Motion of slender bodies in unsteady Stokes flow

Journal of Fluid Mechanics

Volumn 688, Issue , 2011, Pages 66-87

  Barta, Efrath ^a  

^a Bar Code Computers Ltd   (Israel)

Author keywords

Low Reynolds number flows; slender body theory

Indexed keywords

BIOLOGY; BODIES OF REVOLUTION; CAPILLARY FLOW; DRAG; REYNOLDS NUMBER;

DIRECTION OF MOTION; FORMATION AND EVOLUTIONS; FREQUENCY OF OSCILLATION; LOW REYNOLDS NUMBER FLOW; NORMAL DIRECTION; SLENDER-BODY THEORY; SLENDERNESS RATIOS; STREAMLINE PATTERN;

AUTOMOBILE BODIES;

DRAG; REYNOLDS NUMBER; STOKES FORMULA; UNSTEADY FLOW;

HEXAPODA;

EID: 84855499875     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2011.365     Document Type: Article

References (33)

1. BARTA, E. & LIRON, N. 1988 Slender body interactions for low Reynolds numbers. Part II. Body-body interactions. SIAM J. Appl. Maths 48, 1262-1280.
2. BARTA, E. & WEIHS, D. 2004 Flapping comb-wings in Stokes flow. Report no. 2, Project no. 160036, Faculty of Aerospace Engineering, Technion.
3. BARTA, E. & WEIHS, D. 2006 Creeping flow around a finite row of slender bodies in close proximity. J. Fluid Mech. 551, 1-17.
4. BATHELLIER, B., BARTH, F. G., ALBERT, J. T. & HUMPHREY, J. A. C. 2005 Viscosity-mediated motion coupling between pairs of trichobothria on the leg of the spider Cupiennius salei. J. Compar. Physiol. A 191, 733-746. (Pubitemid 41204269)
5. BLAKE, J. R. & SLEIGH, M. A. 1974 Mechanics of ciliary locomotion. Biol. Rev. 49, 85-125.
6. BRENNEN, C. & WINET, H. 1977 Fluid mechanics of propulsion by cilia and flagella. Annu. Rev. Fluid Mech. 9, 339-398.
7. CHEER, A. Y. L. & KOEHL, M. A. R. 1987 Paddles and rakes: fluid flow through bristled appendages of small organisms. J. Theor. Biol. 129, 17-39.
8. CHWANG, A. T. & WU, T. Y. 1975 Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flow. J. Fluid Mech. 67, 787-815.
9. 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, 912-933.
10. D'EĹIA, J., BATTAGLIA, L., SARRAF, S. & CARDONA, A. A boundary element method for oscillating Stokes flow at low frequencies around a rigid body. A boundary element method for oscillating Stokes flow at low frequencies around a rigid body. 2010 In Mecanica Computacional, vol. XXIX (ed. E. Dvorkin, M. Goldschmit & M. Storti).
11. DUDLEY, R. 2000 The Biomechanics of Insect Flight: Form, Function, Evolution. Princeton University Press.
12. ELLINGTON, C. P. 1984 The aerodynamics of hovering insect flight. Part I. The quasi-steady analysis. Phil. Trans. R. Soc. Lond. B 305, 1-15.
13. FENG, J. & JOSEPH, D. D. 1995 The unsteady motion of solid bodies in creeping flows. J. Fluid Mech. 303, 83-102. (Pubitemid 26463900)
14. FRY, S. N., SAYAMAN, R. & DICKINSON, M. H. 2005 The aerodynamics of hovering flight in Drosophila. J. Expl Biol. 208, 2303-2318. (Pubitemid 40912515)
15. GRAY, J. 1928 Ciliary Movement. Cambridge University Press.
16. JOHNSON, R. E. 1980 An improved slender-body theory for Stokes flow. J. Fluid Mech. 99, 411-431.
17. KIM, S. & KARRILA, S. J. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
18. KOHR, M. 2003 An indirect boundary integral method for an oscillatory Stokes flow problem. IJMMS 47, 2961-2976. (Pubitemid 40588003)
19. LAWRENCE, C. J. & WEINBAUM, S. 1986 The force on an axisymmetric body in linearized, time-dependent motion: a new memory term. J. Fluid Mech. 171, 209-218. (Pubitemid 17495775)
20. LAWRENCE, C. J. & WEINBAUM, S. 1988 The unsteady force on a body at low Reynolds number: the axisymmetric motion of a spheroid. J. Fluid Mech. 189, 463-489.
21. LIRON, N. & BARTA, E. 1992 Motion of a rigid particle in Stokes flow: a new second-kind boundary-integral equation formulation. J. Fluid Mech. 238, 579-598.
22. LOEWENBERG, M. 1994 Axisymmetric unsteady Stokes flow past an oscillating finite-length cylinder. J. Fluid Mech. 265, 265-288. (Pubitemid 285109)
23. POZRIKIDIS, C. 1989a A singularity method for unsteady linearized flow. Phys. Fluids A 1 (9), 1508-1520.
24. POZRIKIDIS, C. 1989b A study of linearized oscillatory flow past particles by the boundary-integral method. J. Fluid Mech. 202, 17-41.
25. SANE, S. P. & DICKINSON, M. H. 2002 The control of flight force by a flapping wing: lift and drag production. J. Expl Biol. 204, 2607-2626. (Pubitemid 34861399)
26. SHATZ, L. F. 2004 Singularity method for oblate and prolate spheroids in Stokes and linearized oscillatory flow. Phys. Fluids 16 (3), 664-677. (Pubitemid 38485347)
27. SMITH, S. H. 1997 Slow oscillatory Stokes flow. Q. Appl. Math. 55, 1-22.
28. STOKES, G. G. 1851 On the effect of the internal friction of fluids on the motion of pendulum. Trans. Camb. Phil. Soc. 9, 8.
29. SUNADA, S., TAKASHIMA, H., HATTORI, T., YASUDA, K. & KAWACHI, K. 2002 Fluid-dynamic characteristics of a bristled wing. J. Expl Biol. 205, 2737-2744.
30. TAYLOR, G. K. 2001 Mechanics and aerodynamics of insect flight control. Biol. Rev. Camb. Phil. Soc. 76, 449-471. (Pubitemid 33089591)
31. TSAI, C. C., YOUNG, D. L., FAN, C. M. & CHEN, C. W. 2006 MFS with time-dependent fundamental solutions for unsteady Stokes equations. Engng Anal. Bound. Elem. 30, 897-908. (Pubitemid 44354117)
32. WEIHS, D. & BARTA, E. 2008 Comb wings for flapping flight at extremely low Reynolds numbers. AIAA J. 46 (1), 285-288. (Pubitemid 351158422)
33. ZUSSMAN, E., YARIN, A. L. & WEIHS, D. 2002 A micro-aerodynamic decelerator based on permeable surfaces of nanofibre mats. Exp. Fluids 33, 315-320. (Pubitemid 34962697)