Scattering theory of walking droplets in the presence of obstacles
Remy Dubertrand1; Maxime Hubert1; Peter Schlagheck1; Nicolas Vandewalle1; Thierry Bastin1; John Martin1
1 Departement of Physics, University of Liege
Resumo
Walking droplets that are sustained on the surface of a vibrating liquid, have attracted considerable attention during the past decade due to their remarkable analogy with quantum wave-particle duality. This was initiated by the pioneering experiment by Y. Couder and E. Fort [1], which reported the observation of a diffraction pattern in the angular resolved profile of droplets that propagated across a single slit obstacle geometry. While the occurrence of this wave-like phenomenon can be qualitatively traced back to the coupling of the droplet with its associated surface wave, a quantitative framework for the description of the surface-wave-propelled motion of the droplet in the presence of confining boundaries and obstacles still represents a major challenge. This problem is all the more stimulating as several experiments have already reported clear effects of the geometry on the dynamics of walking droplets [2,3]. Here we present a simple model inspired from quantum mechanics for the dynamics of a walking droplet in an arbitrary geometry [4]. We propose to describe its trajectory using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing conditions at infinity. For a single slit geometry our model is exactly solvable and reproduces some of the features observed experimentally. It stands for a promising candidate to account for the presence of boundaries in the walker's dynamics. References: [1] Y. Couder, and E. Fort, Phys. Rev. Lett. 97, 154101 (2006) [2] D. M. Harris, J. Moukhtar, E. Fort, Y. Couder, J. W. M. Bush, Phys. Rev. E 88, 011001(R) (2013) [3] B. Filoux, M. Hubert, N. Vandewalle, Phys. Rev. E, 92 041004(R) (2015) [4] R. Dubertrand, M. Hubert, P. Schlagheck, N. Vandewalle, T. Bastin, J. Martin, to be submitted
Palavras-chave: Fluidodynamics, Plasma and Turbulence; Nonlinear Dynamics in Thermal and Fluid; Nonlinear Dynamics and Complex systems