Particle spaces

Fig. 10.9. The gradual increase of particle spacing with ageing time.

Reciprocal square root of grain size and particle spacing. mm... 

Figure 5.6. Yield strength in relation lo grain size or particle spacing (courtesy of H.E. Exner).

These equations are based on the assumption of zero particle space charge. In practice, however, charged particles can significantly affect the electric field... 

Fluidised beds have been used previously for the industrial-scale recovery of the antibiotics streptomycin and novobiocin.30 However, more recently, considerable interest has been shown in the use of fluidised beds for the direct extraction of proteins from whole fermentation broths.31 In a packed bed, the adsorbent particles are packed within the contactor. The voidage, that is, the inter-particle space, is minimal and thus feedstock clarification is mandatory to avoid clogging of the bed. In a fluidised/expanded bed, the adsorbent bed is allowed to expand by irrigation with feedstock. Bed voidage is increased, allowing the passage of particulates in the feed. The diameters of the adsorbent beads are exaggerated for illustrative clarity. 

We have discussed our theoretical calculations on metals ranging from very accurate ab initio studies of diatomic and triatomic systems to model studies of larger clusters. Recent improvements in the accuracy to which we can represent both the one-particle and n-particle spaces has significantly improved the reliability of theoretical calculations on small molecules. For example, we are able to predict definitively that AI2 has a Hu ground state even though the state lies within 200 cm . Calculations on clusters indicate that their geometry varies dramatically with cluster size, and that rather large clusters are required before the bulk structure becomes optimal. Since clusters are more... 

Fig. 5.5.7 A 2D slice through a H 3D MR image of the fixed-bed of catalyst particles. The catalyst particles appear as black fluid within the inter-particle space is indicated by lighter shades. Chemical conversion within ten selected volumes within each of the three transverse sections indicated is investigated in Figures 5.5.9-5.5.11. The direction of superficial flow (z) is also shown. Reproduced with permission from Ref. [24], copyright Elsevier (2002).

In these studies, chemical conversion was determined in situ by measuring the lH resonance associated with OH groups present. In practice two such resonances exist associated with chemical species inside and outside the catalyst particles, respectively. The difference in chemical shift between these intra- and inter-particle species arises because of the different electronic environment of the molecules inside the catalyst particles compared to their environment in the bulk fluid in the inter-particle space. In this work, chemical conversion was determined from the MR signal acquired from species in the inter-particle space of the bed because the signal from inside the catalyst particles is also going to be influenced, to an unknown extent, by relaxation time contrast. In addition to possible relaxation contrast effects, there will also be modifications to the chemical shifts of individual species resulting from adsorption onto the catalyst this may cause peak broadening and reduces the accuracy with which we can determine the chemical shift of the species of interest. As follows from eqn (11) which describes the esterification reaction of methanol and acetic acid to form methyl acetate and water ... 

Besides the simplest types of hierarchical organization shown in Figure 9.25, structures with three and more scaling levels are possible. In general, for corpuscular PSs, the shape of psd is determined by PSD and particles space arrangement (PSA). The situations corresponding to the interrelation of PSD and PSA can be classified by a scheme shown in Figure 9.26. 

Figure 9.26 The scheme of the simple interrelation of pore size distributions (psd), particle size distributions (PSD), and particles space arrangement (PSA).

The relationship between particle spacing and mass concentration for particles in a cubical array is given by... 

Table IV indicates the magnitude of particle spacings corresponding to various concentrations assuming a cubical array and a particle density of 1 gm/cm3.

Particle concentration Cp Particle spacing in cubical array (LI Dp)... 

Table VI shows values of ksA, ksR, ksg, ksE, and k as given by Russell (R9) for various particle spacings.

As it has been discussed in previous section, from a practical point of view1, and also for comparison between adsorbents, hydrogen adsorption capacities should be reported in a volumetric basis, which makes necessary to know the sample density. Unfortunately, papers reporting hydrogen adsorption capacities of MOFs in volumetric basis use the crystal density of the materials, which is not realistic for this application because it does not include the inter-particle space. Crystal densities of MOFs can vary between 0.2 and 1.3 g cm 3 36 39, and similar to what happens with tap and packing densities of carbon materials, crystal densities of MOFs decreases when porosity increases. Therefore, as in the case of carbon materials (see Figure 5) a maximum is observed when the hydrogen uptake in volumetric basis is plotted versus the porosity of the MOFs samples, and a compromise between density and porosity is necessary from a practical point of view. 

Continually irradiated by photons and bombarded by high-energy particles, space is radioactive. The only relatively sheltered regions are perhaps those at the heart of dense molecular clouds, as attested by their extremely low temperatures (3-30 K). 

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