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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: costanzo@engr.psu.edu
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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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References

Andrews, D. G. & Mcintyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89 (4), 609–646.Google Scholar
Barnkob, R., Nama, N., Ren, L., Huang, T. J., Costanzo, F. & Kähler, C. J.2017 Acoustically-driven fluid and particle motion in confined and leaky systems (under review).Google Scholar
Bradley, C. E. 1996 Acoustic streaming field structure: the influence of the radiator. J. Acoust. Soc. Am. 100 (3), 1399–1408.Google Scholar
Bradley, C. E. 2012 Acoustic streaming field structure. Part II. Examples that include boundary-driven flow. J. Acoust. Soc. Am. 131 (1), 13–23.CrossRefGoogle ScholarPubMed
Brezzi, F. & Fortin, M. 1991 Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol. 15. Springer.Google Scholar
Bühler, O. 2009 Waves and Mean Flows. Cambridge University Press.CrossRefGoogle Scholar
Chini, G. P., Malecha, Z. & Dreeben, T. D. 2014 Large-amplitude acoustic streaming. J. Fluid Mech. 744, 329–351.CrossRefGoogle Scholar
COMSOL Multiphysics® 5.2, 2016 www.comsol.com.Google Scholar
Ding, X., Li, P., Lin, S. C. S., Stratton, Z. S., Nama, N., Guo, F., Slotcavage, D., Mao, X., Shi, J., Costanzo, F. et al. 2013 Surface acoustic wave microfluidics. Lab on a Chip 13 (18), 3626–3649.Google Scholar
Friend, J. & Yeo, L. 2011 Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev. Mod. Phys. 83 (2), 647–704.Google Scholar
Gurtin, M. E., Fried, E. & Anand, L. 2010 The Mechanics and Thermodynamics of Continua. Cambridge University Press.CrossRefGoogle Scholar
Heltai, L. & Costanzo, F. 2012 Variational implementation of immersed finite element methods. Comput. Meth. Appl. Mech. Engng 229–232, 110–127.Google Scholar
Hindmarsh, A., Brown, P., Grant, K., Lee, S., Serban, R., Shumaker, D. & Woodward, C. 2005 SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 31 (3), 363–396.CrossRefGoogle Scholar
Huang, P. H., Chan, C. Y., Li, P., Nama, N., Xie, Y., Wei, C. H., Chen, Y., Ahmed, D. & Huang, T. J. 2015a A spatiotemporally controllable chemical gradient generator via acoustically oscillating sharp-edge structures. Lab on a Chip 15 (21), 4166–4176.Google Scholar
Huang, P. H., Nama, N., Mao, Z., Li, P., Rufo, J., Chen, Y., Xie, Y., Wei, C. H., Wang, L. & Huang, T. J. 2014 A reliable and programmable acoustofluidic pump powered by oscillating sharp-edge structures. Lab on a Chip 14 (22), 4319–4323.CrossRefGoogle ScholarPubMed
Huang, P. H., Ren, L., Nama, N., Li, S., Li, P., Yao, X., Cuento, R. A., Wei, C. H., Chen, Y., Xie, Y. et al. 2015b An acoustofluidic sputum liquefier. Lab on a Chip 15 (15), 3125–3131.CrossRefGoogle ScholarPubMed
Huang, P.-H., Xie, Y., Ahmed, D., Rufo, J., Nama, N., Chen, Y., Chan, C. Y. & Huang, T. J. 2013 An acoustofluidic micromixer based on oscillating sidewall sharp-edges. Lab on a Chip 13 (19), 3847–3852.Google Scholar
Hughes, T. J. R. 2000 The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover.Google Scholar
Köster, D.2006 Numerical simulation of acoustic streaming on SAW-driven biochips. PhD thesis, Universität Augsburg, Germany.Google Scholar
Köster, D. 2007 Numerical simulation of acoustic streaming on surface acoustic wave-driven biochips. SIAM J. Sci. Comput. 29 (6), 2352–2380.CrossRefGoogle Scholar
Lee, A. 2013 The third decade of microfluidics. Lab on a Chip 13 (9), 1660–1661.Google Scholar
Muller, P. B., Barnkob, R., Jensen, M. J. H. & Bruus, H. 2012 A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces. Lab on a Chip 12 (22), 4617–4627.Google Scholar
Muller, P. B. & Bruus, H. 2015 Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels. Phys. Rev. E 92 (6), 063018.Google ScholarPubMed
Nama, N., Barnkob, R., Mao, Z., Kähler, C. J., Costanzo, F. & Huang, T. J. 2015 Numerical study of acoustophoretic motion of particles in a pdms microchannel driven by surface acoustic waves. Lab on a Chip 15 (12), 2700–2709.Google Scholar
Nama, N., Huang, P. H., Huang, T. J. & Costanzo, F. 2014 Investigation of acoustic streaming patterns around oscillating sharp edges. Lab on a Chip 14 (15), 2824–2836.Google Scholar
Nama, N., Huang, P. H., Huang, T. J. & Costanzo, F. 2016 Investigation of micromixing by acoustically oscillated sharp-edges. Biomicrofluidics 10 (2), 024124.CrossRefGoogle ScholarPubMed
Nyborg, W. L. 1998 Acoustic streaming. In Nonlinear Acoustics (ed. Hamilton, M. F. & Blackstock, D. T.), pp. 207–231. Academic.Google Scholar
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479–517.Google Scholar
Schiesser, W. E. 1991 The Numerical Method of Lines: Integration of Partial Differential Equations. Academic.Google Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77 (3), 977.Google Scholar
Vanneste, J. & Bühler, O. 2011 Streaming by leaky surface acoustic waves. Proc. R. Soc. Lond. A 467 (2130), 1779–1800.Google Scholar
Wang, X. & Liu, W. K. 2004 Extended immersed boundary method using FEM and RKPM. Comput. Meth. Appl. Mech. Engng 193 (12–14), 1305–1321.Google Scholar
Xie, J. H. & Vanneste, J. 2014a Boundary streaming with Navier boundary condition. Phys. Rev. E 89 (6), 063010.Google Scholar
Xie, J. H. & Vanneste, J. 2014b Dynamics of a spherical particle in an acoustic field: a multiscale approach. Phys. Fluids 26 (10), 102001.Google Scholar
Zhang, L. T. & Gay, M. 2007 Immersed finite element method for fluid-structure interactions. J. Fluids Struct. 23 (6), 839–857.Google Scholar