Diffusionhyphen;controlled reactions between solute particles and immobile spherical sinks are studied, using the Monte Carlo method to perform averages over sink configurations. The average steadyhyphen;state solute concentration profilecmacr;(r) in a locally perturbed solution is determined for sink volume fractions fgr;le;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 resultcmacr;(r)prop;rminus;1thinsp;exp(minus;r/lgr;), with the screening length lgr;prop;fgr;minus;1/2, is recovered, whereas for fgr;gsim;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 10minus;3lsim;fgr;lsim;10minus;1in 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.
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