Pitching, bobbing, and performance metrics for undulating finite-length swimming filaments

Physics of Fluids

Volumn 24, Issue 9, 2012, Pages

  Koehler, Stephan ^a   Spoor, Tristan ^a   Tilley, B S ^a  

^a Life Science and Bioengineering Center   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENERGY EFFICIENCY;

ANALYTICAL EXPRESSIONS; ANALYTICAL RESULTS; PARAMETRIC STUDY; PERFORMANCE METRICS; POWER FLUCTUATIONS; RESISTIVE FORCE THEORY; VISCOUS FLUIDS; WORK EXPENDITURE;

RESONANCE;

EID: 84867138361     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4750428     Document Type: Article

References (37)

1. Berg H. The rotary motor of bacterial flagella. Ann. Rev. Biochem. 2003, 72:19-54. 10.1146/annurev.biochem.72.121801.161737.
2. Lighthill J. Mathematical Biofluid Dynamics 1976, (SIAM, University City Science Center, Philadephia, PA, ).
3. Humphries S. Evans J.P. Simmons L.W. Sperm competition: Linking form to function. BMC Evolut. Biol. 2008, 8:1-11. 10.1186/1471-2148-8-319, and .
4. Lauga E. Powers T.R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 2009, 72:1-36. 10.1088/0034-4885/72/9/096601, and .
5. Purcell E.M. Life at low Reynolds number. Am. J. Phys. 1977, 45:3-11. 10.1119/1.10903.
6. Gray J. Hancock G.J. The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 1955, 32:802-814. and .
7. Brennen C. Berg H. Fluid mechanics of propulsion by cilia and flagella. Ann. Rev. Fluid Mech. 1977, 9:339-398. 10.1146/annurev.fl.09.010177.002011, and .
8. Rikmenspoel R. Movements and active moments of bull sperm flagella as a function of temperature and viscosity. J. Exp. Biol. 1984, 108:205-230.
9. Gillies E.A. Cannon R.M. Green R.B. Pacey A.A. Hydrodynamic propulsion of human sperm. J. Fluid Mech. 2009, 625:445-474. 10.1017/S0022112008005685, and .
10. Smith D.J. Gaffney E.A. Gadelha H. Kapur N. Kirkman-Brown J.C. Bend propagation in the flagella of migrating human sperm, and its modulation by viscosity. Cell Motil. Cytoskeleton 2009, 66:220-236. 10.1002/cm.20345, and .
11. Taylor G.I. Analysis of the swimming of microscopic organisms. Proc. R. Soc. London, A 1951, 209:447-461. 10.1098/rspa.1951.0218.
12. Shapere A. Wilczek F. Geometry of self-propulsion at low reynolds number. J. Fluid Mech. 1989, 198:557-585. 10.1017/S002211208900025X, and .
13. Najafi A. Golestanian R. Propulsion at low Reynolds number. J. Phys.: Conden. Matter 2005, 17:S1203-S1208. 10.1088/0953-8984/17/14/009, and .
14. Tam D. Hosoi A.E. Optimal stroke patterns for purcell's three-link swimmer. Phys. Rev. Lett. 2007, 98:068105 1-4. 10.1103/PhysRevLett.98.068105, and .
15. Avron J.E. Raz O. A geometric theory of swimming: Purcell's swimmer and its symmetrized cousin. New J. Phys. 2008, 10:063016 1-19. 10.1088/1367-2630/10/6/063016, and .
16. Friedrich B.M. Juelicher F. Steering chiral swimmers along noisy helical paths. Phys. Rev. Lett. 2009, 103:068102. 10.1103/PhysRevLett.103.068102, and .
17. Spagnolie S.E. Lauga E. The optimal elastic flagellum. Phys. Fluids 2010, 22:031901 1-15. 10.1063/1.3318497, and .
18. Crowdy D.G. Or Y. Two-dimensional point singularity model of a low-Reynolds-number swimmer near a wall. Phys. Rev. E 2010, 81:036313. 10.1103/PhysRevE.81.036313, and .
19. Taylor G.I. The action of waving cylindrical tails in propelling microscopic organisms. Proc. R. Soc. London, A 1952, 211:225-39. 10.1098/rspa.1952.0035.
20. Hancock G.J. The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. London, A 1953, 217:96-121. 10.1098/rspa.1953.0048.
21. Pironneau O. Katz D.F. Optimal swimming of flagellated micro-organisms. J. Fluid Mech. 1974, 66:391-415. 10.1017/S0022112074000279, and .
22. Higdon J.J. L. A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 1979, 90:685-711. 10.1017/S0022112079002482.
23. Brokaw C.J. Computer simulation of flagellar movement. Biophys. J. 1972, 12:564-586. 10.1016/S0006-3495(72)86104-6.
24. Brokaw C.J. Flagellar propulsion. J. Exp. Biol. 2006, 209:985-986. 10.1242/jeb.02120.
25. Johnson R.E. Brokaw C.J. Flagellar hydrodynamics: A comparison between resistive-force theory and slender-body theory. Biophys. J. 1979, 25:113-127. 10.1016/S0006-3495(79)85281-9, and .
26. Martin Sauzade E.L. Elfring G.J. Taylor's swimming sheet: Analysis and improvement of the perturbation series. Physica D 2011, 240:1567-1573. 10.1016/j.physd.2011.06.023, and .
27. Keller J.B. Rubinow S.I. Slender-body theory for slow viscous flow. J. Fluid Mech. 1976, 75:705-714. 10.1017/S0022112076000475, and .
28. Brokaw C.J. Bend propagation by a sliding filament model for flagella. J. Exp. Biol. 1971, 55:289-304.
29. Becker L.E. Koehler S.A. Stone H.A. On self propulsion of micromachines at low reynolds number: Purcell's three-link swimmer. J. Fluid Mech. 2003, 490:15-35. 10.1017/S0022112003005184, and .
30. Yang J. Wolgemuth C.W. Huber G. Kinematics of the swimming of spiroplasma. Phys. Rev. Lett. 2009, 102:218102 1-4. 10.1103/PhysRevLett.102.218102, and .
31. Lighthill J. Flagellar hydrodynamics: The John von Neumann lecture, 1975. SIAM Rev. 1976, 18:161-230. 10.1137/1018040.
32. Batchelor G.K. Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 1970, 44:419-440. 10.1017/S002211207000191X.
33. To speed up calculations we use the routine LMFnlsq available on matlab central file exchange.
34. Many of the symmetry arguments made here are analogous to those for Purcell's swimmer (Ref. 29).
35. Swain D.P. Cycling: Uphill and downhill. Encyclopedia of Sports Medicine and Science 1998, T. Fahey, "," in edited by Internet Society for Sport Science (AUT University, Auckland 0627, New Zealand, ).
36. Brokaw C.J. Automated methods for estimation of sperm flagellar bending parameters. Cell Motil. Cytoskeleton 1984, 4:417-430. 10.1002/cm.970040603.
37. Osterman N. Vilfan A. Finding the ciliary beating pattern with optimal efficiency. Proc. Natl. Acad. Sci. U.S.A. 2010, 108:15727-15732. 10.1073/pnas.1107889108, and .