Void equation

Ba2YCu307 superconductor the calculated porosities for the two samples are 12.9 percent and 32.6 percent, respectively. Assuming that this porosity is in spherical voids, Equations 8 and 9 can be solved in an iterative fashion to give B0 and G0, from which the other elastic moduli can be calculated from Equations 4-7. A similar analysis is performed for the theory of Ledbetter and Datta. The results are given in Table III. 

If terminal velocity is reached in the voids. Equation (22.26) gives ... 

Since the void fraction distribution is independently measurable, the only remaining adjustable parameters are the A, so when surface diffusion is negligible equations (8.23) provide a completely predictive flux model. Unfortunately the assumption that (a) is independent of a is unlikely to be realistic, since the proportion of dead end pores will usually increase rapidly with decreasing pore radius. 

When the void space in an agglomerate is completely filled with a Hquid (Fig. Ic), the capillary state of wetting is reached, and the tensile strength of the wet particle matrix arises from the pressure deficiency in the Hquid network owing to the concave Hquid interfaces at the agglomerate surface. This pressure deficiency can be calculated from the Laplace equation for chcular capillaries to yield, for Hquids which completely wet the particles ... 

Carman equation is not vahd 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... 

This indicates that the target efficiency of the fiber is increased by the proximity of other fibers. The value of Ka averaged 4.5 for values of the void fraction ranging from 0.90 to 0.99. Extending use of the equation to values of , lower than 0.90 may result in large errors. 

In the equation shown above, the first term—including p for density and the square of the linear velocity of u—is the inertial term that will dominate at high flows. The second term, including p. for viscosity and the linear velocity, is the viscous term that is important at low velocities or at high viscosities, such as in liquids. Both terms include an expression that depends on void fraction of the bed, and both change rapidly with small changes in e. Both terms are linearly dependent on a dimensionless bed depth of L/dp. 

Powder X-ray diffraction and SAXS were employed here to explore the microstructure of hard carbon samples with high capacities. Powder X-ray diffraction measurements were made on all the samples listed in Table 4. We concentrate here on sample BrlOOO, shown in Fig. 27. A weak and broad (002) Bragg peak (near 22°) is observed. Well formed (100) (at about 43.3°) and (110) (near 80°) peaks are also seen. The sample is predominantly made up of graphene sheets with a lateral extension of about 20-30A (referring to Table 2, applying the Scherrer equation to the (100) peaks). These layers are not stacked in a parallel fashion, and therefore, there must be small pores or voids between them. We used SAXS to probe these pores. 

Horvath and Lin s equation is very similar to that of Huber and Hulsman, only differing in the magnitude of the power function of (u) in their (A) and (D) terms. These workers were also trying to address the problem of a zero (A) term at zero velocity and the fact that some form of turbulence between particles aided in the solute transfer across the voids between the particles. 

The resistance to liquid flow aroimd particles may be presented by an equation similar to the viscosity equation but with considering the void fraction. Recall that the shear stress is expressed by the ratio of the drag force, R, to the active surface, K27td. The total sphere surface is Ttd and Kj is the coefficient accoimting for that part of the surface responsible for resistance. Considering the influence of void fraction as a function 2( ). we obtain ... 

For a speeified void fraetion, the diameter of the sphere is a measure of the distanee between sludge partieles (Uf = f (d, e, du/dx)). However, it is more praetieal to introduee the hydraulie radius, and instead of O/e) and 2( ), aeeording to equation 30, we assume the following value ... 

Erom the differential mass balanee (Equation 5-321) in terms of the void volume,... 

AP equation arising from simultaneous turbulent kinetie and viseous energy losses that is applieable to all flow types. Ergun s equation relates the pressure drop per unit depth of paeked bed to eharaeteristies sueh as veloeity, fluid density, viseosity, size, shape, surfaee of the granular solids, and void fraetion. The original Ergun equation is ... 

The curves in Fig. 14.1 are not drawn down to zero, as the void fraction in a mixture with solid particles can not be zero. Equation (14.17) makes sense only in connection with equations of motion and particle size,... 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

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