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Theoretical modeling of capillary surfer interactions on a vibrating fluid bath

Anand U. Oza1,*, Giuseppe Pucci2,3, Ian Ho4, and Daniel M. Harris4

  • 1Department of Mathematical Sciences & Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
  • 2Consiglio Nazionale delle Ricerche–Istituto di Nanotecnologia (CNR-NANOTEC), Via P. Bucci 33C, 87036 Rende, Italy
  • 3INFN, Sezione di Lecce, Via per Monteroni, Lecce 73100, Italy
  • 4School of Engineering, Brown University, 184 Hope Street, Providence, Rhode Island 02912, USA

  • *oza@njit.edu
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Phys. Rev. Fluids 8, 114001 – Published 7 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.114001

Abstract

We present and analyze a theoretical model for the dynamics and interactions of “capillary surfers,” which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [I. Ho et al., Phys. Rev. Fluids 8, L112001 (2023)], we reported the results of an experimental investigation of the surfer system, which showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers' positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good agreement with experimental data. Moreover, we conduct a linear stability analysis of bound state solutions and compute numerically the associated eigenvalues. We find that the spacings of the bound states are quantized on the capillary wavelength, with stable branches of equilibria separated by unstable ones. Generally, our work shows that self-propelling objects coupled by capillary waves constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.

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Physics Subject Headings (PhySH)

Corrections

26 February, 2024

Correction: Videos presented in this paper were processed improperly and now appear in the Supplemental Material.

synopsis

Synchronized Surfing of Self-Propelled Particles

Published 7 November, 2023

Millimeter-sized “surfers” can self-propel across a vibrating liquid surface, interacting with other surfers to create collective patterns.

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Capillary surfers: Wave-driven particles at a vibrating fluid interface

Ian Ho, Giuseppe Pucci, Anand U. Oza, and Daniel M. Harris
Phys. Rev. Fluids 8, L112001 (2023)

Article Text

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Outline

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Phys. Rev. Fluids 8, 114001– Published 7 November, 2023
  • Received 13 January 2023
  • Accepted 26 September 2023
  • Corrected 26 February 2024
Article part of CHORUS
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