ArticleProceedings of the National Academy of Sciences of the United States of America2013
Propulsion of microorganisms by a helical flagellum.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2013. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 32 papers.
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Who cites it
32 citing papers in PubMed.
- Soft magnetic microrobots with remote sensing and communication capabilities.Nature communications · 2025Article
- Form and function in biological filaments: a physicist's review.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Review
- Load-dependent resistive-force theory for helical filaments.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Swimming by Spinning: Spinning-Top Type Rotations Regularize Sperm Swimming Into Persistently Progressive Paths in 3D.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- The role of morphological adaptability inmBio · 2025Article
- Geometric phase predicts locomotion performance in undulating living systems across scales.Proceedings of the National Academy of Sciences of the United States of America · 2024Article
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- The nut-and-bolt motion of a bacteriophage sliding along a bacterial flagellum: a complete hydrodynamics model.Scientific reports · 2023Article
- Decoding the hydrodynamic properties of microscale helical propellers from Brownian fluctuations.Proceedings of the National Academy of Sciences of the United States of America · 2023Article
- Light chain 2 is a Tctex-type related axonemal dynein light chain that regulates directional ciliary motility in Trypanosoma brucei.PLoS pathogens · 2022Article
- Self-adaptive and efficient propulsion of Ray sperms at different viscosities enabled by heterogeneous dual helixes.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
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- Brownian fluctuations and hydrodynamics of a microhelix near a solid wall.Scientific reports · 2020Article
- Thrust and Hydrodynamic Efficiency of the Bundled Flagella.Micromachines · 2019Article
- Hydrophobicity Influence on Swimming Performance of Magnetically Driven Miniature Helical Swimmers.Micromachines · 2019Article
- Strictures of a microchannel impose fierce competition to select for highly motile sperm.Science advances · 2019Article
- On the limitations of some popular numerical models of flagellated microswimmers: importance of long-range forces and flagellum waveform.Royal Society open science · 2019Article
- Flagellar number governs bacterial spreading and transport efficiency.Science advances · 2018Article
- Predicting and Optimizing Microswimmer Performance from the Hydrodynamics of Its Components: The Relevance of Interactions.Soft robotics · 2018Article
Corrections and comments
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Authors and funding
5 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The swimming of a bacterium or a biomimetic nanobot driven by a rotating helical flagellum is often interpreted using the resistive force theory developed by Gray and Hancock and by Lighthill, but this theory has not been tested for a range of physically relevant parameters. We test resistive force theory in experiments on macroscopic swimmers in a fluid that is highly viscous so the Reynolds number is small compared to unity, just as for swimming microorganisms. The measurements are made for the range of helical wavelengths λ, radii R, and lengths L relevant to bacterial flagella. The experiments determine thrust, torque, and drag, thus providing a complete description of swimming driven by a rotating helix at low Reynolds number. Complementary numerical simulations are conducted using the resistive force theories, the slender body theories of Lighthill and Johnson, and the regularized Stokeslet method. The experimental results differ qualitatively and quantitatively from the predictions of resistive force theory. The difference is especially large for and/or , parameter ranges common for bacteria. In contrast, the predictions of Stokeslet and slender body analyses agree with the laboratory measurements within the experimental uncertainty (a few percent) for all λ, R, and L. We present code implementing the slender body, regularized Stokeslet, and resistive force theories; thus readers can readily compute force, torque, and drag for any bacterium or nanobot driven by a rotating helical flagellum.
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