Inter-particle spacing

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. 

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 ... 

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. 

Fig. 15. 2-D slice sections through 3-D MR images of water distribution within an initially water-saturated packing of 500-pin glass spheres. Voxel resolution is 94 pm x 94 pm x 94 pm. Data are shown before drying commenced and at three time intervals during the drying process. Only the water within the inter-particle space of the bead packing was imaged (white pixels). No signal was obtained from the solid and gas phases present.

Fig. 23. MR visualization of water flowing within a fixed bed of spherical glass beads the beads have no MR signal intensity associated with them and are identified as black voxels. Flow velocities in the (a) Z-, (b) x-, and (c) y-directions are shown with slices taken in the xy, yz, and vz planes for each of the velocity components. In each xy-image the positions at which the slices in the other two directions were taken are identified. Voxel resolution is 195 pm x 195 pm x 195 pm. The glass beads were of diameter 5mm and were packed within a column of internal diameter 46 mm. Typically, 40% of the flow was carried by approximately 20% of the inter-particle space within any 2-D slice section through the bed, perpendicular to the direction of superficial flow. Regions of high- and low-flow velocity in the direction of superficial flow are highlighted in (a). Reprinted from reference (77), with pennission from Elsevier, Copyright (2001).

Fig. 24. Velocity profile for flow of water through two different regions (highlighted in Fig. 23a) of the inter-particle space within a fixed bed of spherical glass beads. The velocity profiles are measured across the inter-particle space between two packing elements. Profiles are shown for local regions associated with fast and slow fiow velocities, characterized by a local Re of 50 and 12, respectively. At low...

Fig. 40. 2-D slice through a 3-D RARE image of a fixed bed of ion-exchange resin. The image has an isotropic resolution of 97.7 pm x 97.7 pm x 97.7 pm. The image slice in which the local volumes are located for the volume-selective spectroscopy study is identified. The image was acquired by saturating the bed with pure methanol. r2-contrast was exploited in the data acquisition so that signal was acquired only from the methanol in the inter-particle space. Reprinted from reference (84 with permission of Springer Science and Business Media.

Fig. 42. Ti-resolved propagators for water flowing within the inter-particle space of a bed packed with ion-exchange resin ( ) and for water exchanging between inter- and intra-particle environments ( ) during the time scale of the transport measurement. Data are shown for a volumetric feed flow rate of 2inl,inin. to a column of internal diameter 20 mm. Reprinted from reference (J32) with permission from Elsevier, Copyright (2003).

In Fig. 42, the full-width at half maximum of the (narrower) exchange propagator provides an estimate of the effective diffusion coefficient of water molecules moving between the pore space of the catalyst and the inter-particle space of the bed. In this example, the value is 2 x lO- m s which gives a lower limit to the value for the mass transfer coefficient of 4x 10 ms This value was obtained by defining a mass transfer coefficient as Djd where d is a typical distance traveled to the surface of the catalyst that we estimate as half a typical bead dimension (approximately 500 pm). This value of the mass transfer coefficient is consistent with the reaction occurring under conditions of kinetic as opposed to mass transfer control. 

We recall that Bose-Einstein condensation is the macroscopic occupation of the ground state of a system at finite temperature. For a weakly interacting gas, this phase transition occurs when the inter-particle spacing becomes comparable to the thermal de Broglie wavelength A = /2nh /mkBT, where ks is the Boltzmann constant and T is the temperature. A rigorous treatment for the ideal Bose gas yields n > 2.61221 , where n is the density [35]. At a temperature of 50 yuK, for instance, the critical density for hydrogen is 1.8 x 10 cm. ... 

Of course, many suspensions are also shear thinning. For example, when tp > 0.3, viscosity becomes a function of shear rate, since the shear rate is high enough to disturb the inter-particle spaces from their equilibrium. Kreiger (1972) developed the following expression to account for shear thinning ... 

Such relatively simple kinetic models also allowed one to analyze simultaneously the development of radical processes and mass-transfer on different levels (inside catalyst pores, in inter-particle space, in reactor bulk—see for instance Bristolfi et al, 1992 Couwenberg, 1994 Hoebink et al, 1994 Reyes et al, 1993). This can be considered as another important achievement. 

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