8th Liquid Matter Conference September 6-10, 2011 Wien, Austria ...

Tue 611:23-14:00P9.31Subdiffusive in a membrane systemTadeusz Kosztolowicz 1 and Katarzyna Lewandowska 21 Institue of Physics, Jan Kochanowski University, ul. Swietokrzyska 15, 25-406, Kielce,Poland2 Department of Radiological Inforfmatics and Statistics, Medical University of Gdansk,Gdansk, PolandSubdiffusion is related to an infinitely long average time that a random walker waits to make afinite jump. It occurs, among others, in gels and porous media. We study subdiffusion in a system,in which homogeneous thick membrane separates two media; in each of them there are differentanomalous diffusion parameters. Anomalous diffusion is described by the linear differentialequations with Riemann-Liouville fractional time derivative∂C(x,t)∂t= D ∂1−α∂t 1−α ∂ 2 C(x,t)∂x 2 ,where C denotes the concentration of diffusing particles, D is the subdiffusion coefficient,α is the subdiffusion parameter. The boundary conditions requiring that the ratio of substanceconcentrations on both sides of the membrane surface is constant in time. Starting with theGreen’s functions derived for the considered system, we discuss the property of the concentrationsfound in the long time limit for the system where initially the membrane separates pure solventfrom homogeneous solution. Comparing the experimental results to theoretical functions, weestimate the subdiffusion coefficient of PEG2000 in agarose gel. The theoretical function wasfound by solving analytically the subdiffusion equation. We also study a transport in compositesystem where the subdiffusive solvent is separated by a thin membrane from the region wherenormal diffusion occurs. The solutions of the diffusion equation with fractional derivative arefound in the system of interest.[1] T. Kosztołowicz, J. Membr. Sci. 320, 492 (2008).[2] T. Kosztołowicz, K. Dworecki, S. Mrówczynski, Phys. Rev. Lett. 94, 170602 (2005).[3] T. Kosztołowicz, K. Dworecki, S. Mrówczynski, Phys. Rev. E 71, 041105 (2005).[4] T. Kosztołowicz, K. D. Lewandowska, Phys. Scripta T 136, 014020 (2009).[5] T. Kosztołowicz, Acta Phys. Pol. B 38, 1807 (2007). 36, 1635 (2005). T. Kosztołowicz, J.Phys. A 37, 10779 (2004).31