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

Tue 611:23-14:00P2.43Subdiffusion in a system with chemical reactionsTaduesz Kosztolowicz 1 and Katarzyna Lewandowska 21 Institute of Physics, Jan Kochanowski University, ul. Swietokrzyska 15, 25-406, Kielce,Poland2 Department of Radiological Informatics and Statistics, Medical University of Gdansk,Gdansk, PolandSubdiffusion is related to an infinitely long average time that a random walker waits to makea finite jump. It occurs, among others, in gels and porous media. We consider a subdiffusivesystem where transported particles of species A and B chemically react according to the formulaλ A A + λ B B → P (inert), where λ A,B are the stoichiometric coefficients. This process is describedby the nonlinear subdiffusion - reaction equations with fractional time derivatives ∂C A(x,t)∂t=∂ 1−α ∂(D 2 C A (x,t)∂t 1−α A − mkC m ∂x 2A (x, t)CB(x, n t)) ∂C B(x,t)= ∂1−α ∂(D 2 C B (x,t)∂t ∂t 1−α B − nkC m ∂x 2 A (x, t)CB(x, n t))where C A,B denote the particle’s concentrations of species A and B, respectively, m and n are theparameters experimentally determined for each reaction individually and k is the reaction rate.Using the quasistatic approximation method we show that the reaction front x f (t) for the systemwith nonzero subdiffusion coefficients evolves in time as x f (t) = Kt α/2 , with K being controlledby the subdiffusion coefficients [1]. The analytical results are confirmed by the numerical ones [2].We also study the case of one static and one mobile species. Comparing the obtained analyticalformula for this case with the experimental data we find that the transport of acids moleculesinside the tooth enamel during the caries progress is subdiffusive [3].[1] T. Kosztolowicz and K. D. Lewandowska, Phys Rev E 78, 066103 (2008).[2] K. D. Lewandowska and T. Kosztolowicz, Acta Phys Pol B 38, 1847 (2007).[3] T. Kosztolowicz and K. D. Lewandowska, Acta Phys Pol B 37, 37 (2006).43