Effects of micron scale surface profiles on acoustic streaming

  • Junjun LeiEmail author
  • Martyn Hill
  • Carlos Ponce de León Albarrán
  • Peter Glynne-JonesEmail author
Research Paper


Conventional models of boundary-driven streaming such as Rayleigh–Schlichting streaming typically assume smooth device walls. Using numerical models, we predict that micron scale surface profiles/features have the potential to dramatically modify the inner streaming vortices, creating much higher velocity, smaller scale vortices. Although inner streaming is hard to observe experimentally, this effect is likely to prove important in applications such as DNA-tethered microbeads where the flow field near a surface is important. We investigate here the effect of a sinusoidally structured surface in a one-dimensional standing wave field in a rectangular channel using perturbation theory. It was found that inner streaming vortex patterns of scale similar to the profile are formed instead of the much larger eight-vortices-per-wavelength classical inner streaming patterns seen in devices with smooth surfaces, while the outer vortex patterns are similar to that found in a device with smooth surfaces (i.e., Rayleigh streaming). The streaming velocity magnitudes can be orders of magnitude higher than those obtained in a device with smooth surfaces, while the outer streaming velocities are similar. The same inner streaming patterns are also found in the presence of propagating waves. The mechanisms behind the effect are seen to be related to the acoustic velocity gradients around surface features.


Acoustic streaming Boundary-driven streaming Structured surface Microscale vortex 



The authors gratefully acknowledge the financial support for this work received from the EPSRC Doctoral Prize Fellowship (EP/N509747/1), China Scholarship Council (CSC), the EPSRC Fellowship (EP/L025035/1), the National Natural Science Foundation of China (no. 11804060), the Youth Hundred-Talent Programme of Guangdong University of Technology (no. 220413195), the Special Support Plan of Guangdong Province (2014TQ01X542), and the Science and Technology Planning Program of Guangdong Province (2016A010102017). Models used to generate the simulation data supporting this study are openly available from the University of Southampton repository at


  1. Aktas MK, Farouk B (2004) Numerical simulation of acoustic streaming generated by finite-amplitude resonant oscillations in an enclosure. J Acoust Soc Am 116(5):2822–2831CrossRefGoogle Scholar
  2. Amin N, Riley N (1990) Streaming from a sphere due to a pulsating source. J Fluid Mech 210:459–473zbMATHCrossRefGoogle Scholar
  3. Antfolk M et al (2014) Focusing of sub-micrometer particles and bacteria enabled by two-dimensional acoustophoresis. Lab Chip 14(15):2791–2799CrossRefGoogle Scholar
  4. Barnkob R et al (2012) Acoustic radiation- and streaming-induced microparticle velocities determined by microparticle image velocimetry in an ultrasound symmetry plane. Phys Rev E 86(5):056307CrossRefGoogle Scholar
  5. Bläsi B et al (2011) Photon management structures originated by interference lithography. Energy Procedia 8:712–718CrossRefGoogle Scholar
  6. Bruus H (2012a) Acoustofluidics 2: perturbation theory and ultrasound resonance modes. Lab Chip 12(1):20–28CrossRefGoogle Scholar
  7. Bruus H (2012b) Acoustofluidics 10: scaling laws in acoustophoresis. Lab Chip 12(9):1578–1586CrossRefGoogle Scholar
  8. Bruus H et al (2011) Forthcoming lab on a chip tutorial series on acoustofluidics: acoustofluidics-exploiting ultrasonic standing wave forces and acoustic streaming in microfluidic systems for cell and particle manipulation. Lab Chip 11(21):3579–3580CrossRefGoogle Scholar
  9. Chen Y (2015) Nanofabrication by electron beam lithography and its applications: a review. Microelectron Eng 135:57–72CrossRefGoogle Scholar
  10. Chung SK, Cho SK (2008) On-chip manipulation of objects using mobile oscillating bubbles. J Micromech Microeng 18(12):125024CrossRefGoogle Scholar
  11. COMSOL Multiphysics 5.2 (2015).
  12. Costalonga M, Brunet P, Peerhossaini H (2015) Low frequency vibration induced streaming in a Hele-Shaw cell. Phys Fluids 27(1):013101CrossRefGoogle Scholar
  13. Devendran C, Gralinski I, Neild A (2014) Separation of particles using acoustic streaming and radiation forces in an open microfluidic channel. Microfluid Nanofluid 17(5):879–890CrossRefGoogle Scholar
  14. Eckart C (1947) Vortices and streams caused by sound waves. Phys Rev 73(1):68–76zbMATHCrossRefGoogle Scholar
  15. Hahn P, Dual J (2015) A numerically efficient damping model for acoustic resonances in microfluidic cavities. Phys Fluids 27(6):062005CrossRefGoogle Scholar
  16. Hamilton MF, Ilinskii YA, Zabolotskaya EA (2003) Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width. J Acoust Soc Am 113(1):153–160CrossRefGoogle Scholar
  17. Hammarstrom B, Laurell T, Nilsson J (2012) Seed particle-enabled acoustic trapping of bacteria and nanoparticles in continuous flow systems. Lab Chip 12(21):4296–4304CrossRefGoogle Scholar
  18. Hammarstrom B et al (2014) Acoustic trapping for bacteria identification in positive blood cultures with MALDI-TOF MS. Anal Chem 86(21):10560–10567CrossRefGoogle Scholar
  19. Hawwa MA (2015) Sound propagation in a duct with wall corrugations having square-wave profiles. Math Probl Eng 2015:516982MathSciNetzbMATHCrossRefGoogle Scholar
  20. Huang PH et al (2014) A reliable and programmable acoustofluidic pump powered by oscillating sharp-edge structures. Lab Chip 14(22):4319–4323CrossRefGoogle Scholar
  21. Lei J (2017) Formation of inverse Chladni patterns in liquids at microscale: roles of acoustic radiation and streaming-induced drag forces. Microfluid Nanofluidics 21(3):50CrossRefGoogle Scholar
  22. Lei J, Glynne-Jones P, Hill M (2013) Acoustic streaming in the transducer plane in ultrasonic particle manipulation devices. Lab Chip 13(11):2133–2143CrossRefGoogle Scholar
  23. Lei J, Hill M, Glynne-Jones P (2014) Numerical simulation of 3D boundary-driven acoustic streaming in microfluidic devices. Lab Chip 14(3):532–541CrossRefGoogle Scholar
  24. Lei JJ, Glynne-Jones P, Hill M (2016) Modal Rayleigh-like streaming in layered acoustofluidic devices. Phys Fluids 28(1):012004CrossRefGoogle Scholar
  25. Lei JJ, Hill M, Glynne-Jones P (2017a) Transducer-plane streaming patterns in thin-layer acoustofluidic devices. Phys Rev Appl 8(1):014018CrossRefGoogle Scholar
  26. Lei JJ, Glynne-Jones P, Hill M (2017b) Comparing methods for the modelling of boundary-driven streaming in acoustofluidic devices. Microfluid Nanofluidics 21(2):23CrossRefGoogle Scholar
  27. Leibacher I, Hahn P, Dual J (2015) Acoustophoretic cell and particle trapping on microfluidic sharp edges. Microfluid Nanofluidics 19(4):923–933CrossRefGoogle Scholar
  28. Li L et al (2011) Polystyrene sphere-assisted one-dimensional nanostructure arrays: synthesis and applications. J Mater Chem 21(1):40–56CrossRefGoogle Scholar
  29. Li N et al (2012) Mobile acoustic streaming based trapping and 3-dimensional transfer of a single nanowire. Appl Phys Lett 101(9):093113CrossRefGoogle Scholar
  30. Lighthill J (1978) Acoustic streaming. J Sound Vib 61(3):391–418zbMATHCrossRefGoogle Scholar
  31. Lutz BR, Chen J, Schwartz DT (2006) Hydrodynamic tweezers: 1. Noncontact trapping of single cells using steady streaming microeddies. Anal Chem 78(15):5429–5435CrossRefGoogle Scholar
  32. Mason WP (ed) (1965) Acoustic streaming. In: Physical acoustics. Academic, New York, pp 290–295Google Scholar
  33. Mishra P, Hill M, Glynne-Jones P (2014) Deformation of red blood cells using acoustic radiation forces. Biomicrofluidics 8(3):034109CrossRefGoogle Scholar
  34. Muller PB, Bruus H (2014) Numerical study of thermoviscous effects in ultrasound-induced acoustic streaming in microchannels. Phys Rev E 90(4):043016CrossRefGoogle Scholar
  35. Muller PB et al (2012) A numerical study of microparticle acoustophoresis driven by acoustic radiation forces and streaming-induced drag forces. Lab Chip 12:4617–4627CrossRefGoogle Scholar
  36. Muller PB et al (2013) Ultrasound-induced acoustophoretic motion of microparticles in three dimensions. Phys Rev E 88(2):023006MathSciNetCrossRefGoogle Scholar
  37. Nadal F, Lauga E (2014) Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies. Phys Fluids 26(8):082001CrossRefGoogle Scholar
  38. Nama N et al (2014) Investigation of acoustic streaming patterns around oscillating sharp edges. Lab Chip 14(15):2824–2836CrossRefGoogle Scholar
  39. Nyborg WL (1953) Acoustic streaming due to attenuated plane waves. J Acoust Soc Am 25(1):68–75MathSciNetCrossRefGoogle Scholar
  40. Nyborg WL (1958) Acoustic streaming near a boundary. J Acoust Soc Am 30(4):329–339MathSciNetCrossRefGoogle Scholar
  41. Nyborg WL (1998) Acoustic streaming. In: Hamilton MF, Blackstock DT (eds) Nonlinear acoustics. Academic, San DiegoGoogle Scholar
  42. Oberti S, Neild A, Ng TW (2009) Microfluidic mixing under low frequency vibration. Lab Chip 9(10):1435–1438CrossRefGoogle Scholar
  43. Ovchinnikov M, Zhou JB, Yalamanchili S (2014) Acoustic streaming of a sharp edge. J Acoust Soc Am 136(1):22–29CrossRefGoogle Scholar
  44. Rayleigh L (1883) On the circulation of air observed in Kundt’s tube, and on some allied acoustical problems. Philos Trans 175:1–21CrossRefGoogle Scholar
  45. Rednikov AY, Sadhal SS (2004) Steady streaming from an oblate spheroid due to vibrations along its axis. J Fluid Mech 499:345–380MathSciNetzbMATHCrossRefGoogle Scholar
  46. Rednikov AY, Sadhal SS (2011) Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples. J Fluid Mech 667:426–462MathSciNetzbMATHCrossRefGoogle Scholar
  47. Riley N (1975) Steady streaming induced by a vibrating cylinder. J Fluid Mech 68:801–812zbMATHCrossRefGoogle Scholar
  48. Riley N (1987) Streaming from a cylinder due to an acoustic source. J Fluid Mech 180:319–326zbMATHCrossRefGoogle Scholar
  49. Riley N (1992) Acoustic streaming about a cylinder in orthogonal beams. J Fluid Mech 242:387–394zbMATHCrossRefGoogle Scholar
  50. Riley N (1998) Acoustic streaming. Theor Comput Fluid Dyn 10(1–4):349–356zbMATHCrossRefGoogle Scholar
  51. Sadhal SS (2012) Acoustofluidics 13: analysis of acoustic streaming by perturbation methods Foreword. Lab Chip 12(13):2292–2300CrossRefGoogle Scholar
  52. Schlichting H (1932) Berechnung ebener periodischer Grenzschichtstromungen (Calculation of plane periodic boundary layer streaming). Physikalische Zeitschrift 33(8):327–335zbMATHGoogle Scholar
  53. Stuart JT (1965) Double boundary layer in oscillatory viscous flow. J Fluid Mech 24(4):673–687MathSciNetzbMATHCrossRefGoogle Scholar
  54. Tang Q, Hu JH (2015a) Diversity of acoustic streaming in a rectangular acoustofluidic field. Ultrasonics 58:27–34CrossRefGoogle Scholar
  55. Tang Q, Hu JH (2015b) Analyses of acoustic streaming field in the probe-liquid-substrate system for nanotrapping. Microfluid Nanofluidics 19(6):1395–1408CrossRefGoogle Scholar
  56. Tietze S, Schlemmer J, Lindner G (2013) Influence of surface acoustic waves induced acoustic streaming on the kinetics of electrochemical reactions. In: Micro/nano materials, devices, and systems, vol 8923. International Society for Optics and Photonics, p 89231BGoogle Scholar
  57. Tietze S et al (2015) Investigation of the surface condition of an electrode after electropolishing under the influence of surface acoustic waves. In: Proceedings of the 2015 ICU international congress on ultrasonics, vol 70, pp 1039–1042Google Scholar
  58. Valverde JM (2015) Pattern-formation under acoustic driving forces. Contemp Phys 56:1–21CrossRefGoogle Scholar
  59. Wiklund M, Green R, Ohlin M (2012) Acoustofluidics 14: applications of acoustic streaming in microfluidic devices. Lab Chip 12(14):2438–2451CrossRefGoogle Scholar
  60. Yazdi S, Ardekani AM (2012) Bacterial aggregation and biofilm formation in a vortical flow. Biomicrofluidics 6(4):044114CrossRefGoogle Scholar
  61. Zhao X-M, Xia Y, Whitesides GM (1997) Soft lithographic methods for nano-fabrication. J Mater Chem 7(7):1069–1074CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Electro-mechanical EngineeringGuangdong University of TechnologyGuangzhouChina
  2. 2.Faculty of Engineering and Physical SciencesUniversity of SouthamptonSouthamptonUK

Personalised recommendations