Area-averaged mean radius

Area-averaged mean radius in Tomita s scattering theory... 

S is the ratio of the surface area of the medium to its pore volume and stands for equivalent diameter of the pores. The hydraulic (mean) radius m is defined as the ratio of the average pore cross-sectional area to the average wet perimeter, in line with the concept of the equivalent loads (as explained in Section III). All the geometrical parameters from Eq. (19) can be estimated for particulars of the porous media. For example, in the case of aligned fibers, hydraulic radius and equivalent diameter can be expressed by ... 

Ammonia synthesis catalysts, after reduction, have a very porous structure. By comparing the particle density of prereduced catalysts (3.70 gcm ) with that of pure iron (7.86 gcm ) we can estimate an internal void fraction, Sj, of 0.47. What is more important, however, the average pore radius is normally in the range of 300-400 A with a very narrow pore-size distribution. This means that activated catalysts have a surface area in the range between 10 and 20 m g" and that nearly all of their active surface is therefore located within the particles. The intrinsic reaction rate must then be related to the ability of the reactants to gain access to the inner catalyst surface and of ammonia to escape to the external surface of the catalyst particle by diffusion through the pores. Similarly, the heat of reaction, which is released inside the catalyst particles, is transferred to their external surfaces by conduction. 

Accurate values of the small areas existing in macropore systems make it difficult to use Eq. (8-26) to calculate d for interparticle pores. Hence the average radius for systems such as the UO2 pellets discussed in Example 8-6 should be obtained by integrating under the cumulative-volume-vs-u curve shown in Fig. 8-7. Also a single value of d has no meaning for a bidisperse pore system such as that in an alumina pellet. Thus using the total pore volume in Table 8-5 for the low-pressure pellet gives... 

Real foams are typically polydisperse2, which results in changes in the shape of foam cells. The Plateau rules (three films form a border four borders meet at a node) remain valid in all cases. The degree of dispersion in foam may be characterized by its specific surface area. One, however, usually measures some mean values of foam cell geometrical parameters, such as the average number of cells per unit volume, n, or the mean equivalent radius,7,... 

In addition to integer moments (k is an integer), fractional moments appropriate to the non-integer values k are also possible. Of the fractional moments, ntip and m2/3 have physical meaning, characterizing the average radius and the average surface area of drops in unit volume of mixture (area of interface) ... 

The cross section for the [d, n) process is the average value of that fringing area of the nucleus which can be struck by the proton in the deuteron while the neutron passes by untouched. If the mean distance which separates proton and neutron in the deuteron, = 2.2 X10" cm, is small compared with the nuclear radius the average cross section is equal to 2 tzR times the mean value R ) of the projection of this distance R ) on a plane perpendicular to its direction of motion. Thus the cross section is jiRR/, for heavy elements it is about -g- of the geometrical area of the nucleus. Quantitatively, this seems to be about the right cross section but it seems that no accurate measurements have been made to confirm it. 

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