Diffusion Enhancement and Directional Suppression Induced by Reciprocal Flows
Abstract
Reciprocal flows repeatedly return fluid elements to their initial positions, producing no net advective transport on time average. Nevertheless, their interplay with diffusion gives rise to nontrivial transport. To describe this phenomenon, we develop a general theory of effective diffusion under two-dimensional linear flows with arbitrary time dependence. By analyzing the advection-diffusion equation, we derive exact expressions for the mean square displacement and the effective diffusion coefficients for extensional, simple shear, and rotational flows within a single framework. We show that the reciprocal flows universally induce diffusion enhancement. The diffusion tensor exhibits pronounced anisotropy, which can result in directional diffusion suppression in spite of the direction-averaged diffusion enhancement. Our results provide a general framework for diffusion control by time-dependent flows and can provide new strategies for transport manipulation in microfluidic and biological systems.
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BibTeX
@misc{koyano2026diffusion,
title = {{Diffusion Enhancement and Directional Suppression Induced by Reciprocal Flows}},
author = {Yuki Koyano and Hiroyuki Kitahata and Takeshi Ooshida},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12733},
eprint = {2609.12733},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12733},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Diffusion Enhancement and Directional Suppression Induced by Reciprocal Flows
AU - Yuki Koyano
AU - Hiroyuki Kitahata
AU - Takeshi Ooshida
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.12733
UR - https://arxiv.org/abs/2609.12733
AB - Reciprocal flows repeatedly return fluid elements to their initial positions, producing no net advective transport on time average. Nevertheless, their interplay with diffusion gives rise to nontrivial transport. To describe this phenomenon, we develop a general theory of effective diffusion under two-dimensional linear flows with arbitrary time dependence. By analyzing the advection-diffusion equation, we derive exact expressions for the mean square displacement and the effective diffusion coefficients for extensional, simple shear, and rotational flows within a single framework. We show that the reciprocal flows universally induce diffusion enhancement. The diffusion tensor exhibits pronounced anisotropy, which can result in directional diffusion suppression in spite of the direction-averaged diffusion enhancement. Our results provide a general framework for diffusion control by time-dependent flows and can provide new strategies for transport manipulation in microfluidic and biological systems.
ER -