Kinetics of A+B--->0 with Driven Diffusive Motion

TL;DR

This paper investigates the kinetics of a two-species annihilation process with biased motion and excluded volume effects, revealing a t^{-1/3} density decay explained via Burgers equation, differing from isotropic diffusion cases.

Contribution

It introduces a simple Burgers equation-based explanation for the observed t^{-1/3} decay in biased annihilation kinetics, extending understanding of driven diffusive systems.

Findings

Density decays as t^{-1/3} under biased motion

Burgers equation effectively models the asymptotic behavior

Provides insight into spatial distribution of reactants

Abstract

We study the kinetics of two-species annihilation, A+B--->0, when all particles undergo strictly biased motion in the same direction and with an excluded volume repulsion between same species particles. It was recently shown that the density in this system decays as t^{-1/3}, compared to t^{-1/4} density decay in A+B--->0 with isotropic diffusion and either with or without the hard-core repulsion. We suggest a relatively simple explanation for this t^{-1/3} decay based on the Burgers equation. Related properties associated with the asymptotic distribution of reactants can also be accounted for within this Burgers equation description.