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Non-specular reflection of walking droplets

  • Giuseppe Pucci (a1) (a2), Pedro J. Sáenz (a1), Luiz M. Faria (a1) and John W. M. Bush (a1)

Since their discovery by Yves Couder and Emmanuel Fort, droplets walking on a vibrating liquid bath have attracted considerable attention because they unexpectedly exhibit certain features reminiscent of quantum particles. While the behaviour of walking droplets in unbounded geometries has to a large extent been rationalized theoretically, no such rationale exists for their behaviour in the presence of boundaries, as arises in a number of key quantum analogue systems. We here present the results of a combined experimental and theoretical study of the interaction of walking droplets with a submerged planar barrier. Droplets exhibit non-specular reflection, with a small range of reflection angles that is only weakly dependent on the system parameters, including the angle of incidence. The observed behaviour is captured by simulations based on a theoretical model that treats the boundaries as regions of reduced wave speed, and rationalized in terms of momentum considerations.

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Andersen A., Madsen J., Reichelt C., Ahl S. R., Lautrup B., Ellegaard C., Levinsen M. T. & Bohr T. 2015 Double-slit experiment with single wave-driven particles and its relation to quantum mechanics. Phys. Rev. E 92 (1), 013006.
Batelaan H., Jones E., Huang W. C.-W. & Bach R. 2016 Momentum exchange in the electron double-slit experiment. J. Phys. Conf. Series 701, 012007.
Blanchette F. 2016 Modeling the vertical motion of drops bouncing on a bounded fluid reservoir. Phys. Fluids 28 (3), 032104.
Bush J. W. M. 2015a The new wave of pilot-wave theory. Phys. Today 68, 4753.
Bush J. W. M. 2015b Pilot-wave hydrodynamics. Annu. Rev. Fluid Mech. 49, 269292.
Bush J. W. M., Oza A. U. & Molácek J. 2014 The wave-induced added mass of walking droplets. J. Fluid Mech. 755, R7.
Couder Y. & Fort E. 2006 Single particle diffraction and interference at a macroscopic scale. Phys. Rev. Lett. 97, 154101.
Couder Y., Protière S., Fort E. & Boudaoud A. 2005 Dynamical phenomena: walking and orbiting droplets. Nature 437, 208.
Damiano A., Brun P.-T., Harris D. M., Galeano-Rios C. & Bush J. W. M. 2016 Surface topography measurements of the bouncing droplet experiment. Exp. Fluids (submitted).
Eddi A., Fort E., Moisy F. & Couder Y. 2009 Unpredictable tunneling of a classical wave-particle association. Phys. Rev. Lett. 102, 240401.
Eddi A., Sultan E., Moukhtar J., Fort E., Rossi M. & Couder Y. 2011 Information stored in Faraday waves: the origin of path memory. J. Fluid Mech. 674, 433463.
Faraday M. 1831 On the forms and states of fluids on vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 319340.
Faria L. 2016 A model for Faraday pilot-waves over variable topography. J. Fluid Mech. (submitted).
Fort E., Eddi A., Boudaoud A., Moukhtar J. & Couder Y. 2010 Path-memory induced quantization of classical orbits. Proc. Natl Acad. Sci. USA 107 (41), 1751517520.
Gilet T. 2014 Dynamics and statistics of wave-particle interactions in a confined geometry. Phys. Rev. E 90 (5), 052917.
Gilet T. 2016 Quantumlike statistics of deterministic wave-particle interactions in a circular cavity. Phys. Rev. E 93 (4), 042202.
Harris D.2015, The pilot-wave dynamics of walking droplets in confinement. PhD thesis, Massachusetts Institute of Technology.
Harris D. & Bush J. W. M. 2014 Droplets walking in a rotating frame: from quantized orbits to multimodal statistics. J. Fluid Mech. 739, 444464.
Harris D. & Bush J. W. M. 2015 Generating uniaxial vibration with an electrodynamic shaker and external air bearing. J. Sound Vib. 334, 255269.
Harris D., Liu T. & Bush J. W. M. 2015 A low-cost, precise piezoelectric droplet-on-demand generator. Exp. Fluids 56, 8390.
Harris D., Moukhtar J., Fort E., Couder Y. & Bush J. W. M. 2013 Wavelike statistics from pilot-wave dynamics in a circular corral. Phys. Rev. E 88, 011001(R).
Labousse M.2014 Etude d’une dynamique à mémoire de chemin: une expérimentation thórique. PhD thesis, Université Paris 6.
Labousse M., Oza A. U., Perrard S. & Bush J. W. M. 2016 Pilot-wave dynamics in a harmonic potential: quantization and stability of circular orbits. Phys. Rev. E 93 (3), 033122.
Labousse M. & Perrard S. 2014 Non-Hamiltonian features of a classical pilot-wave dynamics. Phys. Rev. E 90 (2), 022913.
Labousse M., Perrard S., Couder Y. & Fort E. 2014 Build-up of macroscopic eigenstates in a memory-based constrained system. New J. Phys. 16 (11), 113027.
Milewski P., Galeano-Rios C., Nachbin A. & Bush J. W. M. 2015 Faraday pilot-wave hydrodynamics: modeling and computation. J. Fluid Mech. 778, 361388.
Molacek J. & Bush J. W. M. 2013a Droplets bouncing on a vibrating fluid bath. J. Fluid Mech. 727, 582611.
Molacek J. & Bush J. W. M. 2013b Droplets walking on a vibrating fluid bath: towards a hydrodynamic pilot-wave theory. J. Fluid Mech. 727, 612647.
Oza A., Harris D. M., Rosales R. R. & Bush J. W. M. 2014 Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. J. Fluid Mech. 744, 404429.
Oza A., Rosales R. R. & Bush J. W. M. 2013 A trajectory equation for walking droplets: a hydrodynamic pilot-wave theory. J. Fluid Mech. 737, 552570.
Perrard S., Labousse M., Fort E. & Couder Y. 2014a Chaos driven by interfering memory. Phys. Rev. Lett. 113, 104101.
Perrard S., Labousse M., Miskin M., Fort E. & Couder Y. 2014b Self-organization into quantized eigenstates of a classical wave-driven particle. Nature Comm. 5, 3219.
Protière S., Boudaoud A. & Couder Y. 2006 Particle wave association on a fluid interface. J. Fluid Mech. 554, 85108.
Wind-Willassen O., Molacek J., Harris D. M. & Bush J. W. M. 2013 Exotic states of bouncing and walking droplets. Phys. Fluids 25, 082002.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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