Effective medium theory for reaction rates and diffusion coefficients of heterogeneous systems

Effective medium theory for reaction rates and diffusion coefficients of heterogeneous systems

Publication Type:

Journal Article

Source:

Physical Review Letters, Volume 102, Number 23 (2009)

URL:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-67249103418&doi=10.1103%2fPhysRevLett.102.238302&partnerID=40&md5=f67881cd60d3914cc302f1edb1c6661c

Keywords:

Diffusion, Diffusion Coefficients, Effective medium theories, Heterogeneous systems, Length scale, Nonlinear reaction, Percolation thresholds, Pulse propagation, Reaction rates, Solvents, Wave speed

Abstract:

A simple effective medium theory is derived for spatially heterogeneous nonlinear reaction-diffusion media. Its validity is tested through comparisons with simulations of front and pulse propagation in systems with spatially varying diffusion coefficients and reaction rates. The theory is able to predict wave speeds if the characteristic front width is much larger than the length scale of the heterogeneities. This condition is violated in media with isolated or weakly connected sites. However, the theory nevertheless provides good results in cases where it correctly predicts the percolation threshold of the medium. © 2009 The American Physical Society.

File Attachment: