Bulk-driven acoustic streaming at resonance in closed microcavities

Jacob Søberg Bach, Henrik Bruus*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.
Original languageEnglish
Article number023104
JournalPhysical Review E
Volume100
Issue number2
Number of pages20
ISSN2470-0045
DOIs
Publication statusPublished - 2019

Cite this

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title = "Bulk-driven acoustic streaming at resonance in closed microcavities",
abstract = "Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.",
author = "Bach, {Jacob S{\o}berg} and Henrik Bruus",
year = "2019",
doi = "10.1103/PhysRevE.100.023104",
language = "English",
volume = "100",
journal = "Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)",
issn = "2470-0045",
publisher = "American Physical Society",
number = "2",

}

Bulk-driven acoustic streaming at resonance in closed microcavities. / Bach, Jacob Søberg; Bruus, Henrik.

In: Physical Review E, Vol. 100, No. 2, 023104, 2019.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Bulk-driven acoustic streaming at resonance in closed microcavities

AU - Bach, Jacob Søberg

AU - Bruus, Henrik

PY - 2019

Y1 - 2019

N2 - Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.

AB - Bulk-driven acoustic (Eckart) streaming is the steady flow resulting from the time-averaged acoustic energy flux density in the bulk of a viscous fluid. In simple cases, like the one-dimensional single standing-wave resonance, this energy flux is negligible, and therefore the bulk-driven streaming is often ignored relative to the boundary-driven (Rayleigh) streaming in the analysis of resonating acoustofluidic devices with length scales comparable to the acoustic wavelength. However, in closed acoustic microcavities with viscous dissipation, two overlapping resonances may be excited at the same frequency as a double mode. In contrast to single modes, the double modes can support a steady rotating acoustic energy flux density and thus a corresponding rotating bulk-driven acoustic streaming. We derive analytical solutions for the double modes in a rectangular-box-shaped cavity including the viscous boundary layers, and use them to map out possible rotating patterns of bulk-driven acoustic streaming. Remarkably, the rotating bulk-driven streaming may be excited by a nonrotating actuation, and we determine the optimal geometry that maximizes this excitation. In the optimal geometry, we finally simulate a horizontal 2×2, 4×4, and 6×6 streaming-roll pattern in a shallow square cavity. We find that the high-frequency 6×6 streaming-roll pattern is dominated by the bulk-driven streaming as opposed to the low-frequency 2×2 streaming pattern, which is dominated by the boundary-driven streaming.

U2 - 10.1103/PhysRevE.100.023104

DO - 10.1103/PhysRevE.100.023104

M3 - Journal article

VL - 100

JO - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

JF - Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)

SN - 2470-0045

IS - 2

M1 - 023104

ER -