CONTENTS 3 Diffusion theory

The experiments of Fan et al. (126) with peanuts carefully sliced with a microtome show that the relationships developed by Boucher et al. (125) are also applicable to at least one oilseed, provided that structural considerations are not complicated by crushing the seed to form flakes. A typical extraction curve is shown (curve B) in Figure 18. As required by diffusion theory, there is a linear relationship between the logarithm of the residual oil content and the extraction time after a short period has elapsed. During this period, however, much of the oil is extracted very rapidly. 

The exhalation of Rn from material surfaces is controlled by the generation rate of Rn in the material, and the transport by diffusion through the material to the surface. The generation rate is determined by the Rn content of the material, and the emanation fraction. The transport through the material is controlled by the diffusion length through the material. The diffusion process is well described mathematically by one-dimensional diffusion theory, so that knowledge of these parameters will allow accurate calculation of the Rn exhalation rate from the material surface. 

NONPOROUS SOLIDS AND DIFFUSION THEORY. The moisture distribution in a solid giving a falling-rate curve like that of Fig. 24.5 is shown as the dotted line in Fig. 24.6, in which the local moisture content is plotted against distance from the surface. Its shape is quahtatively consistent with that called for by assuming that the moisture is flowing by diffusion through the solid, in accordance with Eq. 

The accuracy of the diffusion theory for drying suffers from the fact that the diffusivity usually is not constant but varies with moisture content. It is especially sensitive to shrinkage. The value of D is less at small moisture contents than at large and may be very small near the drying surface. Thus, the moisture distribution called for by the diffusion theory with constant diffusivity is like that shown by the solid line in Fig. 24.6. In practice, an average value of D , established experimentally on the material to be dried, is used. 

The Interim Decay Storage (IDS) facility provides storage for fresh or irradiated fuel for the Fast Test Reactor (FTR), A series of one- and two-dimensional transport and diffusion theory calculations was made -to establish the hUective multiplication factor of the IDS facility when fully loaded with initial driver fuel for the FTR, and also to establish the upper plutonium content of fuel that can be stored in the facility. No consideration was given in these analyses to accidents in which sodium coolant would be lost or fuel spacing changed. 

The selective diffusion theory has been well formulated mathematically and solved by numerical calculations. On the basis of such calculations, flavor retention during spray drying increases with the increase in solids content in the feed, inlet gas temperature and inlet gas flow rate, as well as with the decrease in inlet gas humidity, see Fig. 6.20. All of these conditions favor the early formation of a dry skin on the surface of the droplet (Furuta et ol., 1984). 

In the frame of the free volume diffusion theory, diffusivity changes with the penetrant size and the free volume content of the amorphous phase [76, 89, 90, 91] ... 

Tritium has also been observed in meteorites and material recovered from sateUites (see also Extraterrestrial materials). The tritium activity in meteorites can be reasonably well explained by the interaction of cosmic-ray particles and meteoritic material. The tritium contents of recovered sateUite materials have not in general agreed with predictions based on cosmic-ray exposure. Eor observations higher than those predicted (Discoverer XVII and sateUites), a theory of exposure to incident tritium flux in solar flares has been proposed. Eor observations lower than predicted (Sputnik 4), the suggested explanation is a diffusive loss of tritium during heating up on reentry. 

When a slab of the PE0/PU hydrogel 2.8mm thick was swollen to equilibrium in an aqueous solution of morphine hydrochloride at 37°C, briefly rinsed, then transferred to water at 37°C, the rate of release of morphine was, as predicted by theory, proportional to time t O and 50° 0f the morphine content was released in the first 45 minutes. The release/time plot is shown in Figure 1. Results from experiments like this one can be used to calculate diffusion coefficients (8) in fully swollen hydrogels and help interpret the complex mechanism of diffusion in swelling hydrogels. 

The sequence, position, and distribution of separated components contain a good deal of information on the mixture. If properly measured and interpreted, this can serve many analytical goals without further tests. The quality of this information naturally improves as the system is better understood, characterized, and controlled. Informational content is greatest when, through theory and/or calibration, one can identify zones or peaks located at defined positions in the sequence with specific molecular species At that point, using a suitable sensor (detector), both qualitative and quantitative analyses follow. One can, at the same time, often measure certain physicochemical constants for the components, such as partition coefficients and diffusion constants. 

Some experimental studies point out that the diffusion rate of pure hydrocarbons decreases with the coke content in the zeolite [6-7]. Theoretical approaches by the percolation theory simulate the accessibility of active sites, and the deactivation as a function of time on stream [8], or coke content [9], for different pore networks. The percolation concepts allow one to take into account the change in the zeolite porous structure by coke. Nevertheless, the kinetics of coke deposition and a good representation of the pore network are required for the development of these models. The knowledge of zeolite structure is not easily acquired for an equilibrium catalyst which contains impurity and structural defects. 

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