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...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics 2019-07, Vol.871, p.212-243
Main Authors: Couchman, Miles M. P., Turton, Sam E., Bush, John W. M.
Format: Article
Language:English
Subjects:
Acceleration
Bouncing
Circular orbits
Computational fluid dynamics
Contact force
Dependence
Droplets
Dynamic stability
Dynamics
Fluid flow
Fluid mechanics
Horizontal motion
Hydrodynamics
Interactions
JFM Papers
Oscillations
Phase variations
Trajectories
Vertical motion
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.293