An analytically solvable reaction-diffusion model for chemical dynamics in solutions

Abstract

Abstract Problems with diffusing probability distribution in the presence of sink traps, where the moving entity can be a particle, an entity, or a relevant coordinate in a reaction can represent a variety of physical processes. So far, the theoretical solutions gave time-domain understanding only if the problem had a translational invariance in potential or a mirror symmetry about the trap or the both. In this paper, we present a time-domain solution in the presence of a harmonic potential well ( V ( x ) = 1 2 kx 2 ) with a finite absorbing sink S ( x , t ) . Considering the Smoluchowski equation as the governing equation for the process, a special exit condition given by, S ( x , t ) = k 0 e kt δ ( x - x c e - kt ) can be solved analytically using transformations from a simple model. Interesting insights into the dynamics emerge from the interplay between the initial position of the distribution, diffusivity, position of the sink, etc. The derived survival probability profile gives an understanding of chemical dynamics in condensed phases.