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