title: Fractional calculus applied to the analysis of spectral electrical conductivity of clay-water system.
abstract: The analysis of the low-frequency conductivity spectra of the clay-water mixtures is presented. 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. When scaled with the value of the frequency-independent part of the spectrum the conductivity spectra for samples at different water content values are shown to fit to a single master curve. 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. The results indicate that the experimentally observed dielectric properties originate in anomalous ion transport in clay-water system characterized with time-dependent diffusion coefficient.
authors.affiliation: Applied Physics, Faculty of Civil Engineering, University of Maribor, Smetanova 17, SI-2000 Maribor, Slovenia. dean.korosak@uni-mb.si
authors.forename: Dean
authors.initials: D
authors.lastname: Korosak
authors.forename: Bruno
authors.initials: B
authors.lastname: Cvikl
authors.forename: Janja
authors.initials: J
authors.lastname: Kramer
authors.forename: Renata
authors.initials: R
authors.lastname: Jecl
authors.forename: Anita
authors.initials: A
authors.lastname: Prapotnik
mesh_terms: D004058:Diffusion; D004553:Electric Conductivity; D007616:Kaolin / Q000737:chemistry*; D008962:Models, Theoretical; D014867:Water / Q000032:analysis / Q000737:chemistry
chemical_list: D014867:Water; D007616:Kaolin