STEADY-STATE IN 2-DIMENSIONAL DIFFUSION-CONTROLLED REACTIONS

We investigate the conditions under which a steady state can be reache d in a two-dimensional diffusion-controlled trapping reaction. If ther e is no interaction between trap and diffusing particles, the reaction rate decreases monotonically to zero. Here we show that a logarithmic attractive potential between trap and diffusing particles leads to a finite steady-state reaction rate. A steady state can also be reached if the diffusing particles move under the action of a uniform external field. More unexpectedly, a steady-state rate can be obtained in the absence of any ''assisting field'' if the trap grows due to the absorp tion of the diffusing particles. The reaction rates are calculated in all cases.