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Updated: Sep 8, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Mean first-passage time to a small absorbing target in three-dimensional elongated domains
Denis S Grebenkov1, Alexei T Skvortsov2
1Laboratoire de Physique de la Matière Condensée, UMR No. 7643, CNRS, Ecole Polytechnique, IP Paris, 91120 Palaiseau, France.
Abstract:
We derive an approximate formula for the mean first-passage time (MFPT) to a small absorbing target of arbitrary shape inside an elongated domain of a slowly varying axisymmetric profile. For this purpose, the original Poisson equation in three dimensions is reduced to an effective one-dimensional problem on an interval with a semipermeable semiabsorbing membrane. The approximate formula captures correctly the dependence of the MFPT on the distance to the target, the radial profile of the domain, and the size and the shape of the target. This approximation is validated by Monte Carlo simulations.
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