Propulsion of microorganisms by a helical flagellum

We present code implementing the slender body, regularized Stokeslet, and resistive force theories; readers can readily compute force, torque, and drag for any bacterium or nanobot driven by a rotating helical flagellum

B. Rodenborn; C.-H. Chen; H. L. Swinney; B. Liu; H. P. Zhang


Scholarcy highlights

  • 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
  • Our experiments reveal that resistive force theory fails to provide an accurate description of low Reynolds number swimmers driven by a rotating helical flagellum for helices with λ < 6R and/or L > 3λ, which is the range relevant to bacteria
  • The measurements were made for values of helical pitch λ and length L that include the ranges relevant to bacteria
  • Hancock pioneered the analysis of swimming microorganisms more than a half century ago. His “slender body model” yielded predictions in terms of integrals that could not be nuand the regularized Stokelets method agree well with the laboratory observations; the difference is within the experimental uncertainty
  • The good agreement between measurements and calculations for the flagella suggests that the stationary motor housing, unlike with a moving cell body, does not interact strongly with the flagellum
  • We have shown that slender body theory and regularized Stokeslet theory predictions are in good accord with measurements on low Reynolds number swimmers driven by a rotating helix
  • (The filament radius is a 1⁄4 R=16, and the helical pitch is λ 1⁄4 2:42R.) For flagella longer than L=λ ∼100, the scaled values change slowly, but both the Lighthill and Johnson slender body theory calculations approach the asymptotic value

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