Propulsion of microorganisms by a helical flagellum
Journal
Proceedings of the National Academy of Sciences of the United States of America
Journal Volume
110
Journal Issue
5
Pages
E338-E347
Date Issued
2013
Author(s)
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 ofswimming drivenbyarotating helixatlow 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 ofresistive force theory. The difference is especially large for λ<6R and/or L>3λ, 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.
Subjects
Hydrodynamic interaction; Motility
SDGs
Other Subjects
article; bacterial flagellum; bacterial propulsion; Caulobacter crescentus; Escherichia coli; hydrodynamics; microbiological parameters; nonhuman; priority journal; Rhizobium lupini; Salmonella; simulation; Algorithms; Bacterial Physiological Phenomena; Computer Simulation; Flagella; Models, Biological; Movement; Rotation; Torque
Type
journal article