Statistical analysis of anomalous transport phenomena in complex media

✍ Scribed by Massimiliano Giona

• Publisher: American Institute of Chemical Engineers
• Year: 1991
• Tongue: English
• Weight: 483 KB
• Volume: 37
• Category: Article
• ISSN: 0001-1541
• DOI: 10.1002/aic.690370816

✦ Synopsis

Transport phenomena on complex media are characterized by a subdiffusive regime called anomalous diffusion (Sahimi, 1983;Rammal, 1984). Anomalous diffusion has been observed in porous media (Katz and Thompson, 1985), capillarity networks (Adler, 1985) and percolation beds (Stauffer, 1985). In the last two years a great deal of research work has been carried out on this topic in the chemical engineering field (Sheintuch and Brandon, 1989; Tassopoulos et al., 1989;Sahimi et al., 1990; Siddiqui and Sahimi, 1990). The main features of anomalous diffusion are:

Deviation from Gaussianity Anomalous scaling law of the mean square displacement ( r 2 ( t ) ) vs. t .

with @< 1 (subdiffusive regime). For regular diffusion we have

This relation can be explained in terms of the geometrical constraints imposed on the motion of the diffusing particles by the self-similar symmetry (fractality) of the medium. In fact, porous media and percolation clusters can be considered in a certain lengthscale range as fractal (Havlin, 1989). The concepts of fractal geometry can be therefore applied to transport phenomena on these structures. In this theoretical framework it is possible to show that the exponent @ is given by (Alexander and Orbach, 1982; Havlin, 1989