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Chin. Phys. B, 2014, Vol. 23(11): 114703    DOI: 10.1088/1674-1056/23/11/114703
SPECIAL TOPIC—Non-equilibrium phenomena in soft matters Prev   Next  

Propulsive matrix of a helical flagellum

Zhang He-Penga, Liu Binb, Bruce Rodenbornc, Harry L. Swinneyc
a Department of Physics and Astronomy and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai, China;
b School of Natural Sciences, University of California, Merced, California, USA;
c Department of Physics and Center for Nonlinear Dynamics, University of Texas at Austin, Austin, Texas, USA

We study the propulsion matrix of bacterial flagella numerically using slender body theory and the regularized Stokeslet method in a biologically relevant parameter regime. All three independent elements of the matrix are measured by computing propulsive force and torque generated by a rotating flagellum, and the drag force on a translating flagellum. Numerical results are compared with the predictions of resistive force theory, which is often used to interpret micro-organism propulsion. Neglecting hydrodynamic interactions between different parts of a flagellum in resistive force theory leads to both qualitative and quantitative discrepancies between the theoretical prediction of resistive force theory and the numerical results. We improve the original theory by empirically incorporating the effects of hydrodynamic interactions and propose new expressions for propulsive matrix elements that are accurate over the parameter regime explored.

Keywords:  low-Reynolds-number flows      micro-organism dynamics      bacterial swimming  
Received:  25 July 2014      Revised:  20 October 2014      Accepted manuscript online: 
PACS:  47.63.-b (Biological fluid dynamics)  
  47.63.Gd (Swimming microorganisms)  
  87.17.Jj (Cell locomotion, chemotaxis)  
  87.16.Qp (Pseudopods, lamellipods, cilia, and flagella)  

Project supported by the National Natural Science Foundation of China (Grant No. 11104179), the Shanghai Pujiang Program, China (Grant No. 12PJ1405400), the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, China (Grant No. SHDP201301), and the Innovation Program of Shanghai Municipal Education Commission, China (Grant No. 14ZZ030).

Corresponding Authors:  Zhang He-Peng     E-mail:

Cite this article: 

Zhang He-Peng, Liu Bin, Bruce Rodenborn, Harry L. Swinney Propulsive matrix of a helical flagellum 2014 Chin. Phys. B 23 114703

[1] Scharf B 2002 J. Bacteriology 184 5979
[2] Darnton N C, Turner L, Rojevsky S and Berg H C 2007 J. Bacteriology 189 1756
[3] Spagnolie S E and Lauga E 2011 Phys. Rev. Lett. 106 058103
[4] Rodenborn B, Chen C H, Swinney H L, Liu B and Zhang H P 2013 Proc. Natl. Acad. Sci. USA 110 E338
[5] Zhang L, Abbott J J, Dong L X, Peyer K E, Kratochvil B E, Zhang H X, Bergeles C and Nelson B J 2009 Nano Lett. 9 3663
[6] Nelson B J, Kaliakatsos I K and Abbott J J 2010 Annu. Rev. Biomed. Eng. 12 55
[7] Happel J and Brenner H 1965 Low Reynolds Number Hydrodynamics (Englewood Cliffs, NJ: Prentice Hall)
[8] Kim S and Karrila J S 1991 Microhydrodynamics: Principles and Selected Applications (Boston: Butterworth-Heinemann)
[9] Lauga E and Powers T R 2009 Rep. Prog. Phys. 72 096601
[10] Gray J and Hancock G T 1955 J. Exp. Biol. 32 802
[11] Lighthill J 1976 SIAM Rev. 18 161
[12] Chattopadhyay S, Moldovan R, Yeung C and Wu X L 2006 Proc. Natl. Acad. Sci. USA 103 13712
[13] Chattopadhyay S and Wu X L 2009 Biophys. J. 96 2023
[14] Liu B, Breuer K S and Powers T R 2013 Phys. Fluids 25 061902
[15] Friedrich B M, Riedel-Kruse I H, Howard J and Julicher F 2010 Journal of Experimental Biology 213 1226
[16] Sznitman J, Shen X, Sznitman R and Arratia P E 2010 Phys. Fluids 22 121901
[17] Bayly P V, Lewis B L, Ranz E C, Okamoto R J, Pless R B and Dutcher SK 2011 Bio-phys. J. 100 2716
[18] Maladen R D, Ding Y, Umbanhowar P B, Kamor A, and Goldman D I 2011 Journal of the Royal Society Interface 8 1332
[19] Ding Y, Sharp S S, Wiesenfeld K and Goldman D I 2013 Proc. Natl. Acad. Sci. USA 110 10123
[20] Hu D L, Nirody J, Scott T and Shelley M J 2009 Proc. Natl. Acad. Sci. USA 106 10081
[21] Lorentz H A 1996 J. Eng. Math. 30 19
[22] Cortez R, Fauci L and Medovikov A 2005 Phys. Fluids 17 031504
[23] Lighthill J 1996 J. Eng. Math. 30 25
[24] Purcell E M 1997 Proc. Natl. Acad. Sci. USA 94 11307
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