Oscillating instability in bouncing droplet crystals

¹ Matières et Systèmes Complexes, Université Paris 7 Denis Diderot, CNRS - UMR 7057 - Bâtiment Condorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris cedex 13, France, EU
² Laboratoire de Reproduction et Développement des Plantes, INRA, CNRS, ENS, Université de Lyon, UMR 5667, 46 allée d'Italie, 69364 Lyon Cedex 07, France, EU

^a antonin.eddi@univ-paris-diderot.fr

Received: 13 January 2011
Accepted: 15 March 2011

Abstract

Bouncing droplets on a vibrated liquid bath can interact via the surface waves they emit and form various types of stable crystalline clusters. When increasing the forcing acceleration over an onset value, the aggregates present a global and spontaneous vibration mode. Here, we investigated experimentally these vibrations in hexagonal and square lattice clusters and show that there is a long-range selection amongst the modes. We propose a physical interpretation of the instability based on the intrinsic delay due to wave propagation and a simple model that explains the observed features of the vibrations.