DEPLETION REGION FOR DIFFUSION-CONTROLLED REACTIONS IN A FIELD

The effects of a uniform field on the distribution of mobile particles in the presence of a fixed trap are analyzed. Even small fields are shown to have a drastic effect on magnitudes, such as the reaction rate and the mean distance L from the trap to its nearest neighbor. If the field points towards the trap, a steady state is reached exponentially fast. In this steady state there is a depletion hole next to the trap, whose size depends on the ratio between the drift velocity V and the diffusion coefficient D. If c is the initial concentration of mobile particles, the long-time reaction rate is simply cV. If the field points away from the trap, the maximum of the probability distribution function for the distance to a nearest neighbor moves away from the trap with constant speed (if V=0, L∼t1/4) and the reaction rate decays as t-3/2exp(-V2t/4D), where t is time. © 1995 The American Physical Society.