- Access by Xinjiang University
Taylor's chiral microswimmer
Phys. Rev. Fluids 8, 044201 – Published 28 April, 2023
DOI: https://doi.org/10.1103/PhysRevFluids.8.044201
Abstract
In order to understand the rotational motion of a microswimmer in a Newtonian fluid, we model it as an infinite cylinder with a helical, propagating surface wave. Using the method of series expansion, we calculate the linear and angular velocities of the cylinder, assuming that the wave amplitude is much smaller than the wavelength. To the first order in the wave amplitude, for the first mode of a purely azimuthal wave (that is, when the wavelength equals the cylinder's circumference), the cylinder moves along a circular path in the plane normal to its axis. Otherwise, the first-order velocities of the cylinder are zero, like the Taylor sheet. The time-averaged motion of the cylinder is determined by calculating the second-order velocities; the axial component of the wave vector leads to the linear motion of the cylinder along its axis and the azimuthal component to the angular motion around the axis. With the same stroke, the cylinder is always slower and less efficient than the Taylor sheet.
Physics Subject Headings (PhySH)
Article Text
References (35)
- E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys. 72, 096601 (2009).
- G. Taylor, Analysis of the swimming of microscopic organisms, Proc. R. Soc. London A 209, 447 (1951).
- G. I. Taylor, The action of waving cylindrical tails in propelling microscopic organisms, Proc. R. Soc. London A 211, 225 (1952).
- M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Commun. Pure Appl. Math. 5, 109 (1952).
- J. Blake, Self propulsion due to oscillations on the surface of a cylinder at low Reynolds number, Bull. Austral. Math. Soc. 5, 255 (1971).
- J. R. Blake, A spherical envelope approach to ciliary propulsion, J. Fluid Mech. 46, 199 (1971).
- T. Ishikawa, M. P. Simmonds, and T. J. Pedley, Hydrodynamic interaction of two swimming model micro-organisms, J. Fluid Mech. 568, 119 (2006).
- T. Ishikawa, G. Sekiya, Y. Imai, and T. Yamaguchi, Hydrodynamic interactions between two swimming bacteria, Biophys. J. 93, 2217 (2007).
- M. Farzin, K. Ronasi, and A. Najafi, General aspects of hydrodynamic interactions between three-sphere low-Reynolds-number swimmers, Phys. Rev. E 85, 061914 (2012).
- A. Reynolds, The swimming of minute organisms, J. Fluid Mech. 23, 241 (1965).
- D. F. Katz, On the propulsion of micro-organisms near solid boundaries, J. Fluid Mech. 64, 33 (1974).
- D. G. Crowdy and Y. Or, Two-dimensional point singularity model of a low-Reynolds-number swimmer near a wall, Phys. Rev. E 81, 036313 (2010).
- S. E. Spagnolie and E. Lauga, Hydrodynamics of self-propulsion near a boundary: Predictions and accuracy of far-field approximations, J. Fluid Mech. 700, 105 (2012).
- J. Dunstan, G. Miño, E. Clement, and R. Soto, A two-sphere model for bacteria swimming near solid surfaces, Phys. Fluids 24, 011901 (2012).
- E. Lauga, Propulsion in a viscoelastic fluid, Phys. Fluids 19, 083104 (2007).
- J. Teran, L. Fauci, and M. Shelley, Viscoelastic Fluid Response Can Increase the Speed and Efficiency of a Free Swimmer, Phys. Rev. Lett. 104, 038101 (2010).
- X. N. Shen and P. E. Arratia, Undulatory Swimming in Viscoelastic Fluids, Phys. Rev. Lett. 106, 208101 (2011).
- J. R. Vélez-Cordero and E. Lauga, Waving transport and propulsion in a generalized Newtonian fluid, J. Non-Newtonian Fluid Mech. 199, 37 (2013).
- C. Datt, L. Zhu, G. J. Elfring, and O. S. Pak, Squirming through shear-thinning fluids, J. Fluid Mech. 784, R1 (2015).
- M. S. Krieger, S. E. Spagnolie, and T. R. Powers, Locomotion and transport in a hexatic liquid crystal, Phys. Rev. E 90, 052503 (2014).
- J. Shi and T. R. Powers, Swimming in an anisotropic fluid: How speed depends on alignment angle, Phys. Rev. Fluids 2, 123102 (2017).
- H. Soni, R. A. Pelcovits, and T. R. Powers, Enhancement of Microorganism Swimming Speed in Active Matter, Phys. Rev. Lett. 121, 178002 (2018).
- M. S. Krieger, S. E. Spagnolie, and T. R. Powers, Swimming with small and large amplitude waves in a confined liquid crystal, J. Non-Newtonian Fluid Mech. 273, 104185 (2019).
- N. C. Darnton, L. Turner, S. Rojevsky, and H. C. Berg, On torque and tumbling in swimming Escherichia coli, J. Bacteriol. 189, 1756 (2007).
- J. de Anda, E. Y. Lee, C. K. Lee, R. R. Bennett, X. Ji, S. Soltani, M. C. Harrison, A. E. Baker, Y. Luo, T. Chou et al., High-speed “4D” computational microscopy of bacterial surface motility, ACS Nano 11, 9340 (2017).
- C. N. Dominick and X.-L. Wu, Rotating bacteria on solid surfaces without tethering, Biophys. J. 115, 588 (2018).
- L. Kuźicki, T. L. Jahn, and J. R. Fonesca, Helical nature of the ciliary beat of paramecium multimicronucleatum, J. Protozool. 17, 16 (1970).
- S. E. Spagnolie, B. Liu, and T. R. Powers, Locomotion of Helical Bodies in Viscoelastic Fluids: Enhanced Swimming at Large Helical Amplitudes, Phys. Rev. Lett. 111, 068101 (2013).
- B. Liu, T. R. Powers, and K. S. Breuer, Force-free swimming of a model helical flagellum in viscoelastic fluids, Proc. Natl. Acad. Sci. USA 108, 19516 (2011).
- L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Course of Theoretical Physics, Vol. 6 (Elsevier, 2013).
- G. K. Batchelor, Slender-body theory for particles of arbitrary cross-section in Stokes flow, J. Fluid Mech. 44, 419 (1970).
- J.-L. Pierson, M. Kharrouba, and J. Magnaudet, Hydrodynamic torque on a slender cylinder rotating perpendicularly to its symmetry axis, Phys. Rev. Fluids 6, 094303 (2021).
- J. R. Blake and M. A. Sleigh, Mechanics of ciliary locomotion, Biol. Rev. 49, 85 (1974).
- H. Machemer, Ciliary activity and the origin of metachrony in Paramecium: Effects of increased viscosity, J. Exp. Biol. 57, 239 (1972).
- S. L. Tamm, Ciliary motion in Paramecium: A scanning electron microscope study, J. Cell Biol. 55, 250 (1972).
