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PreprintCC BY-NC-ND 4.0arXiv

Phase-controlled lateral forcing of droplets on a vibrating bath

  • Lawrence A. Wilen
  • Zahra Shamsi
  • Johnathan Hoggarth
  • Bauyrzhan K. Primkulov
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Abstract

We introduce a method for controlling the lateral motion of droplets bouncing on a vibrated liquid bath by superimposing a small periodic rocking motion onto the conventional vertical forcing. We show experimentally that the lateral velocity varies linearly with the rocking amplitude α and sinusoidally with its phase ϕ relative to the vertical forcing, while the response depends strongly on the droplet's vertical bouncing mode. A time-averaged model of a harmonic bouncer yields a time-averaged lateral force F̅x=mgαsin(Φb+ϕ), where Φb is the droplet impact phase. Periodic rocking thus provides a simple, programmable means of exerting lateral forces on bouncing droplets, enabling controlled manipulation of passive and active droplets in pilot-wave hydrodynamics.

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Cite

BibTeXRIS
BibTeX
@misc{wilen2026phasecontrolled,
  title = {{Phase-controlled lateral forcing of droplets on a vibrating bath}},
  author = {Lawrence A. Wilen and Zahra Shamsi and Johnathan Hoggarth and Bauyrzhan K. Primkulov},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10450},
  eprint = {2610.10450},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10450},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Phase-controlled lateral forcing of droplets on a vibrating bath
AU  - Lawrence A. Wilen
AU  - Zahra Shamsi
AU  - Johnathan Hoggarth
AU  - Bauyrzhan K. Primkulov
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10450
UR  - https://arxiv.org/abs/2610.10450
AB  - We introduce a method for controlling the lateral motion of droplets bouncing on a vibrated liquid bath by superimposing a small periodic rocking motion onto the conventional vertical forcing. We show experimentally that the lateral velocity varies linearly with the rocking amplitude α and sinusoidally with its phase ϕ relative to the vertical forcing, while the response depends strongly on the droplet's vertical bouncing mode. A time-averaged model of a harmonic bouncer yields a time-averaged lateral force F̅_x=mgαsin(Φ_b+ϕ), where Φ_b is the droplet impact phase. Periodic rocking thus provides a simple, programmable means of exerting lateral forces on bouncing droplets, enabling controlled manipulation of passive and active droplets in pilot-wave hydrodynamics.
ER  -