Drops walking on a vibrating bath: Towards a hydrodynamic pilot-wave theory

Journal of Fluid Mechanics

Volumn 727, Issue , 2013, Pages 612-647

  Moláček, Jan ^a   Bush, John W M ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Drops; Faraday waves; Waves free surface flows

Indexed keywords

DROP FORMATION; DROPS;

FARADAY WAVES; INCREASING FUNCTIONS; PARAMETER COMBINATION; SPATIOTEMPORAL EVOLUTION; TANGENTIAL COEFFICIENT; THEORETICAL INVESTIGATIONS; THEORETICAL MODELING; WAVES/FREE-SURFACE FLOWS;

HYDRODYNAMICS;

DROPLET; EXPERIMENTAL STUDY; FLUID FLOW; FLUID MECHANICS; HYDRODYNAMICS; THEORETICAL STUDY; VIBRATION; WAVE FIELD;

EID: 84880597216     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2013.280     Document Type: Article

References (29)

1. BENJAMIN, T. & URSELL, F. 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505-515.
2. DE BROGLIE, L. 1987 Interpretation of quantum mechanics by the double solution theory. Ann. Fond. Louis de Broglie 12, 1-23 (English translation).
3. BUSH, J. W. M. 2010 Quantum mechanics writ large. Proc. Natl Acad. Sci. 107, 17455-17456.
4. CHANG, E. J. & MAXEY, M. R. 1994 Unsteady flow about a sphere at low to moderate Reynolds number. Part 1. Oscillatory motion. J. Fluid Mech. 277, 347-379.
5. COUDER, Y. & FORT, E. 2006 Single-particle diffraction and interference at macroscopic scale. Phys. Rev. Lett. 97, 154101.
6. COUDER, Y., FORT, E., GAUTIER, C. H. & BOUDAOUD, A. 2005a From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94, 177801.
7. COUDER, Y., PROTÌERE, S., FORT, E. & BOUDAOUD, A. 2005b Walking and orbiting droplets. Nature 437, 208.
8. EDDI, A., FORT, E., MOISY, F. & COUDER, Y. 2009 Unpredictable tunneling of a classical wave-particle association. Phys. Rev. Lett. 102, 240401.
9. EDDI, A., MOUKHTAR, J., PERRARD, S., FORT, E. & COUDER, Y. 2012 Level splitting at macroscopic scale. Phys. Rev. Lett. 108, 264503.
10. EDDI, A., SULTAN, E., MOUKHTAR, J., FORT, E., ROSSI, M. & COUDER, Y. 2011 Information stored in Faraday waves: the origin of a path memory. J. Fluid Mech. 674, 433-463.
11. EDDI, A., TERWAGNE, D., FORT, E. & COUDER, Y. 2008 Wave propelled ratchets and drifting rafts. Europhys. Lett. 82, 44001.
12. FLÜGGE, S. 1959 Handbuch der Physik: Strömungsmechanik I. Springer.
13. FORT, E., EDDI, A., BOUDAOUD, A., MOUKHTAR, J. & COUDER, Y. 2010 Path-memory induced quantization of classical orbits. Proc. Natl Acad. Sci. 107, 17 515-17 520.
14. GILET, T. & BUSH, J. W. M. 2009 The fluid trampoline: droplets bouncing on a soap film. J. Fluid Mech. 625, 167-203.
15. GOLDMAN, A. J., COX, R. G. & BRENNER, H. 1967 Slow viscous motion of a sphere parallel to a plane wall - I: Motion through a quiescent fluid. Chem. Engng Sci. 22, 637-651.
16. HARRIS, D. M., MOUKHTAR, J., FORT, E., COUDER, Y. & BUSH, J. W. M. 2013 Wave-like statistics from pilot-wave dynamics in a circular corral. Phys Rev. E (submitted).
17. HARTLAND, S. 1971 The pressure distribution in axisymmetric draining films. J. Colloid Interface Sci. 35, 227-237.
18. KUMAR, K. 1996 Linear theory of Faraday instability in viscous liquids. Proc. Math. Phys. Engng Sci. 452, 1113-1126.
19. LAMB, H. 1932 Hydrodynamics. Cambridge University Press.
20. MOLÁČEK, J. & BUSH, J. W. M. 2012 A quasi-static model of drop impact. Phys. Fluids 24, 127103.
21. MOLÁČEK, J. & BUSH, J. W. M. 2013 Drops bouncing on a vibrating bath. J. Fluid Mech. 727, 582-611.
22. OZA, A. U., ROSALES, R. R. & BUSH, J. W. M. 2013 A trajectory equation for walking droplets: hydrodynamic pilot-wave theory. J. Fluid Mech. (submitted).
23. PROSPERETTI, A. 1976 Viscous effects on small-amplitude surface waves. Phys. Fluids 19, 195-203.
24. PROTI ̀ERE, S., BOUDAOUD, A. & COUDER, Y. 2006 Particle-wave association on a fluid interface. J. Fluid Mech. 554, 85-108.
25. PROTI ̀ERE, S., COUDER, Y., FORT, E. & BOUDAOUD, A. 2005 The self-organization of capillary wave sources. J. Phys.: Condens. Matter 17, S3529-S3535.
26. SHIROKOFF, D. 2013 Bouncing droplets on a billiard table. Chaos 23, 013115.
27. TORBY, B. J. 1984 Advanced Dynamics for Engineers. Holt, Rinehart and Winston.
28. WALKER, J. 1978 Drops of liquid can be made to float on the liquid. What enables them to do so? The Amateur Scientist, Sci. Am. 238, 151-158.
29. WIND-WILLASSEN, Ø., MOLÁC̈EK, J., HARRIS, D. M. & BUSH, J. W. M 2013 Exotic states of bouncing and walking droplets. Phys. Fluids (submitted).