Random walk model of subdiffusion - absorption process in a system consisting of two different media separated by a partially permeable wall

Tadeusz Kosztołowicz

Published 2018-07-10Version 1

We present a model of the process of diffusion-absorption of a molecule in a system in which a thin partially permeable membrane separates various media. Different types of diffusion can occur in these media: diffusion, sub-diffusion or slow sub-diffusion. The method is based on a simple random walk model in a discrete system with a thin partially permeable wall. Within this method we firstly consider the particle's random walk in a system with both discrete time and space variables in which a particle can vanish due to absorption with probabilities defined separately for each medium. Then, we move form discrete to continuous variables. We derive the Green's functions for the system. The Green's functions are used to derive boundary conditions at the membrane.