Voids relative fraction

FIGURE 14.13 The dependences of adaptability resource on voids relative fraction for componors UHMPE - A1 (1) and UHMPE - bauxite (2) [56],... 

Maintain geometrical similarity as much as reasonably possible. From practical procurement considerations, the smallest (about 1/8" for the HEM), least expensive, and most readily available mixers have relatively shorter elements (Le/D < 1) and lower void volumes (VF < 0.8) whereas plant-size units have relatively longer elements (Le/D ks 1.5) and larger void volume fractions (VF = 0.9). Thus, if needed, scale-up may be accomplished by breaking geometrical similarity, but deviate only as needed. 

The apparent density p of the cell wall of wood has also been measured by optical methods. In this case the relative fractions of void and cell-wall volumes are determined optically by using thin microtomed sections of wood (29). These data are then combined with measurements of the dry wood density p to give p, based on Equation 4. 

Gas adsorption (N2, Kr) can be used to estimate the relative quantity of zeolite deposited on the support (BET- or Langmuir equation). When a dense substrate is used, ellipsometry gives the film thickness and void volume fraction. Absorption spectroscopies such as FTIR, are adapted to study the membrane material short range structure. 

Calculations were performed for uiireflected spheres of molten UQ, (-1000 kg), the void content, accounted for in the equatlon-of-state [Eq. (1)], by setting the initial system density, p = po (l.-f), where f is the void volume fraction of the sphere. This geometry is conservative for the calculation of kinetic energy relative to fission energy. Static DTF-IV calculations were performed to determine the critical radii of spheres with varying void fractions. The reference density, po, was 8.7 m m , the initial temperature. To, 3123 K (assumed molten), and die initial power, 1 MW. The effective delayed-neutron frac-... 

Free volume present in nanocomposite systems plays a major role in determining the overall performance of the membranes. Positron annihilation lifetime spectroscopy (PALS) is an efficient technique used for the analysis of free volume. The diffusion of permeant through polymeric membranes can be described by two theories, namely, molecular and free-volume theories. According to the free-volume theory, the diffusion is not a thermally activated process as in the molecular model, but it is assumed to be the result of random redistributions of free-volume voids within a polymer matrix. Cohen and Turnbull developed the free-volume models that describe the diffusion process when a molecule moves into a void larger than a critical size, Vc- Voids are formed during the statistical redistribution of free volume within the polymer. It is found that the relative fractional free volume of unfilled polymer decreases on the addition of layered silicates. The decrease is attributed to the interaction between layered silicate and polymer because of the platelet structure and high aspect ratio of layered silicates. The decrease is explained to the restricted mobility of the chain segments in the presence of layered silicates. This results in reduced free-volume concentration or relative fractional free volume [49]. 

Figure 5.22 The relation between the loosely packed matrix relative fraction and the free volume micro voids average radius for EP-1 (1), EP-2 (2) and aged...

Therefore, the settling velocity of the solid phase relative to the wall of an apparatus, depending on the average liquid velocity relative to the sludge with void fraction e, will be... 

But even in this case the fraction of the crystal that is void space" between the spheres depends on the relative radii of the positive and negative ions and will have a different value for each of the 17 crystals. This being so, when we come to introduce the ions into a solvent, and wish to understand the increment in volume of the liquid, the volumes of the various crystals clearly do not provide a satisfactory basis of comparison. 

The pseudohomogeneous reaction term in Equation (11.42) is analogous to that in Equation (9.1). We have explicitly included the effectiveness factor rj to emphasis the heterogeneous nature of the catalytic reaction. The discussion in Section 10.5 on the measurement of intrinsic kinetics remains applicable, but it is now necessary to ensure that the liquid phase is saturated with the gas when the measurements are made. The void fraction s is based on relative areas occupied by the liquid and soUd phases. Thus,... 

This equation is identical to the Maxwell [236,237] solution originally derived for electrical conductivity in a dilute suspension of spheres. Hashin and Shtrikman [149] using variational theory showed that Maxwell s equation is in fact an upper bound for the relative diffusion coefficients in isotropic medium for any concentration of suspended spheres and even for cases where the solid portions of the medium are not spheres. However, they also noted that a reduced upper bound may be obtained if one includes additional statistical descriptions of the medium other than the void fraction. Weissberg [419] demonstrated that this was indeed true when additional geometrical parameters are included in the calculations. Batchelor and O Brien [34] further extended the Maxwell approach. 

The refractive index of amorphous silicon is. within certain limits, a good measure for the density of the material. If we may consider the material to consist of a tightly bonded structure containing voids, the density of the material follows from the void fraction. This fraction / can be computed from the relative dielectric constant e. Assuming that the voids have a spherical shape, / is given by Bruggeman [61] ... 

In bubble columns the static head of the fluid is the dominant component of the pressure drop and consequendy it is important to determine the void fraction of the dispersion. All quanuties will be measured as posidve in the upward direction, this being the direction of flow of the dispersed phase. Assuming that the gas bubbles are of uniform size and are uniformly distributed over any cross section of the column, the gas and liquid velocities relative to the column are... 

Because of the assumptions underlying its derivation, the Kozeny-Carman equation is not valid at void fractions greater than 0.7 to 0.8 (Billings and Wilder, op. cit.). In addition, in situ measurement of the void fraction of a dust layer on a filter fabric is extremely difficult and has seldom even been attempted. The structure of the layer is dependent on the character of the fabric surface as well as on tfie characteristics of the dust, whereas the application of Eq. (17-12) implicitly assumes that K2 is dependent only on the properties of the dust. A smooth fabric surface permits the dust to become closely packed, leading to a relatively high value of K2. If the surface is napped or has numerous extended fibrils, the dust cake formed will be more porous and have a lower value of K2 [Billings and Wilder, op. cit. Snyder and Pring, Ind. Eng. Chem., 47, 960 (1955) and K. T. Semrau, unpublished data, SRI International, Menlo Park, Calif., 1952-1953]. 

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