Reaction-diffusion front crossing a local defect

Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Oct;84(4 Pt 1):041108. doi: 10.1103/PhysRevE.84.041108. Epub 2011 Oct 10.

Abstract

The interaction of a Zeldovich-Frank-Kamenetsky reaction-diffusion front with a localized defect is studied numerically and analytically. For the analysis, we start from conservation laws and develop simple, collective variable, ordinary differential equations for the front position and width. Their solutions are in good agreement with the solutions of the full problem. Finally, using this reduced model, we explain the pinning of the front on a large defect and obtain a quantitative criterion.