Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Institutions: Kobe University, Chiba University, Tottori University
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: 樟脳船を用いたアクティブマターの集団ダイナミクスの解明, Catastrophic Natural Disasters: Studies of Environmental and Social Change and Activities to Reduce Future Vulnerabilities, G2723053638, G4536007758, Earthquake-induced long-term change of landforms and its implication for rational rehabilitations, G4894386991, Universal Understanding of Spatiotemporal Order Induced by Nonreciprocal Interactions, G54783358, G5691674292, Sensing mechanisms of biological touch mimicking Ruffini endings., 流動と拡散の協働現象の一般的な定式化, 自己駆動体運動を記述する反応拡散系モデルとその数理解析, G8074723020
OpenAlex ID: W7212929287