Reaction-diffusion front crossing a local defect

TL;DR

This paper investigates how a reaction-diffusion front interacts with a local defect, using numerical and analytical methods to understand pinning phenomena and develop a simplified model.

Contribution

The study introduces a reduced collective variable model to analyze front-defect interactions and provides a quantitative criterion for front pinning.

Findings

Good agreement between reduced model and full problem solutions

Quantitative criterion for front pinning on large defects

Analytical and numerical methods complement each other

Abstract

The interaction of a Zeldovich 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.