Diffusion in complex systems

Stefan-Maxwell Approach for Bulk-Knudsen Diffusion in Complex System of Capillaries... 

Theoretical Aspects of Anomalous Diffusion in Complex Systems... 

In the preceding section it is seen how the theory of multicomponent systems gives the correct starting formulas for the analysis of ordinary and thermal diffusion in binary systems. Whereas these latter topics have been the subject of considerable investigation, there are a number of types of more complex diffusion problems of engineering interest for which little has been done. Several of these topics are discussed here, and an attempt is made to indicate to what extent they can be interpreted in terms of the theoretical development in the preceding sections. 

Unfortunately, environmental problems do not solely involve dilute binary systems. To mention just one example, the dissolution of a patch of spilled diesel fuel into the groundwater (see below Illustrative Example 19.4) involves diffusion in multicomponent systems for which adequate data are extremely rare. In many cases diffusivities of diluted compounds in air or water must serve as best estimates for more complex systems. Yet, the above remarks should remind us that things may be more complicated. 

Sorption capacity is one of the major properties used for industrial applications of zeolites. H. Lee reviews the aspects of zeolites used as adsorbents. The other papers in the section deal with the theory of sorption and diffusion in porous systems, the variation of sorption behavior upon modification, and the variation of crystal parameters upon adsorption. NMR and ESR studies of sorption complexes are reported. H. Resing reviews the mobility of adsorbed species in zeolites studied by NMR. 

Note that the above study is performed for a simple system. There exists a large body of literature on the study of diffusion in complex quasi-two-dimensional systems—for example, a collodial suspension. In these systems the diffusion can have a finite value even at long time. Schofield, Marcus, and Rice [17] have recently carried out a mode coupling theory analysis of a quasi-two-dimensional colloids. In this work, equations for the dynamics of the memory functions were derived and solved self-consistently. An important aspect of this work is a detailed calculation of wavenumber- and frequency-dependent viscosity. It was found that the functional form of the dynamics of the suspension is determined principally by the binary collisions, although the mode coupling part has significant effect on the longtime diffusion. 

Wei, J., Intraparticle diffusion effects in complex systems of first order reactions. D, The influence of diffusion on the performance of chemical reactors. J. Catal. 1,526 (1962b). 

The combination of direct excitation or cross-polarization NMR experiments with off-MAS sample spinning seems to be the most powerful approach for the study of rotational diffusion of all system constituents. It allows for a chemical identification of all organic system components and simultaneously yields data on their rotational diffusion. Hence, for detailed studies on particle tumbling in complex systems, it represents the preferred experimental condition for all particle dispersions which are stable enough to survive the inertial field during sample spinning for an adequate period of time. ... 

Giorgilli, A. (1995b). Methods of complex analysis in classical perturbation theory. In Benest, D. and Froeschle, C., editors. Chaos and diffusion in Hamiltonian systems. Editions Frontieres. 

Geilikman and Dusseault (1996) approached this problem in a coupled formulation and showed that there exists an optimum mud weight that is a function of material properties and rate of diffusion. For complex systems, finding this optimum a priori is difficult. Nevertheless, understanding the nature and direction of the possible physical changes can go a great distance toward finding the optimum conditions quickly. 

Intraparticle diffusion effects in complex systems of first order reactions. 

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