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Title: Bouncing phase variations in pilot-wave hydrodynamics and the stability of droplet pairs
We present the results of an integrated experimental and theoretical investigation of the vertical motion of millimetric droplets bouncing on a vibrating fluid bath. We characterize experimentally the dependence of the phase of impact and contact force between a drop and the bath on the drop’s size and the bath’s vibrational acceleration. This characterization guides the development of a new theoretical model for the coupling between a drop’s vertical and horizontal motion. Our model allows us to relax the assumption of constant impact phase made in models based on the time-averaged trajectory equation of Moláček and Bush ( J. Fluid Mech. , vol. 727, 2013b, pp. 612–647) and obtain a robust horizontal trajectory equation for a bouncing drop that accounts for modulations in the drop’s vertical dynamics as may arise when it interacts with boundaries or other drops. We demonstrate that such modulations have a critical influence on the stability and dynamics of interacting droplet pairs. As the bath’s vibrational acceleration is increased progressively, initially stationary pairs destabilize into a variety of dynamical states including rectilinear oscillations, circular orbits and side-by-side promenading motion. The theoretical predictions of our variable-impact-phase model rationalize our observations and underscore the critical importance of accounting for variability in the vertical motion when modelling droplet–droplet interactions.  more » « less
Award ID(s):
1727565
PAR ID:
10116855
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Journal of Fluid Mechanics
Volume:
871
ISSN:
0022-1120
Page Range / eLocation ID:
212 to 243
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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