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Updated: Jun 5, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Probability distribution of a trapped brownian particle in plane shear flows
Jochen Bammert1, Walter Zimmermann
1Theoretische Physik I, Universität Bayreuth, 95440 Bayreuth, Germany.
Abstract:
We investigate the statistical properties of an overdamped brownian particle that is trapped by a harmonic potential and simultaneously exposed to a linear shear flow or to a plane Poiseuille flow. Its probability distribution is determined via the corresponding Smoluchowski equation, which is solved analytically for a linear shear flow. In the case of a plane Poiseuille flow, analytical approximations for the distribution are obtained by a perturbation analysis and are substantiated by numerical results. There is good agreement between the two approaches for a wide range of parameters.
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