Diffusion- and drift-controlled reactions in two and three dimensions

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

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

The American Physical Society

Año: 1996 vol. 54 p. 6232 - 6241

1063-651X

We analyze the steady state of a reaction in which mobile reactants diffusing under the action of a uniform field may be absorbed by perfect or imperfect spherical traps. We obtain contour maps for the concentration and for the probability distribution function for the first mobile neighbor of the trap. This permits a clear visualization of the effects of a trap on the statistics of the mobile particles. We also obtain the trapping ~or reaction! rates for the two- and three-dimensional problems, and examine the influence of drift and trapping strength. While in the absence of a field there is no steady state in two dimensions, we show here that the addition of an arbitrarily small field suffices to make it possible. In the small-field limit, the reaction rate vanishes as uln(V/D)u21, where V is the drift velocity and D is the diffusion coefficient.~or reaction! rates for the two- and three-dimensional problems, and examine the influence of drift and trapping strength. While in the absence of a field there is no steady state in two dimensions, we show here that the addition of an arbitrarily small field suffices to make it possible. In the small-field limit, the reaction rate vanishes as uln(V/D)u21, where V is the drift velocity and D is the diffusion coefficient.