Field and dimensionality effects in trapping reaction kinetics

We analyze the main properties of a diffusion-controlled reaction of the type A + T → T in the presence of a field that affects the mobile particles A but not the fixed traps T. For one-dimensional systems a steady state is reached exponentially fast if the field points towards the trap. If the system dimension is two or higher, a steady state is always reached. In this steady state there is an anisotropically perturbed region whose relative size decreases as the system dimension is increased. This perturbed region always contains a depletion zone downstream and, if the field is sufficiently strong, we observe an excess of diffusing reactants upstream from an imperfect trap. We present formulas to calculate the steady-state concentration, the nearest-neighbor distribution, the reaction rate, and the diffusion-controlled growth rate of a droplet.