Interstitial fraction

Interstitial fraction. eThe interstitial volume per unit of a packed column. 

The ratio of the pore fraction to the interstitial fraction has been used as a measure of quality of a size-exclusion column. It is the ratio of the useful volume to the unused volume in a column. However, a better measure is the pore fiaction itself. 

The interstitial fraction of an uncompressed bed of hard spherical particles packed by conventional packing technologies is 40 2%. When hydraulic radial compression is applied to such a bed, it readily densities until an interstitial fraction of 34 1% is obtained at 3 MPa. A further increase in... 

The improvements in bed uniformity and stabitity do not come for free. Accompanying the decrease in interstitial fraction is a decrease in permeability. From Equation (2.S1) we can calculate that a decrease in interstitial fraction from 40% to 34% should result in a decrease in permealnlity (san increase in backpressure) by a factor of 2. This has indeed been observed. 

Czok and Guiochon (18) examined a column prepared from well-aligned fibers made from porous glass obtained from PPG Industries, USA. The dense packing of the fibm leads to a very low interstitial fraction, 9% compared to 40% for a packed bed. If the fibers are 75% porous, one will find a ratio of pore volume to interstitial volume of about 7.5. The same ratio for a packed bed of equally porous particles would yield a ratio of about 1.1. One can see the potential advantage of the bed of fibers. Unfortunately, one can also predict that the low interstitial fraction will result in a low permeability. The efficiency of such a device cannot be predicted a priori, but the results reported were poor. We will discuss this device more in the following section, in which we deal with the evaluation of these alternatives to packed beds. 

Interstitial Fraction e. The interstitial volume per unit of packed column ... 

Thus, one must account for the interstitial fraction of the packed column. 

Leaching is the removal of a soluble fraction, in the form of a solution, from an insoluble, permeable sohd phase with which it is associated. The separation usually involves selective dissolution, with or without diffusion, but in the extreme case of simple washing it consists merely of the displacement (with some mixing) of one interstitial liquid by another with which it is miscible. The soluble constituent may be solid or liquid and it may be incorporated within, chemically combined with, adsorbed upon, or held mechanically in the pore structure of the insoluble material. The insoluble sohd may be massive and porous more often it is particulate, and the particles may be openly porous, cellular with selectively permeable cell walls, or surface-activated. 

Column Operation To assure intimate contact between the counterflowing interstitial streams, the volume fraction of liquid in the foam should be kept below about 10 percent—and the lower the better. Also, rather uniform bubble sizes are desirable. The foam bubbles will thus pack together as blunted polyhedra rather than as spheres, and the suction in the capillaries (Plateau borders) so formed vidll promote good liqiiid distribution and contact. To allow for this desirable deviation from sphericity, S = 6.3/d in the equations for enriching, stripping, and combined column operation [Lemhch, Chem. E/ig., 75(27), 95 (1968) 76(6), 5 (1969)]. Diameter d still refers to the sphere. 

In tire transition-metal monocarbides, such as TiCi j , the metal-rich compound has a large fraction of vacairt octahedral interstitial sites and the diffusion jump for carbon atoms is tlrerefore similar to tlrat for the dilute solution of carbon in the metal. The diffusion coefficient of carbon in the monocarbide shows a relatively constairt activation energy but a decreasing value of the pre-exponential... 

It is important to realize that all static phases will contribute to retention and, as a result, a number of different distribution coefficients will control the retention of the solute. Nevertheless, the situation can be simplified to some extent. The static interstitial volume (Vi(s)) and the pore volume fraction (Vp(i)) will contain mobile... 

F fraction of the static interstitial volume accessible to the solute... 

Since A V is composed of interstitial voids (between the fine particles), the weight fraction of fines in the total assembly is ... 

Thus, for a given particle loading, , the fine fraction in the bimodal assembly is a function of only the diameter ratio, dID a surprisingly simple result for an otherwise complex phenomenon. However, the inclusion of the liquid phase to the above particle assembly should modify the result somewhat. This can be seen very simply by expressing the interstitial particle population of the fines as a function of the continuous phase ... 

The basal metabolic rate for adults is 1 to 1.2 Calories/minute or 60 to 72 Calories/hour. This energy powers the movement of the chest during respiration and the beating of the heart—processes that are obviously necessary for life. However, a surprisingly large fraction of the BMR is used by cells to maintain ionic gradients between their interior and the fluid that surrnunds them (the interstitial fluid nr tissue fluid). 

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 ... 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

As is the case with assessments of the toxicity of dissolved trace metals, the development of sediment quality criteria (SQC) must be based on the fraction of sediment-associated metal that is bioavailable. Bulk sediments consist of a variety of phases including sediment solids in the silt and clay size fractions, and sediment pore water. Swartz et al. (1985) demonstrated that the bioavailable fraction of cadmium in sediments is correlated with interstitial water cadmium concentrations. More recent work (e.g., Di Toro et al, 1990 Allen et al., 1993 Hansen et al, 1996 Ankley et ai, 1996, and references therein) has demonstrated that the interstitial water concentrations of a suite of trace metals is regulated by an extractable fraction of iron sulfides. 

In this case, we use 6 as a small fraction since the actual number of defects is small in relation to the overall number of ions actually present. For the F-Center, the brackets enclose the complex consisting of an electron captured at an anion vacancy. Note that these equations encompass all of the mechanisms that we have postulated for each of the individual reactions. That is, we show the presence of vacancies in the Schottlqr case and interstitial cations for the Frenkel case involving either the cation or anion. The latter, involving an interstitlcd anion is called, by convention, the "Anti-Frenkel" case. The defect reaction involving the "F-Center" is also given. 

Experiments examined a chlorocatechol-contaminated sediment, and interstitial water prepared from it. These showed that the concentrations of total 3,4,5-tri- and tetrachloro-catechols (i.e., including the fraction that is released only after alkaline extraction) were apparently unaltered during prolonged incubation even after addition of cnltnres with established dechlorinating capability for the soluble chlorocatechols (Allard et al. 1994). 

Limiting Equations If the height of a foam-fractionation column is increased sufficiently, a concentration pinch will develop between the counterflowing interstitial streams (Brunner and Lem-lich, loc. cit.). For an enricher, the separation attained will then approach the predictions of Eq. (20-48) and, interestingly enough, Eq. (20-43). 

Where u, is the mobile phase velocity at the column outlet, Fg the column volumetric flow rate, and Ag the column cross-sectional area available to the mobile phase. In a packed bed only a fraction of the column geometric cross-sectional area is available to the mobile phase, the rest is occupied by the solid (support) particles. The flow of mobile phase in a packed bed occurs predominantly through the interstitial spaces the mobile phase trapped within the porous particles is largely stagnant (37-40). 

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