Hydrodynamics of self-propulsion near a boundary: predictions and accuracy of far-field approximations

Journal of Fluid Mechanics

Volumn 700, Issue , 2012, Pages 105-147

  Spagnolie, Saverio E ^a,b   Lauga, Eric ^b  

^a Brown University   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

low Reynolds number flows; micro organism dynamics; swimming flying

Indexed keywords

CRYSTALLOGRAPHY; HYDRODYNAMICS; NAVIER STOKES EQUATIONS; REYNOLDS NUMBER; TRAJECTORIES;

FAR FIELD APPROXIMATION; FULL NUMERICAL SOLUTION; FUNDAMENTAL SOLUTIONS; HYDRODYNAMIC INTERACTION; LOW REYNOLDS NUMBER FLOW; STRESS-FREE SURFACES; SWIMMING TRAJECTORIES; SWIMMING/FLYING;

BIOLOGY;

ACCURACY ASSESSMENT; HYDRODYNAMICS; MICROORGANISM; NUMERICAL MODEL; REYNOLDS NUMBER; STOKES FORMULA; SWIMMING; VISCOUS FLOW;

EID: 84864123640     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.101     Document Type: Article

References (86)

1. AINLEY, J., DURKIN, S., EMBID, R., BIONDALA, P. & CORTEZ, R. 2008 The method of images for regularized Stokeslets. J. Comput. Phys. 227, 4600-4616.
2. ARMITAGE, J. P. & MACNAB, R. M. 1987 Unidirectional, intermittent rotation of the flagellum of rhodobacter sphaeroides. J. Bacteriol. 169, 514-518. (Pubitemid 17010855)
3. BEES, M. A. & CROZE, O. A. 2010 Dispersion of biased swimming micro-organisms in a fluid flowing through a tube. Proc. R. Soc. Lond. A 466, 2057-2077.
4. BERG, H. C. & TURNER, L. 1990 Chemotaxis of bacteria in glass capillary arrays. Biophys. J. 58, 919-930.
5. BERKE, A. P., TURNER, L., BERG, H. C. & LAUGA, E. 2008 Hydrodynamic attraction of swimming microorganisms by surfaces. Phys. Rev. Lett. 101, 038102.
6. BLAKE, J. R. 1971 A spherical envelope approach to ciliary propulsion. J. Fluid Mech. 46, 199-208.
7. BLAKE, J. R. & CHWANG, A. T. 1974 Fundamental singularities of viscous flow. J. Engng Maths 8, 23-29.
8. BOUZARTH, E. L. & MINION, M. L. 2011 Modeling slender bodies with the method of regularized Stokeslets. J. Comput. Phys. 230, 3929-3947.
9. BRADY, J. F. & BOSSIS, G. 1985 The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation. J. Fluid Mech. 155, 105-129. (Pubitemid 15527668)
10. BRENNER, H. 1961 Effect of finite boundaries on the Stokes resistance of an arbitrary particle. J. Fluid Mech. 8, 35-48.
11. CHILDRESS, S. 1981 Mechanics of Swimming and Flying. Cambridge University Press.
12. CHWANG, A. T. & WU, T. Y. T. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows. J. Fluid Mech. 67, 787-815.
13. CISNEROS, L., DOMBROWSKI, C., GOLDSTEIN, R. E. & KESSLER, J. O. 2007 Reversal of bacteria at an obstacle. Phys. Rev. E 73, 030901(R).
14. CORTEZ, R. 2002 The method of regularized Stokeslets. SIAM J. Sci. Comput. 23, 1204-1225.
15. CROWDY, D. G. 2011 Treadmilling swimmers near a no-slip wall at low Reynolds number. Intl J. Non-Linear Mech. 46, 577-585.
16. CROWDY, D. G. & OR, Y. 2010 Two-dimensional point singularity model of a low-Reynoldsnumber swimmer near a wall. Phys. Rev. E 81, 036313.
17. DI LEONARDO, R., ANGELANI, L., DELL'ARCIPRETE, D., RUOCCO, G., IEBBA, V., SCHIPPA, S., CONTE, M. P., MECARINI, F., DE ANGELIS, F. & DI FABRIZIO, E. 2010 Bacterial ratchet motors. Proc. Natl. Acad. Sci. USA 107, 9541-9545.
18. DI LEONARDO, R., DELL'ARCIPRETE, D., ANGELANI, L. & IEBBA, V. 2011 Swimming with an image. Phys. Rev. Lett. 106, 038101.
19. DRESCHER, K., DUNKEL, J., CISNEROS, L. H., GANGULY, S. & GOLDSTEIN, R. E. 2011 Fluid dynamics and noise in bacterial cell-cell and cell-surface scattering. Proc. Natl Acad. Sci. USA 108, 10940-10945.
20. DRESCHER, K., GOLDSTEIN, R. E., MICHEL, N., POLIN, M. & TUVAL, I. 2010 Direct measurement of the flow field around swimming microorganisms. Phys. Rev. Lett. 105, 168101.
21. DRESCHER, K., LEPTOS, K. C., TUVAL, I., ISHIKAWA, T., PEDLEY, T. J. & GOLDSTEIN, R. E. 2009 Dancing volvox: hydrodynamic bound states of swimming algae. Phys. Rev. Lett. 102, 168101.
22. DREYFUS, R., BAUDRY, J., ROPER, M. L., FERMIGIER, M., STONE, H. A. & BIBETTE, J. 2005 Microscopic artificial swimmers. Nature 437, 862-865. (Pubitemid 41486758)
23. ELGETI, J. & GOMPPER, G. 2009 Self-propelled rods near surfaces. Euro. Phys. Lett. 85, 38002.
24. ELGETI, J., KAUPP, U. B. & GOMPPER, G. 2010 Hydrodynamics of sperm cells near surfaces. Biophys. J. 99, 1018-1026.
25. EVANS, A. & LAUGA, E. 2010 Propulsion by passive filaments and active flagella near boundaries. Phys. Rev. E 82, 041915.
26. FAUCI, L. J. & MCDONALD, A. 1995 Sperm motility in the presence of boundaries. Bull. Math. Biol. 57, 679-699.
27. FOURNIER-BIDOZ, S., ARSENAULT, A. C., MANNERS, I. & OZIN, G. A. 2005 Synthetic self-propelled nanorotors. Chem. Commun. 4, 441-443. (Pubitemid 40187654)
28. GALAJDA, P., KEYMER, J., CHAIKIN, P. & AUSTIN, R. 2007 A wall of funnels concentrates swimming bacteria. J. Bacteriol. 189, 8704-8707. (Pubitemid 350210041)
29. GHOSH, A. & FISCHER, P. 2009 Controlled propulsion of artificial magnetic nanostructured propellers. Nanoletters 9, 2243-2245.
30. GIACCH'E, D., ISHIKAWA, T. & YAMAGUCHI, T. 2010 Hydrodynamic entrapment of bacteria swimming near a solid surface. Phys. Rev. E 82, 056309.
31. GOLDMAN, A. J., COX, R. G. & BRENNER, H. 1966 Slow viscous motion of a sphere parallel to a plane wall-I Motion through a quiescent fluid. Chem. Engng Sci. 22, 637-651.
32. GOLESTANIAN, R., LIVERPOOL, T. B. & ADJARI, A. 2007 Designing phoretic micro-and nano-swimmers. New J. Phys. 9, 126.
33. GOTO, T., NAKATA, K., BABA, K., NISHIMURA, M. & MAGARIYAMA, Y. 2005 A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary. Biophys. J. 89, 3771-3779. (Pubitemid 41725600)
34. GRAY, J. & HANCOCK, G. J. 1955 The propulsion of sea-urchin spermatozoa. J. Expl. Biol. 32, 802-814.
35. GUASTO, J. S., JOHNSON, K. A. & GOLLUB, J. P. 2010 Oscillatory flows induced by microorganisms swimming in two dimensions. Phys. Rev. Lett. 105, 168102.
36. HAPPEL, J. & BRENNER, H. 1965 Low Reynolds Number Hydrodynamics. Prentice Hall.
37. HARKES, G., DANKERT, J. & FEIJEN, J. 1992 Bacterial migration along solid surfaces. Appl. Environ. Microbiol. 58, 1500-1505.
38. HARSHEY, R. M. 2003 Bacterial motility on a surface: many ways to a common goal. Ann. Rev. Microbiol. 57, 249-273. (Pubitemid 37392943)
39. HARVEY, R. W. & YOUNG, L. Y. 1980 Enumeration of particle-bound and unattached respiring bacteria in the salt marsh environment. Appl. Environ. Microbiol. 40, 156-160.
40. HERNANDEZ-ORTIZ, J. P., STOLTZ, C. G. & GRAHAM, M. D. 2005 Transport and collective dynamics in suspensions of confined swimming particles. Phys. Rev. Lett. 95, 204501.
41. HERNANDEZ-ORTIZ, J. P., UNDERHILL, P. T. & GRAHAM, M. D. 2009 Dynamics of confined suspensions of swimming particles. J. Phys.: Condens. Matter 21, 204107.
42. HILL, J., KALKANCI, O., MCMURRY, J. L. & KOSER, H. 2007 Hydrodynamic surface interactions enable Escherichia Coli to seek efficient routes to swim upstream. Phys. Rev. Lett. 98, 068101.
43. HOHENEGGER, C. & SHELLEY, M. J. 2010 Stability of active suspensions. Phys. Rev. E 81, 046311.
44. ISHIKAWA, T. & PEDLEY, T. J. 2007 Diffusion of swimming model micro-organisms in a semi-dilute suspension. J. Fluid Mech. 588, 437-462.
45. ISHIKAWA, T., SIMMONDS, M. P. & PEDLEY, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119-160. (Pubitemid 44741348)
46. JIANG, H.-R., YOSHINAGA, N. & SANO, M. 2010 Active motion of a Janus particle by self-thermophoresis in a defocused laser beam. Phys. Rev. Lett. 105, 268302.
47. JOHNSON, R. E. & BROKAW, C. J. 1979 Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory. Biophys. J. 25, 113-127. (Pubitemid 9107850)
48. KANEVSKY, A., SHELLEY, M. J. & TORNBERG, A.-K. 2010 Modelling simple locomotors in Stokes flow. J. Comput. Phys. 229, 958-977.
49. KAYA, T. & KOSER, H. 2009 Characterization of hydrodynamic surface interactions of Escherichia coli cell bodies in shear flow. Phys. Rev. Lett. 103, 138103.
50. KELLER, S. R. & WU, T. Y. T. 1977 A porous prolate-spheroidal model for ciliated micro-organisms. J. Fluid Mech. 80, 259-278.
51. KIM, S. & KARRILA, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Dover.
52. KLAPPER, I. & DOCKERY, J. 2010 Mathematical description of microbial biofilms. SIAM Rev. 52, 221-265.
53. KOLTER, R. & GREENBERG, E. P. 2006 The superficial life of microbes. Nature 441, 300-302.
54. LAUGA, E., DILUZIO, W. R., WHITESIDES, G. M. & STONE, H. A. 2006 Swimming in circles: Motion of bacteria near solid boundaries. Biophys. J. 90, 400-412.
55. LAUGA, E. & POWERS, T. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601.
56. LI, G., TAM, L.-K. & TANG, J. X. 2008 Accumulation of microswimmers near a surface mediated by collision and rotational Brownian motion. Phys. Rev. Lett. 103, 078101.
57. LI, G. & TANG, J. X. 2009 Amplified effect of Brownian motion in bacterial near-surface swimming. Proc. Natl Acad. Sci. USA 105, 18355-18359.
58. LIAO, Q., SUBRAMANIAN, G., DELISA, M. P., KOCH, D. L. & WU, M. 2007 Pair velocity correlations among swimming Escherichia coli bacteria are determined by force-quadrupole hydrodynamic interactions. Phys. Fluids 19, 061701.
59. LIGHTHILL, M. J. 1952 On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers. Commun. Pure Appl. Maths 5, 109-118.
60. LIGHTHILL, M. J. 1996 Helical distributions of Stokeslets. J. Engng Maths 30, 35-78.
61. LIN, Z., THIFFEAULT, J.-L. & CHILDRESS, S. 2011 Stirring by squirmers. J. Fluid Mech. 669, 167-177.
62. LLOPIS, I. & PAGONABARRAGA, I. 2011 Hydrodynamic interactions in squirmer motion: Swimming with a neighbour and close to a wall. J. Non-Newtonian Fluid Mech. 165, 946-952.
63. LYNCH, J. F., LAPPIN-SCOTT, H. M. & COSTERTON, J. W. 2003 Microbial Biofilms. Cambridge University Press.
64. MAGNAUDET, J., TAKAGI, S. & LEGENDRE, D. 2003 Drag, deformation and lateral migration of a buoyant drop moving near a wall. J. Fluid Mech. 476, 115-157. (Pubitemid 36374782)
65. MICHELIN, S. & LAUGA, E. 2010 Efficiency optimization and symmetry-breaking in a model of ciliary locomotion. Phys. Fluids 22, 111901.
66. OTOOLE, G., KAPLAN, H. B. & KOLTER, R. 2000 Biofilm formation as microbial development. Annu. Rev. Microbiol. 54, 49-79.
67. PAK, O. S., GAO, W., WANG, J. & LAUGA, E. 2011 High-speed propulsion of flexible nanowire motors: theory and experiments. Soft Matt. 7, 8169-8181.
68. PAXTON, W. F., KISTLER, K. C., OLMEDA, C. C., SEN, A., ST. ANGELO, S. K., CAO, Y., MALLOUK, T. E., LAMMERT, P. E. & CRESPI, V. H. 2004 Catalytic nanomotors: autonomous movement of striped nanorods. J. Am. Chem. Soc. 126, 13424.
69. POORTINGA, A. T., BOS, R., NORDE, W. & BUSSCHER, H. J. 2002 Electric double layer interactions in bacterial adhesion to surfaces. Surf. Sci. Rep. 47, 1-32. (Pubitemid 34614229)
70. POWER, H. & MIRANDA, G. 1987 Second kind integral equation formulation of Stokes' flows past a particle of arbitrary shape. SIAM J. Appl. Maths 47, 689-698. (Pubitemid 17633025)
71. POZRIKIDIS, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
72. PURCELL, E. M. 1977 Life at Low Reynolds number. Am. J. Phys. 45, 3-11.
73. ROTHSCHILD, L. J. 1963 Non-random distribution of bull spermatazoa in a drop of sperm suspension. Nature (London) 198, 122-1222.
74. R̈UCKNER, G. & KAPRAL, R. 2007 Chemically powered nanodimers. Phys. Rev. Lett. 98, 150603.
75. SAINTILLAN, D. & SHELLEY, M. J. 2008 Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulation. Phys. Rev. Lett. 100, 178103.
76. SHUM, H., GAFFNEY, E. A. & SMITH, D. J. 2010 Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry. Proc. R. Soc. Lond. A 466, 1725-1748.
77. SMITH, D. J. & BLAKE, J. R. 2009 Surface accumulation of spermatozoa: a fluid dynamic phenomenon. Math. Sci. 34, 74-87.
78. SMITH, D. J., GAFFNEY, E. A., BLAKE, J. R. & KIRKMAN-BROWN, J. C. 2009 Human sperm accumulation near surfaces: a simulation study. J. Fluid Mech. 621, 289-320.
79. SPAGNOLIE, S. E. & LAUGA, E. 2010 Jet propulsion without inertia. Phys. Fluids 22, 081902.
80. SWAN, J. W. & KHAIR, A. S. 2008 On the hydrodynamics of 'slip-stick' spheres. J. Fluid Mech. 606, 115-132. (Pubitemid 351850781)
81. TAYLOR, G. I. 1951 Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A 209, 447-461.
82. TUVAL, I., CISNEROS, L., DOMBROWSKI, C., WOLGEMUTH, C. W., KESSLER, J. O. & GOLDSTEIN, R. E. 2005 Bacterial swimming and oxygen transport near contact lines. Proc. Natl. Acad. Sci. USA 102, 2277-2282. (Pubitemid 40279366)
83. VAN LOOSDRECHT, M. C. M., LYKLEMA, J., NORDE, W. & ZEHNDER, A. J. B. 2003 Influence of interfaces on microbial activity. Microbiol. Rev. 54, 75-87.
84. WANG, J. 2009 Can man-made nanomachines compete with nature biomotors? ACS Nano 3, 4-9.
85. ZARGAR, R., NAJAFI, A. & MIRI, M. 2009 Three-sphere low-Reynolds-number swimmer near a wall. Phys. Rev. E 80, 026308.
86. ZHU, L., DO-QUANG, M., LAUGA, E. & BRANDT, L. 2011 Locomotion by tangential deformation in a polymeric fluid. Phys. Rev. E 83, 011901.