Phase control of bouncing droplets and rearrangement of bound states
Phys. Rev. Fluids 11, 014003 – Published 23 January, 2026
DOI: https://doi.org/10.1103/8z1k-c144
Abstract
The hydrodynamic pilot-wave system [Couder et al. Nature (London) 437, 208 (2005)] consists of millimetric drops bouncing on the surface of a vibrating liquid bath. When the droplet's bouncing period is twice that of the vibrational forcing, it achieves resonance with its subharmonic Faraday wave field. The bouncing state may then destabilize into a walking state, in which the droplet self-propels, piloted by its own wave field. Since these Faraday waves are subharmonic with respect to the vibrational driving, there are necessarily two resonant bouncing or walking states, distinguished according to the droplet's impact phase relative to the bath vibration. The interaction between two or more bouncing droplets depends strongly on their relative phase. We here consider a bath driven concurrently by a primary oscillation and a secondary oscillation with half the frequency, and demonstrate that the imposition of the latter allows for controlled switching between the two resonant bouncing states. We demonstrate that when such a switch is applied to a stable lattice of bouncing droplets, the resulting phase changes of the droplets prompt the reconfiguration of the lattice. We further demonstrate that when the pilot wave of a walking droplet is sufficiently large, it may play the role of the secondary bath forcing applied here, prompting switching between the two resonant bouncing states. Our integrated experimental and theoretical study thus informs the behavior of walking droplets in a number of established hydrodynamic quantum analogs.
