Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session M33: Drops: Walking Drops |
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Chair: John Bush, MIT Room: Ballroom A |
Tuesday, November 24, 2015 8:00AM - 8:13AM |
M33.00001: The interaction of a walking droplet and a pillar John Bush, Daniel Harris, Pierre-Thomas Brun Droplets may bounce on the surface of a vibrating fluid bath, propelled forward by their own pilot-wave field. With a view to better understanding the interaction of such walking droplets with boundaries, we consider their impact on a submerged circular pillar. While simple scattering events are the norm, as the Faraday threshold is approached, the drop departs the pillar along a path corresponding to a logarithmic spiral. An effective wave force resulting from the pillar is inferred from the spiral, and takes the form of the Coriolis force that would arise in a frame of reference rotating with the instantaneous angular momentum of the drop about the pillar. An electromagnetic analog is explored. [Preview Abstract] |
Tuesday, November 24, 2015 8:13AM - 8:26AM |
M33.00002: Visualization of hydrodynamic pilot-wave dynamics Victor Prost, Julio Quintela, Daniel Harris, Pierre-Thomas Brun, John Bush We present a low-cost device for examining the dynamics of droplets bouncing on a vibrating fluid bath, suitable for educational purposes. Dual control of vibrational and strobing frequency from a cell phone application allowed us to reduce the total cost to 60 dollars. Illumination with inhomogeneous colored light allows for striking visualization of the droplet dynamics and accompanying wave field via still photography or high-speed videography. [Preview Abstract] |
Tuesday, November 24, 2015 8:26AM - 8:39AM |
M33.00003: Faraday Pilot-Waves: Generation and Propagation Carlos Galeano-Rios, Paul Milewski, Andr\'e Nachbin, John Bush We examine the dynamics of drops bouncing on a fluid bath subjected to vertical vibration. We solve a system of linear PDEs to compute the surface wave generation and propagation. Waves are triggered at each bounce, giving rise to the Faraday pilot-wave field. The model captures several of the behaviors observed in the laboratory, including transitions between a variety of bouncing and walking states, the Doppler effect, and droplet-droplet interactions. [Preview Abstract] |
Tuesday, November 24, 2015 8:39AM - 8:52AM |
M33.00004: Schr\"{o}dinger's drop in a box: wave-droplet interaction in a circular cavity Tristan Gilet A walker is a bouncing droplet on a liquid surface that is horizontally propelled by the Faraday waves it generates. This hydrodynamic wave-particle interaction exhibits many quantum-like behaviors. The horizontal trajectory of a walker becomes chaotic when subject to horizontal confinement. Experiments (Harris et al., PRE 2013) reveal that the statistics of the walker position is shaped by the eigenmodes of the cavity in which it is confined, similarly to a quantum particle in a box. In this talk, I introduce a model of the coupling between a bouncing droplet and a surface wave in a cylindrical container. The resulting iterated map captures many features of experimental observations of walker dynamics under confinement. Moreover, the statistical behavior of the map is shown to be surprisingly similar to the solution of Schr\"{o}dinger equation for a particle in an infinite potential well. This yields an analogy between the Planck constant and the hydrodynamic wave-particle coupling constant. [Preview Abstract] |
Tuesday, November 24, 2015 8:52AM - 9:05AM |
M33.00005: Simulations of walking droplets in a harmonic potential Kristin Dettmers, Dan Harris, Anand Oza, Rodolfo Rosales, John Bush We present the results of a theoretical investigation of the dynamics of droplets walking on the surface of a vibrating bath while subjected to a radial spring force. This system was first explored by Perrard et al. (2014) and Labousse et al. (in preparation), who reported a number of orbital states characterized by a double quantization, in mean radius and angular momentum. Particular attention is given here to characterizing the dependence of the system behavior, specifically the quantization, on the vibrational forcing and the spring force. A number of new exotic orbital states are identified. [Preview Abstract] |
Tuesday, November 24, 2015 9:05AM - 9:18AM |
M33.00006: Stochastic trajectories of a walking drop in a harmonic potential Mason Biamonte, Anand Oza, Andre Nachbin, John W. M. Bush Droplets walking on the surface of a vibrating fluid bath have been shown to exhibit certain features of microscopic, quantum systems. Their dynamics is reminiscent of modern extensions of de Broglie’s pilot-wave theory, according to which charged particles interact with a stochastic field. We here present the results of a theoretical investigation of the influence of such a stochastic field on the pilot-wave dynamics of a droplet walking in a simple harmonic potential. [Preview Abstract] |
Tuesday, November 24, 2015 9:18AM - 9:31AM |
M33.00007: The uncertain trajectory of a pilot-wave Andre Nachbin Yves Couder (Paris 7) and coworkers reported on walking droplets on the surface of a vibrating bath. John Bush (MIT) and coworkers also produced laboratory experiments which were compared to theoretical predictions. Both groups discussed the pilot-wave properties previously thought to be peculiar to the microscopic, quantum realm. Of particular interest is the wavelike statistics for pilot-wave dynamics in a confined domain. We present a one dimensional water wave model for a droplet bouncing in a confined domain. The mathematical model makes use of conformal mapping which allows for the presence of submerged barriers. The computational simulations produce tunneling events. [Preview Abstract] |
Tuesday, November 24, 2015 9:31AM - 9:44AM |
M33.00008: Orbiting pairs of walking droplets Emmanuel Siefert, John W.M. Bush, Anand Oza Droplets may self-propel on the surface of a vibrating fluid bath, pushed forward by their own Faraday pilot-wave field. We present the results of a combined experimental and theoretical investigation of the interaction of pairs of such droplets. Particular attention is given to characterizing the system's dependence on the vibrational forcing of the bath and the impact parameter of the walking droplets. Observed criteria for the capture and stability of orbital pairs are rationalized by accompanying theoretical developments. [Preview Abstract] |
Tuesday, November 24, 2015 9:44AM - 9:57AM |
M33.00009: Onset of chaos in orbital pilot-wave dynamics Lucas Tambasco, Daniel Harris, Anand Oza, Rodolfo Rosales, John Bush We examine the orbital dynamics of droplets self-propelling along the surface of a vibrating bath. Circular orbital motion may arise when the walking droplet is subjected to one of three external~ force fields, the Coriolis force, a simple harmonic force, and a Coulomb force. Particular attention~ is given to a theoretical characterization of the onset of chaos that accompanies the destabilization~ of such circular orbits. [Preview Abstract] |
Tuesday, November 24, 2015 9:57AM - 10:10AM |
M33.00010: Orbiting droplets on a vibrated bath Naresh Sampara, Loic Burger, Tristan Gilet A millimeter-sized oil droplet can bounce on a vertically vibrated liquid bath for unlimited time. It may couple to the surface wave it emits; leading to horizontal self-propulsion called walking. When several walkers coexist close to one another, they either repel or attract each other, in response to the superposition of the waves they generate. Attraction leads to various bound states, including droplets that orbit around each other. We have experimentally investigated the variety of quantized orbital motions exhibited by two, three and more identical walkers, as a function of forcing acceleration. Each motion is quantified in terms of droplet and wave energy. [Preview Abstract] |
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