Interstitial voidage

Note. tora-particle pores are pores within the particle. Inter-particle (interstitial) voidage refers to space between the particles, i.e. in the interstices of the packing. 

As the ligand-protein interaction takes place at the internal surface of porous adsorbents, kinetics and equilibrium of the interaction should be independent of the interstitial voidage within an adsorbent bed. Therefore the equilibrium capacity of an adsorbent will not be influenced by different experimental configurations e.g. batch stirred tank, batch fluidized bed, frontal application to packed or fluidized beds. The major difference arises from the medium from which the protein is isolated. As fluidized beds are used for whole broth adsorption, the properties of the broth have to be considered regarding the possible influence of components which are removed in conventional primary recovery steps and therefore are not present during the initial chromatography operations in a standard downstream process. These are on one hand nucleic... 

Figure 16(a). The term Cohesionless was therefore used to describe materials which have a negligible shear strength under zero normal load (an = 0). On the other hand, Jenike found that the yield loci of cohesive materials differ significantly from a straight line and have a nonzero intercept, indicated by C. Moreover, the position of the locus for a cohesive powder is a strong function of the interstitial voidage of the material. Fig 16(b) shows the typical yield locus for cohesive materials. 

As with bulk density, permeability is a function ofpacking voidage and its uniformity, and in practice, it is best measured. It can vary substantially with previous compaction of the sample. An example is the change in bulk density—and therefore interstitial voidage—that occurs with a material as it moves through a hopper. By applying a load to the upper surface of the bed, permeability may be also determined as a function of solids consolidation pressure (see Bulk Flow Properties ). Permeability is a decreasing function of applied solids pressure, and bulk density is often written in log form, or... 

Initiating and sustaining the flow of a fine powder bed is impeded by the differential between the pressure in the interstitial voidage of the particles and ambient pressure as the bulk expands to commence flow, and also as it expands further during travel along the flow path. Figure 3.14 illustrates the influence of interstitial pressure on flow through an orifice. 

The interstitial spaee existing between a mass of partieles ean also be important e.g. in retaining filtrate liquor whieh may lead to oeelusions if overgrown, and lienee the partieulate voidage or void fraetion , e, is defined, as follows. 

The voidage (e) of abed of particles is the fraction of the bed volume occupied by the interstitial space between the particles. Its value depends upon the geometrical configuration of the beads, the pattern in which they are arranged within bed, the size distribution of the particles and the ratio of mean particle and contactor diameter. The bed voidage can be calculated using the following equation ... 

At any level in the transition region, there will be a balance between the mixing effects attributable to (a) axial dispersion and to (b) the segregating effect which will depend on the difference between the interstitial velocity of the liquid and that interstitial velocity which would be required to produce a bed of the same voidage for particles of that size on their own. On this basis a model may be set up to give the vertical concentration profile of each component in terms of the axial mixing coefficients for the large and the small particles. 

Here uR is the velocity at which the solute band moves along the column and u is the velocity of the mobile phase that is, u = (superficial velocity)/e, where superficial velocity is volumetric flow rate divided by cross-sectional area of column and s is the fractional volume of column occupied by mobile phase. Most column packings are porous, in which case s includes both interstitial and pore (intraparticle) voidage, as defined in the note to Table 19.1, and here u is less than the interstitial velocity. 

If now the cross-sectional area which determines the interstitial velocity for a given volumetric flow rate is proportional to the interparticle voidage, it follows that... 

Dl is the axial dispersion coefficient, z distance, v the interstitial fluid velocity, and the voidage of the adsorbent bed) together with the adsorption rate expression for each component, which can be written in the general form ... 

Figure 7.7 Normalised interstitial velocity versus voidage. The closed symbols are experimental measurements. The inviscid prediction (7.48), is plotted as a full line, while the wake corrected model (7.49) is plotted as open symbols.

In the equations above, subscript i denotes a gas species, subscript j represents a specific step t denotes time z is bed axial distance c is gas phase mole fraction q denotes adsorbed phase mole fraction i is reaction stoichiometry for the species / , is the rate of reaction v is interstitial fluid velocity vq is inlet gas velocity Dz is dispersion coefficient k is LDF coefficient b is sorption coefficient e is bed voidage. For both the pressurization (j = 1) and the adsorp-... 

Particulate and Aggregative Fluidization. When the fluid phase is liquid, the difference in the densities of fluid and solid is not very large, and the particle size is small, the bed is fluidized homogeneously with an apparent uniform bed structure as the fluid velocity exceeds the minimum fluidization velocity. The fluid passes through the interstitial spaces between the fluidizing particles without forming solids-free bubbles or voids. This state of fluidization characterizes particulate fluidization. In particulate fluidization, the bed voidage can be related to the superficial fluid velocity by the Richardson-Zaki equation. The particulate fluidization occurs when the Froude number at the minimum fluidization is less than 0.13 [9],... 

Z)gd and Z)gj. are both assumed to be independent of position, and Ug r) is the local interstitial gas velocity. If the axial dispersion is much smaller than the radial dispersion, the axial dispersion term can be dropped (van Zoonen, 1962 Yang et al., 1983 Martin et al., 1992 Gayan et al., 1997 Namkung and Kim, 2000). Otherwise, one needs to fit both the axial and the radial dispersion coefficients, which can involve much higher uncertainties (Bader et al., 1988). The radial velocity profile, Mg(r), and local voidage, s, are required to fit the radial dispersion coefficient, but most studies have assumed a flat radial velocity profile in fitting Eq. (37) to tracer concentration profiles. 

Now assume that the dense (and wake) phase voidage remains constant at its minimum fluidisation value. If the voidage does not change then the permeability is unlikely to change and the interstitial gas velocity must be maintained at U if the bed is to remain fluidised without a net force lifting particles out of... 

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