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Eckart streaming with nonlinear high-order harmonics: An example at gigahertz

Shiyu Li

Weiwei Cui

Thierry Baasch

Bin Wang and Zhixiong Gong*

  • State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China

  • State Key Laboratory of Ocean Engineering, School of Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China and Key Laboratory of Marine Intelligent Equipment and System, Ministry of Education, China

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Phys. Rev. Fluids 9, 084201 – Published 8 August, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.084201

Abstract

Acoustic streaming shows great potential in applications such as bubble dynamics, cell aggregation, and nanosized particle isolation in the biomedical and drug industries. As the acoustic shock distance decreases with the increase of incident frequency, the nonlinear propagation effect will play a role in acoustic streaming, e.g., Eckart (bulk) streaming at a few gigahertz. However, the theory of source terms of bulk streaming is still missing at this stage when high-order acoustic harmonics play a role. In this paper, we derive the source term including the contribution of high-order harmonics. The streaming-induced hydrodynamic flow is assumed to be incompressible and no shock wave occurs during the nonlinear acoustic propagation as restricted by the traditional Goldberg number Γ<1 or Γ≈1, which indicates the importance of nonlinearity relative to dissipation. The derived force terms allow evaluating bulk streaming with high-order harmonics at gigahertz and provide an exact expression compared to the existing empirical formulas. Numerical results show that the contribution of higher-order harmonics increases the streaming flow velocity by more than 20%. Our approach clearly demonstrates the errors inherent in the expression introduced by Nyborg which should be avoided in numerical computations as it includes part of the acoustic radiation force that does not lead to acoustic streaming.

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Phys. Rev. Fluids 9, 084201– Published 8 August, 2024
  • Received 1 March 2024
  • Accepted 19 July 2024
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