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Updated: Jun 5, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Mapping of diffusion in a channel with abrupt change of diameter
Pavol Kalinay1, Jerome K Percus
1Institute of Physics, Slovak Academy of Sciences, Dúbravska cesta 9, 84511 Bratislava, Slovakia.
Abstract:
Mapping of the diffusion equation in a channel of varying cross section onto the longitudinal coordinate is already a well studied procedure for a slowly changing radius. We examine here the mapping of diffusion in a channel with abrupt change of diameter. In two dimensions, our considerations are based on solution of the exactly solvable geometry with abruptly doubled width at x=0. We verify the surmise of Berezhkovskii [J. Chem. Phys. 131, 224110 (2009)] that one-dimensional diffusion behaves as free in such channels everywhere except at the point of change, which looks like a local trap for the particles. Applying the method of "sewing" of solutions, we show that this picture is valid also for three-dimensional symmetric channels.
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