Analytical solution in Laplace domain of Smoluchowski equation for a flat potential with a rectangular sink

Abstract

We propose a new method for finding the exact analytical solution in Laplace domain for the problem where a particle is diffusing on a flat potential in the presence of a rectangular sink of arbitrary width and height. In our model, diffusive motion is described by the Smoluchowski equation. Our method with this sink of rectangular shape is very general and can be used to deal with other potentials. We have derived exact analytical expression for rate constants using our model. This is the first model where the exact analytical solution in closed form is found in the case of a sink of arbitrary width. This model is more realistic for understanding reaction–diffusion systems that all other existing models available in literature.