Diffusion and trapping at arbitrary trap size and concentration

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Abstract
The average trapping rate and effective steady-state diffusion coefficient are derived for a particle hopping in a medium containing a random distribution of static traps. The traps may be of arbitrary size and concentration as long as they are allowed to overlap. Results are based on the author’s previous calculation of the spatially averaged survival probability. The finite-density corrections are much smaller than found by previous workers but in good agreement with simulations. Validity of a diffusion-reaction equation is established for steady-state conditions and the distribution of filled traps. (Only ideal sinks with no detrapping are considered.) Cases where the macroscopic trap concentration varies with position and there is a distribution of trap sizes are also considered. Transient motion of the nontrapped particles is shown to be nondiffusive, both theoretically and by simulations.