizes as the catalyst for which I>A,eff is to be calculated. The... 

The prediction of >A,p(r) in Eqn. (9-16) requires some understanding of how a molecule diffuses in a porous material. The nature of diffusion will depend on the size of the pores. Consider a straight round pore of radius r as shown below. The pore contains molecules of a fluid that are diffusing along the axial coordinate (z-dimension) of the pore. 

Knudsen Diffusion (Gases) Suppose that a gas is diffusing in a straight, round pore with a radius r that is much larger than molecular dimensions. The molecules in the pore will be in random thermal motion and will collide with other gas molecules and with the walls of the pore. The mean free path is defined as the average distance that a molecule travels before it collides with another molecule. The mean free path can be predicted approximately from kinetic theory, for a pure gas. 

Up to this point, attention has been focused on calculating diffusion coefficients in straight, round pores. The final challenge is to use this background to calculate DA.p(r) in Eqn. (9-16). Recall that DA.p(r) is the diffusion coefficient of A in an assembly of straight, round pores that has the same distribution of pore sizes as the catalyst. To perform this calculation, something must be known about the pore-size distribution y(r). 

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