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Role of edge effects and fluid depth in azimuthal Faraday waves

P. Wilson1, X. Shao2, J. R. Saylor1, and J. B. Bostwick1,*

  • 1Department of Mechanical Engineering, Clemson University, Clemson, South Carolina 29634, USA
  • 2Department of Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA

  • *jbostwi@clemson.edu
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Phys. Rev. Fluids 7, 014803 – Published 24 January, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.014803

Abstract

Faraday waves are created in experiment by mechanically vibrating a cylindrical container. Frequency scans are performed, and the acceleration threshold above which a surface wave appears is measured using a laser light approach, giving the instability tongue in frequency-acceleration space. The spatial structure of the surface wave, which conforms to the cylindrical container for wavelengths comparable to the container size, is determined using long-exposure-time white light imaging and is defined by the mode number pair (n,ℓ). Edge conditions at the container sidewall are controlled to create a (i) pinned or (ii) freely sliding contact-line. The driving frequency with the smallest threshold acceleration is identified as the natural frequency for that particular mode number pair. A theoretical model is developed using a viscous potential approximation to compute the natural oscillations of a viscoelastic material in a cylindrical container with a flat interface for both a pinned and a freely sliding contact-line. A closed-form expression is given for the freely sliding case, and a Rayleigh-Ritz procedure is used for the pinned case. The agreement is good between theoretical predictions and experimental observations for Triton/water mixtures, glycerol/water mixtures, and agarose gels, notwithstanding the large range in parameter space and the very different boundary conditions considered.

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Phys. Rev. Fluids 7, 014803– Published 24 January, 2022
  • Received 19 May 2021
  • Accepted 4 January 2022
Article part of CHORUS
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