Diffusion hypothesis

The flux terms are usually modeled by invoking a gradient-diffusion hypothesis. For example, one of the simplest models is... 

The crystal growth rate has been found in many eases to be extremely rapid, more rapid than can be accounted for on the diffusion hypothesis thus Tammann (foe. cit.) found for benzophe-none a maximum crystallisation velocity of 2 4 mm. per minute (Walton and Judd, J. Phys. Ohem. xvni, 722,1914). Much higher values, e.g. 6840 mm. per minute for water and 60,000 mm. per minute for phosphorus (Gernez, O.R, xcv. 1278, 1882) have been recorded. In some cases the rate was found independent of the speed of rotation of the stirrer and occasionally the reaction velocity followed a bimolecular law instead of the simple unimolecular expression which holds true for solution. 

Clarke, Kassel, and Storeh5 interpret the slow adsorption on chromic oxide gel as in part a diffusion of an already adsorbed layer to secondary centres of adsorption but Burwell and Taylor criticize the whole diffusion hypothesis, partly on the grounds that the temperature coefficient of the rate of adsorption is not that to be expected for diffusion.6 It may not, however, be easy to distinguish between the gross characteristics of an activated diffusion along the surface, and of an activated adsorption indeed it seems just admissible to consider the former as a localized form of the latter. 

Weak Acid" and "Intermediate-Diffusion" Hypotheses. Two hypotheses (which are not necessarily mutually exclusive) have been proposed for the entry and systemic mobility of chemicals in the phloem the "weak-acid" hypothesis proposed by Crisp and colleagues (5), and the "intermediate-diffusion" hypothesis proposed by Edgington and Peterson (4). These are illustrated in Figure 5. 

The "intermediate diffusion" hypothesis proposes that the critical determinant of phloem mobility is the optimum permeability coefficient of a given molecule, P. P is calculated as ... 

This is not an easy question to answer, nor is it appropriate for us to address it in detail in a review paper. Rather, we refer to a detailed study of the validity of (7) as well as of other air pollution models that has been carried out by Lamb and Seinfeld (20). We restrict this discussion to a summary of the limitations in (7) which are introduced as a result of the eddy diffusivity hypothesis. In particular. Lamb and... 

Furthermore a great deal of experimental evidences exists which does not agree with the diffusion hypothesis. 

Another criterion linked to the diffusion hypothesis, suggested by Sing and Merril , provides for MWD narrowing through partial poisoning of the catalyst, since it causes a lowering of Thiele modulus (lower C values). It was found, on the contrary that, by treating TiClj with various poisons, it was possible to obtain even... 

The modeled transport equations for z differ mainly in the diffusion and secondary source term. Launder and Spalding (1972) and Chambers and Wilcox (1977) discuss the differences and similarities in more detail. The variable, z = e is generally preferred since it does not require a secondary source, and a simple gradient diffusion hypothesis is fairly good for the diffusion (Launder and Spalding, 1974 Rodi, 1984). The turbulent Prandtl number for s has a reasonable value of 1.3, which fits the experimental data for the spread of various quantities at locations far from the walls, without modification of any constants. Because of these factors, the k-s model of turbulence has been the most extensively studied and used and is recommended as a baseline model for typical internal flows encountered by reactor engineers. 

Already in 1976, this diffusion hypothesis was considered [15] a conceivable, but very crude estimate of the overabundance (by a factor lO ) in Ap mercury stars. The main problem was lack of data for highly ionized species (such as Hg and Hg ) deeper down in the star. Everybody agrees that the diffusion hypothesis of Michaud necessitates a very calm photosphere, where diffusion takes place unperturbed by any variable directional flows (in spite of the turbulent wind around 5 km/s observed [30, 38] in Przybylski s star HD 101065), a scenario which is indeed more likely in A main-sequence stars than in almost all other stars. 

Dunn J.E. and Chen T. (1993) Critical evaluation of the diffusion hypothesis in the theory of porous media volatile organic compounds (VOC) sources and sinks. In Nagda N.L.(ed) Proceedings of Modeling of Indoor Air Quality and Exposure, ASTM STP 1205, 64 - 80. 

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