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Updated: Sep 22, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Characterizing scale dependence of effective diffusion driven by fluid flows.

Yohei Kono¹, Yoshihiko Susuki², Takashi Hikihara¹

¹Department of Electrical Engineering, Kyoto University, 615-8510 Kyoto, Japan.

Physical Review. E

|May 20, 2022

Summary

This study introduces a new method to measure effective diffusion without scale separation, revealing how Péclet number impacts tracer movement in complex fluid flows.

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Area of Science:

Fluid dynamics
Transport phenomena
Statistical mechanics

Background:

Effective diffusion describes tracer movement in complex flows.
Classical models often assume scale separation between advection and diffusion.
This assumption limits applicability in many real-world scenarios.

Purpose of the Study:

To develop a method for characterizing effective diffusivity without scale separation.
To investigate the scale dependence of effective diffusivity on the Péclet number.
To analyze discrepancies from classical limits in specific flow types.

Main Methods:

Proposing an alternate method to identify effective diffusivity.
Utilizing a test advection-diffusion equation with a pulse initial condition.
Minimizing the L∞ distance between test equation solutions and diffusion with mean drift.

Main Results:

Demonstrating scale dependence of effective diffusivity for gyre and shear flows.
Showing discrepancies from classical limits derived with scale separation.
Identifying molecular diffusion across flow cells and suppressed drift as origins of discrepancies.

Conclusions:

The proposed method accurately characterizes effective diffusivity beyond scale separation.
Scale dependence is significant and deviates from classical predictions.
Understanding these deviations is crucial for accurate modeling of transport in complex fluids.