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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.
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This content will become publicly available on September 11, 2026
Microswimmer dynamics in a Hele-Shaw droplet
Bacterial motility is strongly influenced by confinement. Here, we derive an asymptotic solution for the flow about a microswimmer enclosed in a weakly deformable Hele-Shaw drop—a drop sandwiched between two solid planes. For a microswimmer modelled as a dipole, we explore the swimmer’s trajectory, the evolution of the droplet interface and the drop velocity. The results show that at steady state, the dipole induces droplet translation with a velocity independent of the dipole location and in the same direction as the dipole orientation. The trajectory of the swimming dipole is significantly affected by droplet deformability. This article is part of the theme issue ‘Biological fluid dynamics: emerging directions’.
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- Award ID(s):
- 2126498
- PAR ID:
- 10644288
- Publisher / Repository:
- Royal Society.
- Date Published:
- Journal Name:
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 383
- Issue:
- 2304
- ISSN:
- 1364-503X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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