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Updated: Dec 12, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Mean first passage time for a particle diffusing on a disk with two absorbing traps at the boundary
1Defence Science and Technology, 506 Lorimer Street, Fishermans Bend, Victoria 3207, Australia.
Abstract:
The problem of survival of a Brownian particle diffusing on a disk with a reflective boundary that has two absorbing arcs is treated analytically. The framework of boundary homogenization is applied to calculate the effective trapping rate of the disk boundary, and this enables estimation of the mean first passage time. The method of conformal mapping is applied to transform the original system to a simpler geometrical configuration (a flat reflective boundary with a periodic configuration of identical absorbing strips) for which the analytical solution is known. The expression for the mean first passage time is simplified for some limiting cases (small arc or small gap). The derived analytical expressions compare favorably with the results of Brownian particle simulations and other analytical results from the literature.
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