DIFFUSION-CONTROLLED AND DRIFT-CONTROLLED REACTIONS IN 2 AND 3 DIMENSIONS

We analyze the steady state of a reaction in which mobile reactants di ffusing under the action of a uniform field may be absorbed by perfect or imperfect spherical traps. We obtain contour maps for the concentr ation and for the probability distribution function for the first mobi le neighbor of the trap. This permits a clear visualization of the eff ects of a trap on the statistics of the mobile particles. We also obta in the trapping (or reaction) rates for the two- and three-dimensional problems, and examine the influence of drift and trapping strength. W hile in the absence of a held there is no steady state in two dimensio ns, we show here that the addition of an arbitrarily small field suffi ces to make it possible. In the small-field limit, the reaction rate v anishes as \ln(V/D)\(-1), where V is the drift velocity and D is the d iffusion coefficient.