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Growth of liquid-gas interfacial perturbations driven by acoustic waves

Brandon Patterson* and Eric Johnsen†

  • Department of Mechanical Engineering, University of Michigan, 1231 Beal Avenue, Ann Arbor, Michigan 48109, USA

  • *awesome@umich.edu
  • †ejohnsen@umich.edu
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Phys. Rev. Fluids 3, 074002 – Published 13 July, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.074002

Abstract

Diagnostic ultrasound has been shown to cause lung hemorrhage in a variety of mammals, though the underlying damage mechanisms are still unclear. Motivated by this problem, we use numerical simulations to investigate the interaction of an ultrasound wave with the alveolar tissue-air interface. A planar, single-cycle, trapezoidal waveform propagates in tissue (modeled as water) and impinges upon an alveolus of the lung (modeled as air); to represent the alveolar surface roughness, the interface consists of a small-amplitude single-mode perturbation. Because of the sharp density gradient at the interface, we hypothesize that ultrasound waves, despite their relatively low amplitude, deposit sufficient baroclinic vorticity to drive perturbation growth. Our simulations show that the perturbation amplitude grows to sizes many times larger than the original value, well after the wave has passed. We demonstrate that conventional (linear) acoustics cannot account for such deformations; instead, the perturbation growth is driven by nonlinear effects: the baroclinic vorticity deposited along the interface, due to the misalignment of the pressure gradient (across the wave) and the density gradient (across the perturbed gas-liquid interface). Based on dimensional analysis and scaling, we observe that the perturbation amplitude and length of the interface scale with the circulation density and grow according to power laws in time. If the time interval between the pressure increase and decrease is sufficient, both deposit vorticity of the same sign, thus enhancing the perturbation growth; conversely, if the interval is too short, the vorticity deposited by the pressure increase is canceled by the decrease. A further consequence is that one may be able to control the growth of such perturbed interfaces by modulating the incoming waveform.

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Phys. Rev. Fluids 3, 074002– Published 13 July, 2018
  • Received 21 November 2017
Article part of CHORUS
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