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Dispersion of confined microswimmers with diffuse reflection boundary condition: asymptotic and transient solutions

Published online by Cambridge University Press:  02 September 2025

Hanhan Zeng ,
Weiquan Jiang Open the ORCID record for Weiquan Jiang [Opens in a new window] ,
Mingyang Guan Open the ORCID record for Mingyang Guan [Opens in a new window] ,
Joseph Hun-wei Lee  and
Guoqian Chen Open the ORCID record for Guoqian Chen [Opens in a new window]
Hanhan Zeng
Affiliation:
Laboratory of Systems Ecology and Sustainability Science, College of Engineering, Peking University, Beijing 100871, PR China
Weiquan Jiang
Affiliation:
National Observation and Research Station of Coastal Ecological Environments in Macao; Macao Environmental Research Institute, Faculty of Innovation Engineering, Macau University of Science and Technology, Macao SAR 999078, PR China
Mingyang Guan
Affiliation:
Laboratory of Systems Ecology and Sustainability Science, College of Engineering, Peking University, Beijing 100871, PR China
Joseph Hun-wei Lee
Affiliation:
National Observation and Research Station of Coastal Ecological Environments in Macao; Macao Environmental Research Institute, Faculty of Innovation Engineering, Macau University of Science and Technology, Macao SAR 999078, PR China
Guoqian Chen*
Affiliation:
Laboratory of Systems Ecology and Sustainability Science, College of Engineering, Peking University, Beijing 100871, PR China National Observation and Research Station of Coastal Ecological Environments in Macao; Macao Environmental Research Institute, Faculty of Innovation Engineering, Macau University of Science and Technology, Macao SAR 999078, PR China
*
Corresponding author: Guoqian Chen, gqchen@pku.edu.cn
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Abstract

Dispersion of microswimmers is widespread in environmental and biomedical applications. In the category of continuum modelling, the present study investigates the dispersion of microswimmers in a confined unidirectional flow under a diffuse reflection boundary condition, instead of the specular reflection and the Robin boundary conditions prevailing in existing studies. By the moment analysis based on the Smoluchowski equation, the asymptotic and transient solutions are directly obtained, as validated against random walk simulations, to illustrate the effects of mean flow velocity, swimming velocity and gyrotaxis on the migration and distribution patterns of elongated microswimmers. Under the diffuse reflection boundary condition, microswimmers are found more likely to exhibit M-shaped low-shear trapping and even pronounced centreline aggregation, and elongated shape affects depletion at the centreline. Along the flow direction, they readily form unimodal distributions oriented downstream, resulting in prominent downstream migration. Near the centreline, the migration is almost entirely downstream, while upstream and vertical migrations are confined near the boundaries. When the mean flow velocity and swimming velocity are comparable, the system undergoes a temporal transition from M-shaped low-shear trapping to M-shaped high-shear trapping and ultimately to centreline aggregation. The downstream migration continuously strengthens over time, while the upstream first strengthens and then weakens. Moreover, the coupling between swimming-induced diffusion and convective dispersion leads to non-monotonic, fluctuating trends in both drift velocity and dispersivity over time. These results contribute to a deeper understanding of the underlying mechanisms governing the locomotion and control of natural and synthetic microswimmers.

JFM classification

Biological Fluid Dynamics: Swimming/flying Mass Transport: Dispersion

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JFM Papers
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Journal of Fluid Mechanics , Volume 1018 , 10 September 2025 , A27
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© The Author(s), 2025. Published by Cambridge University Press

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