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Dynamics of rotating helices in a viscous fluid

Published online by Cambridge University Press:  13 June 2025

Chijing Zang ,
Luke Omodt ,
Moumita Dasgupta  and
Xiang Cheng Open the ORCID record for Xiang Cheng [Opens in a new window]
Chijing Zang
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA
Luke Omodt
Affiliation:
Department of Physics, Augsburg University, Minneapolis, MN 55455, USA
Moumita Dasgupta
Affiliation:
Department of Physics, Augsburg University, Minneapolis, MN 55455, USA
Xiang Cheng*
Affiliation:
Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN 55455, USA Saint Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414, USA
*
Corresponding author: Xiang Cheng, xcheng@umn.edu
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Abstract

We investigate the dynamics of a pair of rigid rotating helices in a viscous fluid, as a model for bacterial flagellar bundle and a prototype of microfluidic pumps. Combining experiments with hydrodynamic modelling, we examine how spacing and phase difference between the two helices affect their torque, flow field and fluid transport capacity at low Reynolds numbers. Hydrodynamic coupling reduces the torque when the helices rotate in phase at constant angular speed, but increases the torque when they rotate out of phase. We identify a critical phase difference, at which the hydrodynamic coupling vanishes despite the close spacing between the helices. A simple model, based on the flow characteristics and positioning of a single helix, is constructed, which quantitatively predicts the torque of the helical pair in both unbounded and confined systems. Finally, we show the influence of spacing and phase difference on the axial flux and the pump efficiency of the helices. Our findings shed light on the function of bacterial flagella and provide design principles for efficient low-Reynolds-number pumps.

JFM classification

Biological Fluid Dynamics: Micro-organism dynamics Low-Reynolds-number flows: Slender-body theory Biological Fluid Dynamics: Propulsion
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 1013 , 25 June 2025 , R1
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Zang et al. supplementary material movie 1

Flow field of two rotating helices at a separation $d/R = 5$ and a phase difference $\\Delta \\phi=0$ in the axial plane ($x$-$z$ plane with $y=0$). The top row shows the experimental flow field obtained via PIV, while the bottom row presents results from SBT simulations. The left column illustrates the $z$-component of velocity ($v_z$), and the right column depicts the $r$-component of velocity ($v_r$). Velocities are normalized by $\\omega R$. White lines and arrows are streamlines. Notably, experiments reveal an upward flow $(+z)$ near the wall, whereas SBT simulations in an unbounded fluid consistently show flow in the $-z$ direction. The movie shows one rotation period $2\\pi/\\omega = 12.5$ s.
Download Zang et al. supplementary material movie 1(File)
File 2.3 MB
Supplementary material: File

Zang et al. supplementary material movie 2

Flow field of two rotating helices at a separation $d/R = 5$ and a phase difference $\\Delta \\phi=0$ in the meridional plane ($x$-$y$ plane). The color indicates the magnitude of the in-plane velocity $v_{x-y} = \\sqrt{v_x^2+v_y^2}$ normalized by the rotation speed $\\omega R$. The top row shows the experimental flow field obtained via PIV, while the bottom row presents results from SBT simulations. White lines and arrows are streamlines. The movie shows one rotation period $2\\pi/\\omega = 12.5$ s.
Download Zang et al. supplementary material movie 2(File)
File 2.6 MB