title: Subdiffusion in a system with thin membranes.
abstract: We study both theoretically and experimentally a process of subdiffusion in a system with two thin membranes. The theoretical model uses Green's functions obtained for the membrane system by means of the generalized method of images. These Green's functions are combinations of the fundamental solutions to a fractional subdiffusion equation describing subdiffusion in a homogenous, unbounded system. Using Green's functions we find analytical formulas describing the time evolution of concentration profiles and the time evolution of the amount of substance that remains in the region between the membranes. The concentration profiles fulfill a new boundary condition at the membrane, in which the membrane permeability is assumed to change over time according to the special formula presented in the paper. These concentration profiles fulfill a standard subdiffusion equation with fractional Riemann-Liouville time derivative only approximately, but they coincide very well with the experimental data. Fitting the theoretical functions in with the experimental results, we also estimate the subdiffusion coefficient of polyethylene glycol 2000 in agarose hydrogel.
authors.affiliation: Institute of Physics, Jan Kochanowski University, ul Świętokrzyska 15, 25-406 Kielce, Poland. tadeusz.kosztolowicz@ujk.kielce.pl
authors.forename: Tadeusz
authors.initials: T
authors.lastname: Kosztołowicz
authors.forename: Kazimierz
authors.initials: K
authors.lastname: Dworecki
authors.forename: Katarzyna D
authors.initials: KD
authors.lastname: Lewandowska