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Resonance of droplets in constricted capillary tubes: Critical factors and nonlinearity

Chao Zeng1, Wen Deng1,*, and M. Bayani Cardenas2

  • 1Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, Missouri 65409, USA
  • 2Department of Geological Sciences, The University of Texas at Austin, Austin, Texas 78712, USA

  • *wendeng@mst.edu
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Phys. Rev. Fluids 5, 083604 – Published 12 August, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.083604

Abstract

Resonance of droplets in constricted capillary tubes responding to external vibratory excitation can be theoretically characterized by the abstract coefficients such as resonant frequency and rate of damping. A physically sound model, however, is needed to relate these abstract coefficients to the fluid properties of two-phase fluid, geometric properties of tube, and features of excited waves. A hydrodynamic model, based on the moving-boundary control volume concept and the transient oscillatory velocity profile, was developed to characterize the resonance of droplets. This model was validated against computational fluid dynamics simulation results expressed in both time and frequency domains. Dominant factors including Ohnesorge number, viscosity ratio, density ratio, and aspect ratio which control resonance were systematically investigated for their influences on the resonance of droplets. The nonlinearity in light of the initial position of front droplet meniscus and the amplitude of oscillation was distinguished and validated by the theoretical model.

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Phys. Rev. Fluids 5, 083604– Published 12 August, 2020
  • Received 25 March 2020
  • Accepted 22 July 2020
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