Depletion region for diffusion-controlled reactions in a field

C.A. CONDAT; G.J. SIBONA; C.E. BUDDE

PHYSICAL REVIEW E - STATISTICAL PHYSICS, PLASMAS, FLUIDS AND RELATED INTERDISCIPLINARY TOPICS

The American Physical Society

Año: 1995 vol. 51 p. 2839 - 2843

1063-651X

The effects of a uniform field on the distribution of mobile particles in the presence of a fixed trap are analyzed. Even small fields arte 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 c½V½. 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 a constant speed (if V = 0, <L> ~ t1/4) and the reaction rate decays as t-3/2exp(-V2t/4D), where t is the time.