Applications of fractional calculus to diffusion transport in clay-water system

Details Applications of fractional calculus to diffusion transport in clay-water system Applications of fractional calculus to diffusion transport in clay-water system

2005-09-09

arxiv.org/abs/cond-mat/0509230v1

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. The conductivity spectra for samples at different water content values are shown to collapse to a single master curve when appropriately rescaled. The frequency dependence of the conductivity is shown to follow the power-law with the exponent n=0,67 before reaching the frequency-independent part. It is argued that the observed conductivity dispersion is a consequence of the anomalously diffusing ions in the clay-water system. The fractional Langevin equation is then used to describe the stochastic dynamics of the single ion.

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