Diffusion of multiple species with excluded-volume effects

Type
Article

Authors
Bruna, Maria
Chapman, S. Jonathan

KAUST Grant Number
KUK-C1-013-04

Online Publication Date
2012-11-28

Print Publication Date
2012-11-28

Date
2012-11-28

Abstract
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial differential equations. In this paper we consider multiple interacting subpopulations/species and study how the inter-species competition emerges at the population level. Each individual is described as a finite-size hard core interacting particle undergoing Brownian motion. The link between the discrete stochastic equations of motion and the continuum model is considered systematically using the method of matched asymptotic expansions. The system for two species leads to a nonlinear cross-diffusion system for each subpopulation, which captures the enhancement of the effective diffusion rate due to excluded-volume interactions between particles of the same species, and the diminishment due to particles of the other species. This model can explain two alternative notions of the diffusion coefficient that are often confounded, namely collective diffusion and self-diffusion. Simulations of the discrete system show good agreement with the analytic results. © 2012 American Institute of Physics.

Citation
Bruna M, Chapman SJ (2012) Diffusion of multiple species with excluded-volume effects. J Chem Phys 137: 204116. Available: http://dx.doi.org/10.1063/1.4767058.

Acknowledgements
This publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST). M. B. acknowledges financial support from EPSRC. The authors also thank M. Burger for helpful discussions and P. Degond for pointing out the connection between Onsager relations and symmetric systems.

Publisher
AIP Publishing

Journal
The Journal of Chemical Physics

DOI
10.1063/1.4767058

PubMed ID
23205990

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