### Abstract

We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

Original language | English (US) |
---|---|

Pages (from-to) | 600-630 |

Number of pages | 31 |

Journal | Journal of Fluid Mechanics |

Volume | 825 |

DOIs | |

State | Published - Aug 25 2017 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering

### Cite this

*Journal of Fluid Mechanics*,

*825*, 600-630. https://doi.org/10.1017/jfm.2017.338

}

*Journal of Fluid Mechanics*, vol. 825, pp. 600-630. https://doi.org/10.1017/jfm.2017.338

**Acoustic streaming : An arbitrary Lagrangian-Eulerian perspective.** / Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco.

Research output: Contribution to journal › Review article

TY - JOUR

T1 - Acoustic streaming

T2 - An arbitrary Lagrangian-Eulerian perspective

AU - Nama, Nitesh

AU - Huang, Tony Jun

AU - Costanzo, Francesco

PY - 2017/8/25

Y1 - 2017/8/25

N2 - We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

AB - We analyse acoustic streaming flows using an arbitrary Lagrangian Eulerian (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the Lagrangian flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the Lagrangian velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.

UR - http://www.scopus.com/inward/record.url?scp=85025477595&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85025477595&partnerID=8YFLogxK

U2 - 10.1017/jfm.2017.338

DO - 10.1017/jfm.2017.338

M3 - Review article

C2 - 29051631

AN - SCOPUS:85025477595

VL - 825

SP - 600

EP - 630

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -