Monte Carlo study of a model of diffusion-controlled reactions

Abstract

Diffusion-controlled reactions between solute particles and immobile spherical sinks are studied, using the Monte Carlo method to perform averages over sink configurations. The average steady-state solute concentration profile c̄(r) in a locally perturbed solution is determined for sink volume fractions φ≤0.3, by numerically solving the diffusion equation in the monopolar+dipolar approximation of diffusive couplings between the sinks. At low volume fractions the analytical result c̄(r)∝r−1 exp(−r/λ), with the screening length λ∝φ−1/2, is recovered, whereas for φ≳0.1 significant deviations from this functional form are found. The Monte Carlo method is shown to be most accurate and efficient in the region 10−3≲φ≲10−1 in which (a) a system of only 25 sinks suffices, and (b) the monopolar approximation alone is sufficiently accurate. In this regime the reaction rate coefficient calculated numerically is found to be in good agreement with previous analytical theories.