Trapping by static sinks: An exact result based on fluctuating nonequilibrium thermodynamics

The theory of fluctuating nonequilibrium thermodynamics is applied to the trapping of particles by stationary sinks. Earlier treatments of this problem are based on the Smoluchowski theory and have examined the effect of interaction among the sinks. Using a calculation which involves the effects of both diffusion and the rate of trapping, we obtain the static and dynamic structure factors for a system of static sinks with diffusing particles that are replaced at a steady rate. We examine in detail the limiting case of dilute diffusing particles, for which the statistical distribution of sinks remains unperturbed. Using a self-consistent procedure to calculate the trapping rate, we obtain a transcendental equation for the trapping rate constant which agrees with the lowest order density corrections calculated by others. Experiments for testing the density dependence of the trapping rate constant are proposed.