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Acoustic streaming: an arbitrary Lagrangian–Eulerian perspective

Published online by Cambridge University Press:  21 July 2017

Nitesh Nama ,
Tony Jun Huang  and
Francesco Costanzo Open the ORCID record for Francesco Costanzo [Opens in a new window]
Nitesh Nama
Affiliation:
Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA
Tony Jun Huang
Affiliation:
Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708, USA
Francesco Costanzo*
Affiliation:
Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA 16802, USA Center for Neural Engineering, The Pennsylvania State University, University Park, PA 16802, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Mathematical Foundations: Computational methods Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 600 - 630
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Copyright
© 2017 Cambridge University Press 

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