Skip to main content

News about Scitation

In December 2016 Scitation will launch with a new design, enhanced navigation and a much improved user experience.

To ensure a smooth transition, from today, we are temporarily stopping new account registration and single article purchases. If you already have an account you can continue to use the site as normal.

For help or more information please visit our FAQs.

banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
1. G. J. Hancock, “The self-propulsion of microscopic organisms through liquids,” Proc. R. Soc. London, Ser. A 217, 96121 (1953).
2. R. E. Johnson and C. J. Brokaw, “Flagellar hydrodynamics: A comparison between resistive-force theory and slender-body theory,” Biophys. J. 25(1), 113127 (1979).
3. R. Cortez, “The method of regularized Stokeslets,” SIAM J. Sci. Comput. 23, 12041225 (2001).
4. G. I. Taylor, Low-Reynolds Number Flows (National Committee for Fluid Mechanics Films, 1997), available from
5. E. M. Purcell, “Life at low Reynolds number,” Am. J. Phys. 45, 311 (1977).
6. D. Tam and A. E. Hosoi, “Optimal stroke patterns for Purcell's three-link swimmer,” Phys. Rev. Lett. 98(6), 068105 (2007).
7. E. Passov and Y. Or, “Dynamics of Purcell's three-link microswimmer with a passive elastic tail,” Eur. Phys. J. E 35(8), 78 (2012).
8. A. Najafi and R. Golestanian, “Simple swimmer at low Reynolds number: Three linked spheres,” Phys. Rev. E 69, 062901 (2004).
9. K. Polotzek and B. M. Friedrich, “A three-sphere swimmer for flagellar synchronization,” New J. Phys. 15, 045005 (2013).
10. R. Ledesma-Aguilar, H. Loewen, and J. M. Yeomans, “A circle swimmer at low Reynolds number,” Eur. Phys. J. E 35(8), 70 (2012).
11. F. Y. Ogrin, P. G. Petrov, and C. P. Winlove, “Ferromagnetic microswimmers,” Phys. Rev. Lett. 100, 21810212181024 (2008).
12. S. K. Lai, Y. Y. Wang, D. Wirtz, and J. Hanes, “Micro-and macrorheology of mucus,” Adv. Drug Delivery Rev. 61(2), 86100 (2009).
13. L. Hall-Stoodley, J. W. Costerton, and P. Stoodley, “Bacterial biofilms: From the natural environment to infectious diseases,” Nat. Rev. Microbiol. 2(2), 95108 (2004).
14. N. Verstraeten, K. Braeken, B. Debkumari, M. Fauvart, J. Fransaer, J. Vermant, and J. Michiels, “Living on a surface: Swarming and biofilm formation,” Trends Microbiol. 16(10), 496506 (2008).
15. G. R. Fulford, D. F. Katz, and R. L. Powell, “Swimming of spermatozoa in a linear viscoelastic fluid,” Biorheology 35, 295310 (1998).
16. T. Normand and E. Lauga, “Flapping motion and force generation in a viscoelastic fluid,” Phys. Rev. E 78(6), 061907 (2008).
17. E. Lauga, “Life at high Deborah number,” Europhys. Lett. 86, 64001 (2009).
18. G. J. Elfring, O. S. Pak, and E. Lauga, “Two-dimensional flagellar synchronization in viscoelastic fluids,” J. Fluid Mech. 646, 505 (2010).
19. X. N. Shen and P. E. Arratia, “Undulatory swimming in viscoelastic fluids,” Phys. Rev. Lett. 106(20), 208101 (2011).
20. E. Lauga, “Propulsion in a viscoelastic fluid,” Phys. Fluids 19, 083104108310413 (2007).
21. H. C. Fu, C. W. Wolgemuth, and T. R. Powers, “Swimming speeds of filaments in nonlinearly viscoelastic fluids,” Phys. Fluids 21, 033102103310210 (2009).
22. L. Zhu, E. Lauga, and L. Brandt, “Self-propulsion in viscoelastic fluids: Pushers vs. pullers,” Phys. Fluids 24(5), 051902105190217 (2012).
23. J. Teran, L. Fauci, and M. Shelley, “Viscoelastic fluid response can increase the speed and efficiency of a free swimmer,” Phys. Rev. Lett. 104, 03810110381014 (2010).
24. S. K. Lai, D. E. O'Hanlon, S. Harrold, S. T. Man, Y. Y. Wang, R. Cone, and J. Hanes, “Rapid transport of large polymeric nanoparticles in fresh undiluted human mucus,” Proc. Natl. Acad. Sci. U.S.A. 104(5), 1482 (2007).
25. D. F. Katz and S. A. Berger, “Flagellar propulsion of human sperm in cervical mucus,” Biorheology 17(1–2), 169 (1980).
26. N. J. Balmforth, D. Coombs, and S. Pachmann, “Microelastohydrodynamics of swimming organisms near solid boundaries in complex fluids,” Q. J. Mech. Appl. Math. 63(3), 267294 (2010).
27. X. Shen, D. Gagnon, and P. Arratia, “Undulatory swimming in shear-thinning fluids,” Bull. Am. Phys. Soc. 57, M1700005 (2012),
28. T. D. Montenegro-Johnson, A. A. Smith, D. J. Smith, D. Loghin, and J. R. Blake, “Modelling the fluid mechanics of cilia and flagella in reproduction and development,” Eur. Phys. J. E 35(10), 111 (2012).
29. R. N. Mills and D. F. Katz, “A flat capillary tube system for assessment of sperm movement in cervical mucus,” Fertil. Steril. 29, 4347 (1978).
30. D. F. Katz, J. W. Overstreet, and F. W. Hanson, “A new quantitative test for sperm penetration into cervical mucus,” Fertil. Steril. 33, 179 (1980).
31. D. J. Smith, E. A. Gaffney, H. Gadêlha, N. Kapur, and J. C. Kirkman-Brown, “Bend propagation in the flagella of migrating human sperm, and its modulation by viscosity,” Cell Motil. Cytoskeleton 66, 220236 (2009).
32. N. Phan-Thien, Understanding Viscoelasticity: Basics of Rheology (Springer Verlag, Berlin, 2002).
33. P. J. Carreau, D. De Kee, and M. Daroux, “An analysis of the viscous behaviour of polymeric solutions,” Can. J. Chem. Eng. 57(2), 135140 (1979).
34. J. J. L. Higdon, “A hydrodynamic analysis of flagellar propulsion,” J. Fluid Mech. 90, 685711 (1979).
35. G. I. Taylor, “Analysis of the swimming of microscopic organisms,” Proc. R. Soc. London, Ser. A 209, 447461 (1951).
36. A. T. Chwang and T. Y. Wu, “A note on the helical movement of micro-organisms,” Proc. R. Soc. London, Ser. B 178, 327346 (1971).
37. G. K. Batchelor, An Introduction to Fluid Mechanics (Cambridge University Press, New York, 1967).
38. D. Crowdy, “Treadmilling swimmers near a no-slip wall at low Reynolds number,” Int. J. Non-Linear Mech. 46, 577585 (2011).
39. D. Crowdy, S. Lee, O. Samson, E. Lauga, and A. E. Hosoi, “A two-dimensional model of low-Reynolds number swimming beneath a free surface,” J. Fluid Mech. 681(1), 2447 (2011).
40. C. S. Peskin, “Flow patterns around heart valves: A numerical method,” J. Comput. Phys. 10, 252271 (1972).
41. L. J. Fauci and C. S. Peskin, “A computational model of aquatic animal locomotion,” J. Comput. Phys. 77, 85108 (1988).
42. K. Drescher, R. E. Goldstein, N. Michel, M. Polin, and I. Tuval, “Direct measurement of the flow field around swimming microorganisms,” Phys. Rev. Lett. 105(16), 168101 (2010).
43. J. R. Blake and M. A. Sleigh, “Mechanics of ciliary locomotion,” Biol. Rev. 49, 85125 (1974).
44. S. Childress, Mechanics of Swimming and Flying (Cambridge University Press, Cambridge, 1981).
45. C. Brennen and H. Winet, “Fluid mechanics of propulsion by cilia and flagella,” Annu. Rev. Fluid Mech. 9, 339398 (1977).
46. J. R. Blake, “A spherical envelope approach to ciliary propulsion,” J. Fluid Mech. 46, 199208 (1971).
47. T. Ishikawa, M. P. Simmonds, and T. J. Pedley, “Hydrodynamic interaction of two swimming model micro-organisms,” J. Fluid Mech. 568, 119160 (2006).
48. Z. Lin, J. L. Thiffeault, and S. Childress, “Stirring by squirmers,” J. Fluid Mech. 669, 167177 (2011).
49. S. Michelin and E. Lauga, “Optimal feeding is optimal swimming for all Péclet numbers,” Phys. Fluids 23, 101901110190113 (2011).
50. S. T. Mortimer, “A critical review of the physiological importance and analysis of sperm movement in mammals,” Hum. Reprod. Update 3, 403439 (1997).
51. D. J. Smith, “A boundary element regularized Stokeslet method applied to cilia-and flagella-driven flow,” Proc. R. Soc. London, Ser. A 465(2112), 36053626 (2009).
52. J. R. Blake, “Self-propulsion due to oscillations on the surface of a cylinder at low Reynolds number,” Bull. Austral. Math. Soc. 5, 255264 (1971).

Data & Media loading...


Article metrics loading...



Shear-thinning is an important rheological property of many biological fluids, such as mucus, whereby the apparent viscosity of the fluid decreases with shear. Certain microscopic swimmers have been shown to progress more rapidly through shear-thinning fluids, but is this behavior generic to all microscopic swimmers, and what are the physics through which shear-thinning rheology affects a swimmer's propulsion? We examine swimmers employing prescribed stroke kinematics in two-dimensional, inertialess Carreau fluid: shear-thinning “generalized Stokes” flow. Swimmers are modeled, using the method of femlets, by a set of immersed, regularized forces. The equations governing the fluid dynamics are then discretized over a body-fitted mesh and solved with the finite element method. We analyze the locomotion of three distinct classes of microswimmer: (1) conceptual swimmers comprising sliding spheres employing both one- and two-dimensional strokes, (2) slip-velocity envelope models of ciliates commonly referred to as “squirmers,” and (3) monoflagellate pushers, such as sperm. We find that morphologically identical swimmers with different strokes may swim either faster or slower in shear-thinning fluids than in Newtonian fluids. We explain this kinematic sensitivity by considering differences in the viscosity of the fluid surrounding propulsive and payload elements of the swimmer, and using this insight suggest two reciprocal sliding sphere swimmers which violate Purcell's Scallop theorem in shear-thinning fluids. We also show that an increased flow decay rate arising from shear-thinning rheology is associated with a reduction in the swimming speed of slip-velocity squirmers. For sperm-like swimmers, a gradient of thick to thin fluid along the flagellum alters the force it exerts upon the fluid, flattening trajectories and increasing instantaneous swimming speed.


Full text loading...


Access Key

  • FFree Content
  • OAOpen Access Content
  • SSubscribed Content
  • TFree Trial Content
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd