Journal
PHYSICS OF FLUIDS
Volume 26, Issue 8, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4891568
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Funding
- NSF [CBET-0966452, CMMI-1333242]
- Hertz Foundation
- Danish National Advanced Technology Foundation
- [DMS-1007967]
- [DMS-1115278]
- [DMS-1318942]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1115278, 1318942] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Chem, Bioeng, Env, & Transp Sys [0966452] Funding Source: National Science Foundation
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1333242] Funding Source: National Science Foundation
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We present the results of a numerical investigation of droplets walking on a rotating vibrating fluid bath. The drop's trajectory is described by an integro-differential equation, which is simulated numerically in various parameter regimes. As the forcing acceleration is progressively increased, stable circular orbits give way to wobbling orbits, which are succeeded in turn by instabilities of the orbital center characterized by steady drifting then discrete leaping. In the limit of large vibrational forcing, the walker's trajectory becomes chaotic, but its statistical behavior reflects the influence of the unstable orbital solutions. The study results in a complete regime diagram that summarizes the dependence of the walker's behavior on the system parameters. Our predictions compare favorably to the experimental observations of Harris and Bush [Droplets walking in a rotating frame: from quantized orbits to multimodal statistics, J. Fluid Mech. 739, 444-464 (2014)]. (c) 2014 AIP Publishing LLC.
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