A boundary element regularized Stokeslet method applied to cilia-and flagella-driven flow

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 465, Issue 2112, 2009, Pages 3605-3626

  Smith, D J ^a,b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b BIRMINGHAM CHILDREN S HOSPITAL NHS FOUNDATION TRUST   (United Kingdom)

Author keywords

Boundary element; Cilia; Flagella; Regularized Stokeslet; Slender body theory

Indexed keywords

BIOLOGY; BODIES OF REVOLUTION; CAPILLARY FLOW; SHIP STEERING EQUIPMENT;

ANALYTIC INTEGRATION; BASIS FUNCTIONS; BOUNDARY ELEMENTS; BOUNDARY INTEGRALS; DISCRETIZATIONS; FIXED NUMBERS; MESH SIZE; NUMBER OF DEGREES OF FREEDOM; NUMERICAL ERRORS; NUMERICAL QUADRATURE; PATCH DIMENSIONS; REGULARIZATION PARAMETERS; SLENDER-BODY THEORY; STOKESLET; STOKESLET METHODS;

BOUNDARY ELEMENT METHOD;

EID: 73149123537     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2009.0295     Document Type: Article

References (48)

1. Ainley, J., Durkin, S., Embid, R., Boindala, P. & Cortez, R. 2008 The method of images for regularised Stokeslets. J. Comput. Phys. 227, 4600-4616. (doi:10.1016/j.jcp.2008.01.032)
2. Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44, 419-440. (doi:10.1017/ S002211207000191X)
3. Becker, L. E., Koehler, S. A. & Stone, H. A. 2003 On self-propulsion of micro-machines at low reynolds number: Purcell's three-link swimmer. J. Fluid Mech. 490, 15-35. (doi:10.1017/ S0022112003005184) (Pubitemid 37164461)
4. Blake, J. R. 1971 A note on the image system for a stokeslet in a no-slip boundary. Proc. Camb. Phil. Soc. 70, 303-310. (doi:10.1017/S0305004100049902)
5. Blake, J. R. 1972 A model for the micro-structure in ciliated organisms. J. Fluid Mech. 55, 1-23. (doi:10.1017/S0022112072001612)
6. Burgers, J. M. 1938 On the motion of small particles of elongated form suspended in a viscous liquid. Kon. Ned. Akad. Wet. Verhand. (Eerste Sectie) 16, 113.
7. Chwang, A. T. & Wu, T. Y. 1975 Hydrodynamics of the low-Reynolds number flows. Part 2. The singularity method for Stokes flows. J. Fluid Mech. 67, 787-815. (doi:10.1017/ S0022112075000614)
8. Cisneros, L. H., Cortez, R., Dombrowski, C., Goldstein, R. E. & Kessler, J. O. 2007 Fluid dynamics of self-propelled microorganisms, from individuals to concentrated populations. Exp. Fluids 43, 737-753. (doi:10.1007/s00348-007-0387-y) (Pubitemid 350074176)
9. Cisneros, L. H., Kessler, J. O., Ortiz, R., Cortez, R. & Bees, M. 2008 Unexpected bipolar flagellar arrangements and long-range flows driven by bacteria near solid boundaries. Phys. Rev. Lett. 101, 168102. (doi:10.1103/PhysRevLett.101.168102)
10. Clarke, R. J., Jensen, O. E., Billingham, J. & Williams, P. M. 2006 Three-dimensional flow due to a microcantilever oscillating near a wall: an unsteady slender-body analysis. Proc. R. Soc. A 462, 913-933. (doi:10.1098/rspa.2005.1607) (Pubitemid 44922130)
11. Cortez, R. 2001 The method of regularized stokeslets. SIAM J. Sci. Comput. 23, 1204-1225. (doi:10.1137/S106482750038146X)
12. Cortez, R., Fauci, L. & Medovikov, A. 2005 The method of regularized stokeslets in three dimensions: analysis, validation and application to helical swimming. Phys. Fluids 17, 1-14. (doi:10.1063/1.1830486) (Pubitemid 40426364)
13. Dresdner, R. D., Katz, D. F. & Berger, S. A. 1980 The propulsion by large-amplitude waves of uniflagellar micro-organisms of finite length. J. Fluid Mech. 97, 591-621. (doi:10.1017/ S0022112080002716)
14. Fauci, L. & Dillon, R. 2006 Biofluidmechanics of reproduction. Ann. Rev. Fluid Mech. 38, 371-394. (doi:10.1146/annurev.fluid.37.061903.175725) (Pubitemid 43240181)
15. Flores, H., Lobaton, E., Méndez-Diez, S., Tlupova, S. & Cortez, R. 2005 A study of bacterial flagellar bundling. Bull. Math. Biol. 67, 137-168. (doi:10.1016/j.bulm.2004.06.006) (Pubitemid 40181072)
16. Fulford, G. R. & Blake, J. R. 1986 Muco-ciliary transport in the lung. J. Theor. Biol. 121, 381-402. (doi:10.1016/S0022-5193(86)80098-4)
17. Gillies, E. A., Cannon, R. M., Green, R. B., & Pacey, A. A. 2009 Hydrodynamic propulsion of human sperm. J. Fluid Mech. 625, 444-473. (doi:10.1017/S0022112008005685)
18. Gray, J. & Hancock, G. J. 1955 The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32, 802-814.
19. Gueron, S. & Levit-Gurevich, K. 1999 Energetic considerations of ciliary beating and the advantage of metachronal coordination. Proc. Natl. Acad. Sci. USA 96, 12 240-12 245. (doi:10.1073/pnas.96.22.12240) (Pubitemid 29513485)
20. Gueron, S. & Levit-Gurevich, K. 2001 A three-dimensional model for ciliary motion based on the internal 9 + 2 structure. Proc. R. Soc. Lond. A 268, 599-607. (doi:10.1098/rspb.2000.1396) (Pubitemid 32269848)
21. Gueron, S. & Liron, N. 1992 Ciliary motion modeling, and dynamic multicilia interactions. Biophys. J. 63, 1045-1058. (doi:10.1016/S0006-3495(92) 81683-1)
22. Hancock, G. J. 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. Lond. A. 217, 96-121. (doi:10.1098/rspa.1953.0048)
23. Higdon, J. J. L. 1979a. A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685-711. (doi:10.1017/S0022112079002482)
24. Higdon, J. J. L. 1979b The hydrodynamics of flagellar propulsion: helical waves. J. Fluid Mech. 94, 331-351. (doi:10.1017/S0022112079001051)
25. Hirokawa, N., Okada, Y. & Tanaka, Y. 2009 Fluid dynamic mechanism responsible for breaking the left-right symmetry of the human body: the nodal flow. Ann. Rev. Fluid Mech. 41, 53-72. (doi:10.1146/annurev.fluid.010908.165141)
26. Johnson, R. E. 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411-431. (doi:10.1017/S0022112080000687)
27. Leadbeater, B., Yu, Q., Kent, J. & Stekel, D. 2009 Three-dimensional images of choanoflagellate loricae. Proc. R. Soc. A 276, 3. (doi:10.1098/rspb. 2008.0844)
28. Lighthill, M. J. 1976 Flagellar hydrodynamics: the John von Neumann lecture. SIAM Rev. 18, 161-230. (doi:10.1137/1018040)
29. Liron, N. 1978 Fluid transport by cilia between parallel plates. J. Fluid Mech. 86, 705-726. (doi:10.1017/S0022112078001354)
30. Liron, N. & Mochon, S. 1976 The discrete-cilia approach to propulsion of ciliated micro-organisms. J. Fluid Mech. 75, 593-607. (doi:10.1017/ S0022112076000402)
31. Mitran, S. 2007 Metachronal wave formation in a model of pulmonary cilia. Comput. Struct. 85, 763-774. (doi:10.1016/j.compstruc.2007.01.015) (Pubitemid 46719353)
32. Orme, B. A. A., Blake, J. R. & Otto, S. R. 2003 Modelling the motion of particles around choanoflagellates. J. Fluid Mech. 475, 333-355. (doi:10.1017/S0022112002002914) (Pubitemid 36251653)
33. Pettitt, M. E., Orme, B. A. A., Blake, J. R. & Leadbeater, B. S. C. 2002 The hydrodynamics of filter feeding in choanoflagellates. Eur. J. Protistol. 38, 313-332. (doi:10.1078/0932-4739-00854) (Pubitemid 36100970)
34. Phan-Thien, N., Tran-Cong, T. & Ramia, M. 1987 A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 185, 533-549. (doi:10.1017/S0022112087003008)
35. Pozrikidis, C. 1992 Boundary integral and singularity methods for linearized viscous flow. Cambridge, UK: Cambridge University.
36. Pozrikidis, C. 2002 A practical guide to boundary-element methods with the software library BEMLIB. Boca Raton, FL: Chapman & Hall/CRC.
37. Purcell, E. M. 1977 Life at low Reynolds number. Am. J. Phys. 45, 3-11. (doi:10.1119/1.10903)
38. Ramia, M., Tullock, D. L. & Phan-Thien, N. 1993 The role of hydrodynamic interaction in the locomotion of microorganisms. Biophys. J. 65, 755-778. (doi:10.1016/S0006-3495(93)81129-9)
39. Sanderson, M. J. & Sleigh, M. A. 1981 Ciliary activity of cultured rabbit tracheal epithelium: beat pattern and metachrony. J. Cell Sci. 47, 331-341.
40. Sleigh, M. A., Blake, J. R. & Liron, N. 1988 The propulsion of mucus by cilia. Am. Rev. Respir. Dis. 137, 726-741.
41. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2007 Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid. Bull. Math. Biol. 69, 1477-1510. (doi:10.1007/s11538- 006-9172-y) (Pubitemid 46955663)
42. Smith, D. J., Blake, J. R. & Gaffney, E. A. 2008a Fluid mechanics of nodal flow due to embryonic primary cilia. J. R. Soc. Interface 5, 567-573. (doi:10.1098/rsif.2007.1306)
43. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2008b Modelling mucociliary clearance. Respir. Physiol. Neurobiol. 163, 178-188. (doi:10.1016/j.resp.2008.03.006)
44. Smith, D. J., Gaffney, E. A. & Blake, J. R. 2009a Mathematical modelling of cilia-driven transport of biological fluids. Proc. R. Soc. A 465, 2417-2439. (doi:10.1098/rspa.2009.0018)
45. Smith, D. J., Gaffney, E. A., Blake, J. R. & Kirkman-Brown, J. C. 2009b Human sperm accumulation near surfaces: a simulation study. J. Fluid Mech. 621, 289-320. (doi:10.1017/ S0022112008004953)
46. Tam, D. & Hosoi, A. 2007 Optimal stroke patterns for Purcells three-link swimmer. Phys. Rev. Lett. 98, 068105. (doi:10.1103/PhysRevLett.98. 068105) (Pubitemid 46246671)
47. Tornberg, A.-K. & Shelley, M. J. 2004 Simulating the dynamics and interactions of flexible fibers in Stokes flows. J. Comput. Phys. 196, 8-40. (doi:10.1016/j.jcp.2003.10.017) (Pubitemid 38521660)
48. Tuck, E. O. 1964 Some methods for flows past slender bodies. J. Fluid Mech. 18, 619-635. (doi:10.1017/S0022112064000453)