Boltzmann-Matano method

Figure 3-9 Calculated D by applying the Boltzmann-Matano method (open circles) and the algorithm of Sauer and Freise (1962)...

If the diffusivities are functions of concentration, the Boltzmann-Matano method, described in Section 4.3 for the binary case, can be employed if the initial and boundary conditions are appropriate. The diffusion equations are... 

Figure 1.13. Components of the Boltzmann—Matano method in Eq. (1.2) applicable to an experimental spreading profile.

SNA Snabl, M., Ondrejeek, M., Chab, V., Chvoj, Z., Stenzel, W., Conrad, H., Bradshaw, A. M. Surface diffusion ofK on Pd(III) coverage dependence of the diffusion coefficient determined with the Boltzmann-Matano method. J. Chem. Phys. 108 (1998) 4212. 

We adopted a second method called the Boltzmann-Matano interface method [see Eq. (5)], which is more accurate for the purely diffusive process. Notice that Ma et al. successfully employed this method, since the spreading profiles they measured exhibit little mass buildup at the front and negligible dewetting. 

Hence, J c = c is obtained. This method is associated with Boltzmann 14) and was developed by Matano (24). Some results are given in Table III. The saturation water content, was 19.67% by weight of water the values of Cq are given in the table. Da should be, and was, within error, independent of Cq. The variation of Da with concentration... 

Model calculations were carried out by the example of a parabohc dependence of the interdiffusion coefficient for a binary system. The efficiency of the method was demonstrated for significant perturbations of the model experimental concentration profile up to 10% with respect to the exact values. The additional smoothing component of the discrepancy functional expressed as squared entropy production can be set to solve any inverse problems of heat and mass transfer. The suggested method, unlike the Matano-Boltzmann method, can be generalized to multicomponent systems with arbitrary sample configurations. 

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