Skip to main content

Acoustic streaming: an arbitrary Lagrangian–Eulerian perspective

  • Nitesh Nama (a1), Tony Jun Huang (a2) and Francesco Costanzo (a1) (a3)

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.

Corresponding author
Email address for correspondence:
Hide All
Andrews, D. G. & Mcintyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech. 89 (4), 609646.
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).
Bradley, C. E. 1996 Acoustic streaming field structure: the influence of the radiator. J. Acoust. Soc. Am. 100 (3), 13991408.
Bradley, C. E. 2012 Acoustic streaming field structure. Part II. Examples that include boundary-driven flow. J. Acoust. Soc. Am. 131 (1), 1323.
Brezzi, F. & Fortin, M. 1991 Mixed and Hybrid Finite Element Methods, Springer Series in Computational Mathematics, vol. 15. Springer.
Bühler, O. 2009 Waves and Mean Flows. Cambridge University Press.
Chini, G. P., Malecha, Z. & Dreeben, T. D. 2014 Large-amplitude acoustic streaming. J. Fluid Mech. 744, 329351.
COMSOL Multiphysics® 5.2, 2016
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), 36263649.
Friend, J. & Yeo, L. 2011 Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev. Mod. Phys. 83 (2), 647704.
Gurtin, M. E., Fried, E. & Anand, L. 2010 The Mechanics and Thermodynamics of Continua. Cambridge University Press.
Heltai, L. & Costanzo, F. 2012 Variational implementation of immersed finite element methods. Comput. Meth. Appl. Mech. Engng 229–232, 110127.
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), 363396.
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), 41664176.
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), 43194323.
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), 31253131.
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), 38473852.
Hughes, T. J. R. 2000 The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover.
Köster, D.2006 Numerical simulation of acoustic streaming on SAW-driven biochips. PhD thesis, Universität Augsburg, Germany.
Köster, D. 2007 Numerical simulation of acoustic streaming on surface acoustic wave-driven biochips. SIAM J. Sci. Comput. 29 (6), 23522380.
Lee, A. 2013 The third decade of microfluidics. Lab on a Chip 13 (9), 16601661.
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), 46174627.
Muller, P. B. & Bruus, H. 2015 Theoretical study of time-dependent, ultrasound-induced acoustic streaming in microchannels. Phys. Rev. E 92 (6), 063018.
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), 27002709.
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), 28242836.
Nama, N., Huang, P. H., Huang, T. J. & Costanzo, F. 2016 Investigation of micromixing by acoustically oscillated sharp-edges. Biomicrofluidics 10 (2), 024124.
Nyborg, W. L. 1998 Acoustic streaming. In Nonlinear Acoustics (ed. Hamilton, M. F. & Blackstock, D. T.), pp. 207231. Academic.
Peskin, C. S. 2002 The immersed boundary method. Acta Numerica 11, 479517.
Schiesser, W. E. 1991 The Numerical Method of Lines: Integration of Partial Differential Equations. Academic.
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77 (3), 977.
Vanneste, J. & Bühler, O. 2011 Streaming by leaky surface acoustic waves. Proc. R. Soc. Lond. A 467 (2130), 17791800.
Wang, X. & Liu, W. K. 2004 Extended immersed boundary method using FEM and RKPM. Comput. Meth. Appl. Mech. Engng 193 (12–14), 13051321.
Xie, J. H. & Vanneste, J. 2014a Boundary streaming with Navier boundary condition. Phys. Rev. E 89 (6), 063010.
Xie, J. H. & Vanneste, J. 2014b Dynamics of a spherical particle in an acoustic field: a multiscale approach. Phys. Fluids 26 (10), 102001.
Zhang, L. T. & Gay, M. 2007 Immersed finite element method for fluid-structure interactions. J. Fluids Struct. 23 (6), 839857.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 9
Total number of PDF views: 235 *
Loading metrics...

Abstract views

Total abstract views: 426 *
Loading metrics...

* Views captured on Cambridge Core between 21st July 2017 - 19th September 2018. This data will be updated every 24 hours.