Eur. Phys. J. B (2013) 86: 186
https://doi.org/10.1140/epjb/e2013-31132-3

Regular Article

Interference related corrections to classical gas diffusion in a system of small heterogeneities

¹ Moscow Engineering Physics Institute, 31, Kashirskoe shosse, 115409 Moscow, Russia
² Karpov Institute of Physical Chemistry, 10, Vorontsovo Pole, 105064 Moscow, Russia
³ Moscow Institute of Physics and Technology, Institutsky per., 9, 141700 Dolgoprudny, Moscow region, Russia
⁴ School of Engineering, Griffith University, 4111 QLD Brisbane, Australia

^a e-mail: i.agranovski@griffith.edu.au

Received: 17 December 2012
Received in final form: 21 February 2013
Published online: 24 April 2013

Abstract

Diffusion of an ideal gas in a system of small spherical heterogeneities (collective of particles and a system of small cavities in homogeneous medium) is considered. The effective diffusion coefficient is calculated using methods of multiple scattering theory. Some possible contribution to diffusion of multiple passing closed loops on the trajectory of a molecule is considered. The interest to such loops is related to constructive interference of amplitudes corresponding to two alternative ways of the loop passing (clockwise and counterclockwise). This interference always exists, irrespective to the medium disorder. In this paper, we show that the interference corrections to classical diffusion lead to appearance of low frequency macroscopic oscillations of the gas concentration and complete stagnation of the diffusion process. The latter resembles the Anderson localization of electrons in a system of impurities in an ideal lattice.