Oza, Anand U.5; Wind-Willassen, Øistein4; Harris, Daniel M.5; Rosales, Rodolfo R.5; Bush, John W. M.5
1 Department of Applied Mathematics and Computer Science, Technical University of Denmark2 Mathematics, Department of Applied Mathematics and Computer Science, Technical University of Denmark3 Massachusetts Institute of Technology4 Dynamical Systems, Department of Applied Mathematics and Computer Science, Technical University of Denmark5 Massachusetts Institute of Technology
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 multi-modal statistics,” J. Fluid Mech. 739, 444–464 (2014)].