Uniform distribution ordering

If the solute is uniformly distributed through the soHd phase the material near the surface dissolves first to leave a porous stmcture in the soHd residue. In order to reach further solute the solvent has to penetrate this outer porous region the process becomes progressively more difficult and the rate of extraction decreases. If the solute forms a large proportion of the volume of the original particle, its removal can destroy the stmcture of the particle which may cmmble away, and further solute maybe easily accessed by solvent. In such cases the extraction rate does not fall as rapidly. 

By comparison, the multiple spinnerette per bank process requites additional effort prior to laydown in order to compensate for the gaps between the individual spinnerettes. Failure to present a filament array to the laydown screen, which is not uniformly distributed, can result in spot-to-spot variations in fiber density and a web that has the appearance of blotch. 

First-order sehemes use a uniform distribution aeross an element and seeond-order sehemes use a linear distribution aeross the element as shown in Fig. 9.16. Higher-order adveetion sehemes use more eomplex distributions aeross an element [29]. The distributions aeross the donor eell must be eon-strained to prevent numerieal oseillations. As an illustration, for seeond-order van Leer sehemes, the slope is limited using (9.15) and Fig. 9.17. The slope... 

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

Early kinetic work127 showed that the formation of both ortho and para products was a first-order process and that the rates of reaction were insensitive to added acid or base and to change of solvent. The activation parameters were of the same order of magnitude for both reactions and the suggestion was made that both had a similar rate-determining step. Schmid et a/.128 showed that the formation of a dienone intermediate in the para rearrangement was also reversible since the radioactivity from allyl 2,6-dimethyl-4-allyl-y-14C phenyl ether LXXXVII became uniformly distributed in the y carbon atoms of the O- and C-allyl groups... 

Depending on the process conditions, different profiles of the active phase over the particle will be obtained. A completely uniform distribution of the active material over the particle is not always the optimum profile for impregnated catalysts. It is possible to purposely generate profiles in order to improve the catalyst performance. Fig. 3.28 shows four major types of active phase distribution in catalyst spheres. 

At temperatures of the order 700 - 900 K the surface point defects play the dominant role in controlling the various eledrophysical parameters of adsorbent on the content of ambient medium [32]. As it has been mentioned in section 1.6, these defects are being formed in the temperature domain in which the respective concentration of volume defects is very small. In fact, cooling an adsorbent down to room temperature results violation of uniform distribution due to redistribution of defects. The availability of non-homogeneous defect distribution led to creation of a new model of depleted surface layer based on the phenomenon of oxidation of surface defects [182] which is an alternative to existing model of the Shottky barrier [183]. 

Finally, recent work of Iversen et al. has carefully examined the bias associated to the accumulation of the error on low-order reflexions, and attempted a correction of the MaxEnt density [39]. The study, based on a number of noisy data sets generated with Monte Carlo simulations, has produced less non-uniform distribution of residuals, and has given quantitative estimate of the bias introduced by the uniform prior prejudice. For more details on this work, we refer the reader to the chapter by Iversen that appears in this same book. 

In order to evaluate equation 44-77 it is necessary to assume a distribution for the variability of AEs and AEx, and in the earlier chapter the distribution used was the Normal distribution here, therefore, we want to now evaluate this function for the case of a uniform distribution. We note here that much of the discussion in the earlier chapter concerning the evaluation of equation 44-77 applies now as well, so it behooves... 

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