Reaction Front Dynamics in Diffusion-Controlled Particle-Antiparticle Annihilation: Experiments and Simulations

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Abstract
When electrons diffuse into a domain of holes, or defects into a domain of anti-defects, or molecules A meet molecules B with a reaction: A + B → C, what are the time characteristics of the reaction front and and reaction rate? A scaling argument by Galfi and Racz predicts that the reaction boundary will propagate as t½ (the more numerous particles penetrating the less numerous antiparticles domain). The width of the reaction front should increase as t⅙ and the rate of reaction as t−⅔. Monte Carlo simulations confirm the first prediction but suggest that the reaction boundary may be even more compact. Experiments were performed in round and square capillary domains, using colored reactant A molecules, colorless B molecules and a colorless product (C). Preliminary results support the t½ reaction front propagation rate. This is the same as the Einstein diffusion law for a non-reacting dye (which we also confirmed experimentally with the same apparatus). However, the width of the reaction front is significantly more compact than that of a diffusion front.