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 ArticleSource:
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=f67881cd60d3914cc302f1edb1c6661cKeywords:
Diffusion, Diffusion Coefficients, Effective medium theories, Heterogeneous systems, Length scale, Nonlinear reaction, Percolation thresholds, Pulse propagation, Reaction rates, Solvents, Wave speedAbstract:
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.