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Drops bouncing on a vibrating bath

  • Jan Moláček (a1) and John W. M. Bush (a1)
Abstract
Abstract

We present the results of a combined experimental and theoretical investigation of millimetric droplets bouncing on a vertically vibrating fluid bath. We first characterize the system experimentally, deducing the dependence of the droplet dynamics on the system parameters, specifically the drop size, driving acceleration and driving frequency. As the driving acceleration is increased, depending on drop size, we observe the transition from coalescing to vibrating or bouncing states, then period-doubling events that may culminate in either walking drops or chaotic bouncing states. The drop’s vertical dynamics depends critically on the ratio of the forcing frequency to the drop’s natural oscillation frequency. For example, when the data describing the coalescence–bouncing threshold and period-doubling thresholds are described in terms of this ratio, they collapse onto a single curve. We observe and rationalize the coexistence of two non-coalescing states, bouncing and vibrating, for identical system parameters. In the former state, the contact time is prescribed by the drop dynamics; in the latter, by the driving frequency. The bouncing states are described by theoretical models of increasing complexity whose predictions are tested against experimental data. We first model the drop–bath interaction in terms of a linear spring, then develop a logarithmic spring model that better captures the drop dynamics over a wider range of parameter space. While the linear spring model provides a faster, less accurate option, the logarithmic spring model is found to be more accurate and consistent with all existing data.

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Email address for correspondence: bush@math.mit.edu
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T. Benjamin & F. Ursell 1954 The stability of the plane free surface of a liquid in vertical periodic motion. Proc. R. Soc. Lond. A 225, 505515.

J. W. M. Bush 2010 Quantum mechanics writ large. Proc. Natl. Acad. Sci. 107, 17 45517 456.

Y. K. Cai 1989 Phenomena of a liquid drop falling to a liquid surface. Exp. Fluids 7, 388394.

B. Ching , M. W. Golay & T. J. Johnson 1984 Droplet impacts upon liquid surfaces. Science 226, 535537.

Y. Couder & E. Fort 2006 Single-particle diffraction and interference at macroscopic scale. Phys. Rev. Lett. 97, 154101.

Y. Couder , E. Fort , C. H. Gautier & A. Boudaoud 2005a From bouncing to floating: noncoalescence of drops on a fluid bath. Phys. Rev. Lett. 94, 177801.

Y. Couder , S. Protière , E. Fort & A. Boudaoud 2005b Dynamical phenomena: walking and orbiting droplets. Nature 437, 208.

R. B. Davis & L. N. Virgin 2007 Non-linear behaviour in a discretely forced oscillator. Intl J. Non-Linear Mech. 42, 744753.

A. Eddi , A. Boudaoud & Y. Couder 2011a Oscillating instability in bouncing droplet crystals. Europhys. Lett. 94, 20004.

A. Eddi , A. Decelle , E. Fort & Y. Couder 2009a Archimedean lattices in the bound states of wave interacting particles. Europhys. Lett. 87, 56002.

A. Eddi , E. Fort , F. Moisy & Y. Couder 2009b Unpredictable tunneling of a classical wave–particle association. Phys. Rev. Lett. 102, 240401.

A. Eddi , J. Moukhtar , S. Perrard , E. Fort & Y. Couder 2012 Level splitting at macroscopic scale. Phys. Rev. Lett. 108, 264503.

A. Eddi , D. Terwagne , E. Fort & Y. Couder 2008 Wave propelled ratchets and drifting rafts. Europhys. Lett. 82, 44001.

B. Eichwald , M. Argentina , X. Noblin & F. Celestini 2010 Dynamics of a ball bouncing on a vibrated elastic membrane. Phys. Rev. E 82, 016203.

R. M. Everson 1986 Chaotic dynamics of a bouncing ball. Physica D 19, 355383.

M. Faraday 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 299340.

E. Fermi 1949 On the origin of the cosmic radiation. Phys. Rev. 75, 11691174.

R. L. C. Flemmer & C. L. Banks 1986 On the drag coefficient of a sphere. Powder Technol. 48, 217221.

G. B. Foote 1975 The water drop rebound problem: dynamics of collision. J. Atmos. Sci. 32, 390402.

E. Fort , A. Eddi , A. Boudaoud , J. Moukhtar & Y. Couder 2010 Path-memory induced quantization of classical orbits. Proc. Natl. Acad. Sci. 107, 17 51517 520.

T. Gilet & J. W. M. Bush 2009a Chaotic bouncing of a droplet on a soap film. Phys. Rev. Lett. 102, 014501.


A. Gopinath & D. L. Koch 2001 Dynamics of droplet rebound from a weakly deformable gas–liquid interface. Phys. Fluids 13, 35263532.

S. Hartland 1969 The effect of circulation patterns on the drainage of the film between a liquid drop and a deformable liquid–liquid interface. Chem. Engng Sci. 24, 611613.

S. Hartland 1970 The profile of the draining film between a fluid drop and a deformable fluid–liquid interface. Chem. Engng J. 1, 6775.

O. W. Jayaratne & B. J. Mason 1964 The coalescence and bouncing of water drops at an air/water interface. Proc. R. Soc. Lond. A 280, 545565.


K. Kumar 1996 Linear theory of Faraday instability in viscous liquids. Proc. Math. Phys. Engng Sci. 452, 11131126.

J. M. Luck & A. Mehta 1993 Bouncing ball with a finite restitution: chattering, locking, and chaos. Phys. Rev. E 48, 39883997.

G. A. Luna-Acosta 1990 Regular and chaotic dynamics of the damped Fermi accelerator. Phys. Rev. A 42, 71557162.


J. Moláček & J. W. M. Bush 2012 A quasi-static model of drop impact. Phys. Fluids 24, 127103.

J. Moláček & J. W. M. Bush 2013 Drops walking on a vibrating bath: towards a hydrodynamic pilot-wave theory. J. Fluid Mech. 727, 612647.

K. Okumura , F. Chevy , D. Richard , D. Quéré & C. Clanet 2003 Water spring: a model for bouncing drops. Europhys. Lett. 62, 237243.

P. Pieranski 1983 Jumping particle model. Period doubling cascade in an experimental system. J. Phys. (Paris) 44, 573578.

P. Pieranski & R. Bartolino 1985 Jumping particle model. Modulation modes and resonant response to a periodic perturbation. J. Phys. (Paris) 46, 687690.


A. Prosperetti & H. N. Oguz 1993 The impact of drops on liquid surfaces and the underwater noise of rain. Annu. Rev. Fluid Mech. 25, 577602.

S. Protière , S. Bohn & Y. Couder 2008 Exotic orbits of two interacting wave sources. Phys. Rev. E 78, 036204.


S. Protière & Y. Couder 2006 Orbital motion of bouncing drops. Phys. Fluids 18, 091114.

D. Richard , C. Clanet & D. Quéré 2002 Surface phenomena: contact time of a bouncing drop. Nature 417, 811.

D. Richard & D. Quéré 2000 Bouncing water drops. Europhys. Lett. 50, 769775.

R. M. Schotland 1960 Experimental results relating to the coalescence of water drops with water surfaces. Discuss. Faraday Soc. 30, 7277.

D. Terwagne , T. Gilet , N. Vandewalle & S. Dorbolo 2008 From bouncing to boxing. Chaos 18, 041104.

J. Zou , P. F. Wang , T. R. Zhang , X. Fu & X. Ruan 2011 Experimental study of a drop bouncing on a liquid surface. Phys. Fluids 23, 044101.

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  • EISSN: 1469-7645
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