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Regular version of the site

Article

Diffusion Fractional Models for a Complex Porous Media in a Random Force Field for 3D Case

European Journal of Scientific Research. 2013. Vol. 95. No. 3. P. 436-443.
Kozyrev O.

Fractional differential equation of particle transfer in porous and tubular media was obtained in the paper. It differs from the generally accepted ones by the dependence of the effective diffusion coefficient on the concentration. Together with 1D case problem also 3D problem of diffusion in normal random field was analyzed. For scales, lager then correlation lengths, fractional diffusion equation was derived which is valid for any time intervals. Diffusion equations in fractional derivatives in the limiting case of a zero correlation length of a random field of porosity or tube curvature were shown to be reduced to an ordinary diffusion equation with a renormalized diffusion coefficient. In case of a non-zero correlation length a general solution for the average square of the particle shift during random wandering was found. It was also found that in a certain time interval the coefficient of diffusion is time dependent, i.e. anomalous diffusion takes place.