Effective bulk

The limiting cases of greatest interest correspond to conditions in which the mean free path lengths are large and small, respectively, compared with the pore diameters. Recall from the discussion in Chapter 3 that the effective Knudsen diffusion coefficients are proportional to pore diameter and independent of pressure, while the effective bulk diffusion coefficients are independent of pore diameter and inversely proportional to pressure. 

Experimental measurements of viscosity almost always are recommended when dealing with slurries and extrapolations should be made with caution. Most theoretically based expressions for liquid viscosity are not appropriate for practical calculations or require actual measurements to evaluate constants. For nonclustering particles, a reasonable correlation may be based on the ratio of the effective bulk viscosity, /ig, to the viscosity of the liquid. This ratio is expressed as a function of the volume fraction of liquid x in the slurry for a reasonable range of compositions ... 

For powders and granular solids, there are two types of antistatic agents surface- and volume-active additives. Surface-active agents, which increase the surface conductivity of individual particles, are effective because triboelectric charge is always situated on the surfaces of individual particles. Most if not all surface-active agents are hygroscopic and thus attract a thin film of water to the surface it is this moisture that is responsible forthe increased surface conduction (van Drumpt, 1991). The effective bulk resistivity of the particles % -may be estimated by assuming that the particles are spherical and of radius R (Jones, 1995). 

The effective bulk polyimide resistivity can be extracted from comparison of the measured curves in Figure 6 with this model, and values at 100°C and 158°C are shown in Figure 7, which is a reproduction of the Arrhenius plots of Figure 4. It is seen that both the values of the resistivity and the temperature dependence are in good agreement with those obtained from the dc conduction measurements. In addition, the saturated value of the measured threshold instability is well predicted by the model. 

Material Properties. The elementary form of the analysis used requires the following properties of propellant during cure tensile modulus, effective bulk modulus, and propellant volume change. Each of these properties changes with temperature and time elapsed since casting. Because of the unusual nature of the material (sticky, wet, explosive, gravel ), special tests, equipment, and techniques were developed for these measurements. 

This same apparatus permits estimates to be made of the so-called jacketed compressibility (the reciprocal of the effective bulk modulus) during early cure. This is accomplished by applying momentary pressure to the bed alone (ram pressure) and observing the corresponding bed volume change in the water meniscus. 

Sieve analysis using standard mesh screens is commonly used to determine particle size and size distribution of pellets and the reader is referred to standard texts for further information (61). Several types of densities have been defined for pellets based on interparticulate (void fraction) and intraparticulate pore volumes and include true, apparent, effective, bulk and tapped. The bulk and tapped densities may be obtained using simple devices, such as that used to evaluate granulations in tableting, while the true and apparent densities need more complex techniques based on mercury intrusion, gas flow, powder displacement, imaging or minimum fluidization velocity (62). 

A Regime Since diffusion in this regime is macroscopically similar to diffusion in a homogeneous material possessing an effective bulk diffusivity (Eq. 9.4), it may be analyzed by the methods described in Chapters 4 and 5. 

Derive an equation similar to Eq. 9.4 for the effective bulk self-diffusivity, ( D), in the presence of fast dislocation diffusion. Assume that the dislocations are present at a density, p, corresponding to the dislocation line length in a unit volume of material. 

Exercise 9.1 yielded an expression, Eq. 9.18, for the enhancement of the effective bulk self-diffusivity due to fast self-diffusion along dislocations present in the material at the density, p. Find a corresponding expression for the enhancement of the effective bulk self-diffusivity of solute atoms due to fast solute self-diffusion along dislocations. Assume that the solute atoms segregate to the dislocations according to simple McLean-type segregation where c2 c2L = k — constant, where cf5 is the solute concentration in the dislocation cores and cXL is the solute concentration in the crystal. 

Solid food materials have dielectric properties dependent upon their composition. In many instances, particularly when developing microwavable food products, it is necessary to know the effective bulk microwave properties of the product, crushed, as is, or when agglomerated together. Typical examples are peas, beans, com, pasta, flour... 

The effective bulk dielectric constant is determined by measuring the distance between a maximum and minimum value of amplitude. The bulk loss factor is determined by measuring the amplitude of the signal under the sample with the loop, as a function of plunger distance from the beginning of the sample. 

We considered that nucleophilic addition is promoted when electron transfer from the reagent to the substrate is facilitated.41 Consequently, we proposed that X, Y and Z be classified according to their electrophilicity, as measured by the energy of their antibonding orbitals o cx, o CY and o cz. Thus, the best electron acceptor is considered to be the bulkiest group. This approach uses only one parameter and eliminates the tricky problem of defining effective bulk. See, however, the discussion on pp. 168-169. 

Figure 6. Pressure dependencies of the bulk modulus obtained by the direct numerical differentiation of the in situ volumetric measurements of the glassy B203 under pressure ( relaxed modulus) in the two different runs of compression (solid symbols) and decompression (open symbols). The significant jumps of the effective bulk modulus between the final of compression and onset of decompression for both runs correspond to the jumps between relaxed and almost unrelaxed values. The inset shows pressure dependences of the first coordination number for B from the recent X-ray diffraction data. Both data are from Ref. [129].

There is a basis17 to assume that in the studied samples1 both the oxygen diffusion decrease, and the copper diffusion enhancement are caused by the influence of the co-segregation at dislocations. This is also consistent with the fact pointed in study15 that twin boundaries in the 123 matrix do not contribute apparently to the effective bulk oxygen diffusion. 

When the inclusion is an air bubble in a viscoelastic solid the shear modulus of the air is zero, and also it is reasonable to neglect the bulk modulus of the air since it is several orders of magnitude less than the bulk modulus of the solid. The Kerner mean field model then predicts the following expression for the effective bulk modulus of the air-polymer composite,... 

From Eq.21 it follows that the imaginary party of the effective bulk modulus K is much larger than the imaginary part of K. Therefore, sound waves are strongly attenuated in this type of material. The viscoelastic polymer-air microbubbles composites are particularly useful in the design of broadband, transition type anechoic coatings for underwater... 

Under the effect of uniform hydrostatj.c pressure and uniform tension, the effective bulk modulus, K = 1/P, and effective shear modulus, p, are calculated. The result is... 

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