Core diffusion

Fast diffusion paths grain boundary and dislocation core diffusion... 

This model requires an excess of sulfate over reducible carbon. Concentrations may be measured in solutions squeezed from sediment cores, diffusion coefficients are known from standard chemical data tables and sedimentation rates determined from 14C, 210Pb, or 230Th dating. Therefore, this model finds its best use in the recovery of the kinetics of organic matter decay. A discussion of this and similar equations and numerical applications may be found in Berner (1980). 

The core diffuses through the wall at a slow rate due to the influence of an exterior fluid such as water or by an elevated temperature. 

The shrinking core reaction mode is not necessarily limited to non-porous unreacted solids. With a fast reaction in a porous solid, diffusion into the core and chemical reaction occur in parallel. The mechanism of the process is very similar to the mechanism of the catalysed gas-solid reactions where the Thiele modulus is large, the effectiveness factor is small and the reaction is confined to a thin zone (Section 3.3.1). This combination of reaction with core diffusion gives rise to a reaction zone which, although not infinitely thin but diffuse, nevertheless advances into the core at a steady rate. 

If the reacting core is impermeable, reaction will take place at the surface of the core, whereas if the core has some degree of porosity the combination of chemical reaction and limited core diffusivity will give rise to a more extended reaction zone. In either case, the overall rate of reaction will be proportional to the area of the reaction front. 

Fig. 3.1a,b. a The ischaemic penumbra. The perfusion (PI) lesion delineates the extent of hypoperfusion and the diffusion (DWI) lesion outlines the infarct core. The difference between the two lesions (perfusion-diffusion mismatch) represents the ischaemic penumbra, tissue at risk of progression to infarction, b Patient imaged at 3 h after onset of left hemiparesis and neglect with large PI (time to peak - TTP) lesion and smaller DWI lesion. At day 3 reperfusion has not occurred and the infarct core (diffusion lesion) has expanded greatly into the region of acute perfusion-diffusion mismatch. This is consistent with the perfusion-diffusion mismatch area representing the ischaemic penumbra... 

Figure 3 Types of Pt profiles obtained in co-impregnation experiments. Type (1), outer shell, sharply defined (2), outer shell, diffuse (3), outer shell, diffuse to centre (4), inner shell, sharply defined (5), inner shell, diffuse (6), inner shell, diffuse to centre (7), core, sharply defined (8), core, diffuse (9), linearly increasing from centre...

Solids play different roles in the different processes. In direct coal liquefaction, a part of the solid is dissolved in liquid (mainly in the preheater) and a part (i.e. mineral matter) may act as a catalyst for the hydrogenation reactions. In Fischer-Tropsch slurry processes, solids are catalysts. Finally, in chemical cleaning of coal, only a part of solid (i.e. sulfur) takes part in the reaction following the shrinking core diffusion/ reaction mechanism. The role of solids in the design and scaleup of the reactors for the three processes is therefore different. 

It is interesting to note that the result (8.379) is independent of both r and r. Thus we find that in this approximation the probability of a fast neutron from the core diffusing out into the reflector, slowing down there, and finally returning to the core to be absorbed there as a slow neutron is the same for all combinations of origin and terminus. 

A greatly simplified treatment can be achieved, if it is possible to assume that the lateral diffusion into the bulk is absolutely negligible with respect to the core diffusion (Fig. 6.42, left). The bulk transport then takes place on a completely separate... 

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