## Abstract

Based on first- and second-order perturbation theory, we present a
numerical study of the temporal buildup and decay of unsteady acoustic
fields and acoustic streaming flows actuated by vibrating walls in the
transverse cross-sectional plane of a long straight microchannel under
adiabatic conditions and assuming temperature-independent material
parameters. The unsteady streaming flow is obtained by averaging the
time-dependent velocity field over one oscillation period, and as time
increases, it is shown to converge towards the well-known steady
time-averaged solution calculated in the frequency domain. Scaling
analysis reveals that the acoustic resonance builds up much faster than
the acoustic streaming, implying that the radiation force may dominate
over the drag force from streaming even for small particles. However,
our numerical time-dependent analysis indicates that pulsed actuation
does not reduce streaming significantly due to its slow decay. Our
analysis also shows that for an acoustic resonance with a quality factor
Q, the amplitude of the oscillating second-order velocity component is Q times larger than the usual second-order steady time-averaged velocity component. Consequently, the well-known criterion v1≪cs for the validity of the perturbation expansion is replaced by the more restrictive criterion v1≪cs/Q. Our numerical model is available as supplemental material in the form of comsol model files and matlab scripts.

Original language | English |
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Article number | 063018 |

Journal | Physical Review E |

Volume | 92 |

Issue number | 6 |

Number of pages | 13 |

ISSN | 2470-0045 |

DOIs | |

Publication status | Published - 2015 |