Transverse transport of microswimmers in oscillatory channel flows
Abstract
Motile microorganisms inhabit oscillatory flows encountered in physiological and engineering systems, yet the influence of flow unsteadiness on their shear-induced preferential concentration remains less understood. We investigate transverse transport of elongated microswimmers in oscillatory pressure-driven channel flow using complementary Langevin simulations and two- and one-dimensional Fokker-Planck models. Agreement between particle-based and continuum descriptions across governing parameters establishes the fidelity of the Fokker-Planck formulation for swimmer transport in oscillatory shear flows. Our analysis demonstrates that oscillatory forcing fundamentally modifies classical steady-flow shear-trapping. We find that increasing Womersley number Wo reduces centerline depletion by confining oscillatory shear to thinner near-wall regions. In contrast, increasing frequency ratio β, of swimmer rotational diffusion rate and flow oscillation frequency, promotes sustained orientational anisotropy, and leads to a saturating increase in centerline depletion. In the weak-swimming limit, we derive a hierarchy of coupled orientational moments, enabling analytical solutions at arbitrary temporal harmonic order. The asymptotic solutions establish a universal transfer law showing that, for a given swimmer shape, the normalized leading-order orientational response depends solely on β. Reconstruction of the orientational distribution yields closed-form expressions for the swimmer concentration profile and depletion index, ID. Our asymptotic solution recovers the steady-flow weak-shear scaling of ID with flow Peclet number, Pef, of ID ∝ Pef2, and reveals that oscillatory forcing attenuates this response by a factor 16β2/(1+16β2). These results provide a theoretical framework to predict transverse transport of microswimmers in oscillatory channel flows.
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BibTeX
@misc{ram2026transverse,
title = {{Transverse transport of microswimmers in oscillatory channel flows}},
author = {Raghav Ram and Ashwin Ramachandran},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06393},
eprint = {2609.06393},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06393},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Transverse transport of microswimmers in oscillatory channel flows
AU - Raghav Ram
AU - Ashwin Ramachandran
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06393
UR - https://arxiv.org/abs/2609.06393
AB - Motile microorganisms inhabit oscillatory flows encountered in physiological and engineering systems, yet the influence of flow unsteadiness on their shear-induced preferential concentration remains less understood. We investigate transverse transport of elongated microswimmers in oscillatory pressure-driven channel flow using complementary Langevin simulations and two- and one-dimensional Fokker-Planck models. Agreement between particle-based and continuum descriptions across governing parameters establishes the fidelity of the Fokker-Planck formulation for swimmer transport in oscillatory shear flows. Our analysis demonstrates that oscillatory forcing fundamentally modifies classical steady-flow shear-trapping. We find that increasing Womersley number Wo reduces centerline depletion by confining oscillatory shear to thinner near-wall regions. In contrast, increasing frequency ratio β, of swimmer rotational diffusion rate and flow oscillation frequency, promotes sustained orientational anisotropy, and leads to a saturating increase in centerline depletion. In the weak-swimming limit, we derive a hierarchy of coupled orientational moments, enabling analytical solutions at arbitrary temporal harmonic order. The asymptotic solutions establish a universal transfer law showing that, for a given swimmer shape, the normalized leading-order orientational response depends solely on β. Reconstruction of the orientational distribution yields closed-form expressions for the swimmer concentration profile and depletion index, I_D. Our asymptotic solution recovers the steady-flow weak-shear scaling of I_D with flow Peclet number, Pe_f, of I_D ∝ Pe_f^2, and reveals that oscillatory forcing attenuates this response by a factor 16β^2/(1+16β^2). These results provide a theoretical framework to predict transverse transport of microswimmers in oscillatory channel flows.
ER -