Self-diffusion Terms Links

The diffusion coefficients Du and D22 are the principal or "self diffusion coefficients and the off-diagonal quantities D12 and D21 are mutual diffusion coefficients. Even when Onsager s reciprocal relations (31) are valid for the appropriate flow equations so that D12 = D21, there are still three diffusion coefficients generally required to describe the diffusion process. It is noted that even if dC Jbx = 0, the flow of Component 1 is linked to that of Component 2 through the term — Di2dC2/dx, and is not zero. 

Diffusion in zirconia is closely linked to ionic conductivity. Consequently, some diffusion data has already been presented in Sect. 5. This section will include additional results particularly for monoclinic zirconia. Oxygen self-diffusion at a pressure of 300 Torr, as determined by testing zirconia spheres of diameters between 75 and 105 jam, behaves as shown in Fig. 17 [57], where D is the diffusion coefficient, t is time, and a is the sphere radius. At a pressure of 700 Torr, the behavior changes to that shown in Fig. 18 [58]. In this case D is the self-diffusion coefficient and the rest of the terms are as defined before, with a = 100-150 jam. Both of these experiments were performed in an oxygen atmosphere of 180-160. The self-diffusion coefficients calculated from the diffusion data obey Arrhenius expressions as illustrated in Fig. 19 [57, 58]. The linear fits describing the diffusion coefficient at 300 and 700 Torr, are given by ... 

Therefore, the power-law behavior itself is a self-similar phenomenon, i.e., doubling of the time is matched by a specific fractional reduction of the function, which is independent of the chosen starting time self-similarity, independent of scale is equivalent to a statement that the process is fractal. Although not all power-law relationships are due to fractals, the existence of such a relationship should alert the observer to seriously consider whether the system is self-similar. The dimensionless character of a is unique. It might be a reflection of the fractal nature of the body (both in terms of structure and function) and it can also be linked with species invariance. This means that a can be found to be similar in various species. Moreover, a could also be thought of as the reflection of a combination of structure of the body (capillaries plus eliminating organs) and function (diffusion characteristics plus clearance concepts). 

The influence of correlation between pore to pore transit rates in porous materials has been investigated [27]. The porous material is again assumed to consist of a cross-linked network of randomly oriented pores diffusion of molecules in the network is represented as a self-correlated random walk. On passing to the limit--pore diameter much smaller than the characteristic length of the material-the form of equation 16 is justified for porous materials with uniform porosity. However, a correction term appears in the effective diffusion coefficient to account for the correlation between successive steps in the random walk. By lumping the correction factor into the effective diffusion coefficient, equation 16 can still adequately represent diffusion in porous materials. 

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