Abstract  : 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.

Tambasco, L., Harris, D., Oza, A., Rosales, R., & Bush, J. (2015, November). Onset of chaos in orbital pilot-wave dynamics. In APS Meeting Abstracts.

Paper available on researchgate.net/ (Requires free login)

A technical entry by the american team reproducing the synthetic Schlieren free surface measurment already implemented successfully by the Paris Team.

Damiano, A. P., Brun, P. T., Harris, D. M., Galeano-Rios, C. A., & Bush, J. W. (2016). Surface topography measurements of the bouncing droplet experiment. Experiments in Fluids, 57(10), 163.

Brun, P. T., Harris, D. M., Prost, V., Quintela, J., & Bush, J. W. (2016). Shedding light on pilot-wave phenomena. Physical Review Fluids, 1(5), 050510.

ABSTRACT

This paper is associated with a video winner of a 2015 APS/DFD Gallery of Fluid Motion Award. The original video is available from the Gallery of Fluid Motion,

http://dx.doi.org/10.1103/APS.DFD.2015.GFM.V0064

http://link.aps.org/pdf/10.1103/PhysRevFluids.1.050510

Harris, D. M., & Bush, J. W. (2015). Generating uniaxial vibration with an electrodynamic shaker and external air bearing. Journal of Sound and Vibration,334, 255-269.

Electrodynamic shakers are widely used in experimental investigations of vibrated fluids and granular materials. However, they are plagued by undesirable internal resonances that can significantly impact the quality of vibration. In this work, we measure the performance of a typical shaker and characterize the influence that a payload has on its performance. We present the details of an improved vibration system based on a concept developed by Goldman (2002) [1] which consists of a typical electrodynamic shaker with an external linear air bearing to more effectively constrain the vibration to a single axis. The principal components and design criteria for such a system are discussed. Measurements characterizing the performance of the system demonstrate considerable improvement over the unmodified test shaker. In particular, the maximum inhomogeneity of the vertical vibration amplitude is reduced from approximately 10 percent to 0.1 percent; moreover, transverse vibrations were effectively eliminated.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2015/01/Harris-Shaker.pdf

Harris, D. M., Liu, T., & Bush, J. W. (2015). A low-cost, precise piezoelectric droplet-on-demand generator. Experiments in Fluids, 56(4), 1-7.

We present the design of a piezoelectric droplet-on-demand generator capable of producing droplets of highly repeatable size ranging from 0.5 to 1.4 mm in diameter. The generator is low cost and simple to fabricate. We demonstrate the manner in which droplet diameter can be controlled through variation of the piezoelectric driving waveform parameters, outlet pressure, and nozzle diameter.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2015/04/Harris-DropGenerator.pdf

Oza, A. U., Harris, D. M., Rosales, R. R., & Bush, J. W. (2014). Pilot-wave dynamics in a rotating frame: on the emergence of orbital quantization. Journal of Fluid Mechanics, 744, 404-429.

We present the results of a theoretical investigation of droplets walking on a
rotating vibrating fluid bath. The droplet’s trajectory is described in terms of an
integro-differential equation that incorporates the influence of its propulsive wave
force. Predictions for the dependence of the orbital radius on the bath’s rotation
rate compare favourably with experimental data and capture the progression from
continuous to quantized orbits as the vibrational acceleration is increased. The orbital
quantization is rationalized by assessing the stability of the orbital solutions, and may
be understood as resulting directly from the dynamic constraint imposed on the drop
by its monochromatic guiding wave. The stability analysis also predicts the existence
of wobbling orbital states reported in recent experiments, and the absence of stable
orbits in the limit of large vibrational forcing

http://math.mit.edu/~auoza/JFM_2.pdf

Harris, D. M., & Bush, J. W. (2014). Droplets walking in a rotating frame: from quantized orbits to multimodal statistics. Journal of Fluid Mechanics, 739, 444-464.

We present the results of an experimental investigation of a droplet walking on the
surface of a vibrating rotating fluid bath. Particular attention is given to demonstrating
that the stable quantized orbits reported by Fort et al. (Proc. Natl Acad. Sci.,
vol. 107, 2010, pp. 17515–17520) arise only for a finite range of vibrational
forcing, above which complex trajectories with multimodal statistics arise. We first
present a detailed characterization of the emergence of orbital quantization, and
then examine the system behaviour at higher driving amplitudes. As the vibrational
forcing is increased progressively, stable circular orbits are succeeded by wobbling
orbits with, in turn, stationary and drifting orbital centres. Subsequently, there is a
transition to wobble-and-leap dynamics, in which wobbling of increasing amplitude
about a stationary centre is punctuated by the orbital centre leaping approximately
half a Faraday wavelength. Finally, in the limit of high vibrational forcing, irregular
trajectories emerge, characterized by a multimodal probability distribution that reflects
the persistent dynamic influence of the unstable orbital states.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2014/01/HB-JFM-2014.pdf

Wind-Willassen, Ø., Moláček, J., Harris, D. M., & Bush, J. W. (2013). Exotic states of bouncing and walking droplets. Physics of Fluids, 25, 082002.

http://windw.dk/2013Bouncing.pdf

Phase diagram refinement : the different styles of bouncing

Harris, D. M., Moukhtar, J., Fort, E., Couder, Y., & Bush, J. W. (2013). Wavelike statistics from pilot-wave dynamics in a circular corral. Physical Review E, 88(1), 011001.

Abstract : Bouncing droplets can self-propel laterally along the surface of a vibrated fluid bath by virtue of a resonant interaction with their own wave field. The resulting walking droplets exhibit features reminiscent of microscopic quantum particles. Here we present the results of an experimental investigation of droplets walking in a circular corral. We demonstrate that a coherent wavelike statistical behavior emerges from the complex underlying dynamics and that the probability distribution is prescribed by the Faraday wave mode of the corral. The statistical behavior of the walking droplets is demonstrated to be analogous to that of electrons in quantum corrals.

http://math.mit.edu/~bush/wordpress/wp-content/uploads/2013/07/Harris-Corrals-2013.pdf

Statistical behavior of a walking droplet in a confined geometry