Skip to main content Accessibility help
×
Home
Hostname: page-component-56f9d74cfd-h4v4t Total loading time: 0.204 Render date: 2022-06-27T08:09:28.151Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

The appearance of boundary layers and drift flows due to high-frequency surface waves

Published online by Cambridge University Press:  20 July 2012

Ofer Manor
Affiliation:
MicroNanophysics Research Laboratory, School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia The Melbourne Centre for Nanofabrication, Clayton, VIC 3800, Australia
Leslie Y. Yeo
Affiliation:
MicroNanophysics Research Laboratory, School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia
James R. Friend*
Affiliation:
MicroNanophysics Research Laboratory, School of Electrical and Computer Engineering, RMIT University, Melbourne, VIC 3001, Australia The Melbourne Centre for Nanofabrication, Clayton, VIC 3800, Australia
*
Email address for correspondence: james.friend@rmit.edu.au

Abstract

The classical Schlichting boundary layer theory is extended to account for the excitation of generalized surface waves in the frequency and velocity amplitude range commonly used in microfluidic applications, including Rayleigh and Sezawa surface waves and Lamb, flexural and surface-skimming bulk waves. These waves possess longitudinal and transverse displacements of similar magnitude along the boundary, often spatiotemporally out of phase, giving rise to a periodic flow shown to consist of a superposition of classical Schlichting streaming and uniaxial flow that have no net influence on the flow over a long period of time. Correcting the velocity field for weak but significant inertial effects results in a non-vanishing steady component, a drift flow, itself sensitive to both the amplitude and phase (prograde or retrograde) of the surface acoustic wave propagating along the boundary. We validate the proposed theory with experimental observations of colloidal pattern assembly in microchannels filled with dilute particle suspensions to show the complexity of the boundary layer, and suggest an asymptotic slip boundary condition for bulk flow in microfluidic applications that are actuated by surface waves.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Alvarez, M., Friend, J. R. & Yeo, L. Y. 2008 Surface vibration induced spatial ordering of periodic polymer patterns on a substrate. Langmuir 24, 1062910632.CrossRefGoogle ScholarPubMed
2. Arzt, R. M., Salzmann, E. & Dransfeld, K. 1967 Elastic surface waves in quartz at 316 MHz. Appl. Phys. Lett. 10, 165167.CrossRefGoogle Scholar
3. Brunet, P., Baudoin, M., Matar, O. & Zoueshtiagh, F. 2010 Droplet displacements and oscillations induced by ultrasonic surface acoustic waves: a quantitative study. Phys. Rev. E 81, 036315.CrossRefGoogle ScholarPubMed
4. Cheeke, J. D. N. & Morisseau, P. 1982 Attenuation of Rayleigh waves on a LiNbO3 crystal in contact with a liquid He bath. J. Low Temp. Phys. 46, 319330.CrossRefGoogle Scholar
5. Chladni, E. 1787 Entdeckungen über die Theorie des Klanges. Weidmanns, Erben und Reich.Google Scholar
6. Craster, R. V. 1996 A canonical problem for fluid–solid interfacial wave coupling. Proc. R. Soc. Lond. A 452, 16951711.CrossRefGoogle Scholar
7. Dorrestijn, M., Bietsch, A., Açkaln, T., Raman, A., Hegner, M., Meyer, E. & Gerber, C. H. 2007 Chladni figures revisited based on nanomechanics. Phys. Rev. Lett. 98, 026102.CrossRefGoogle Scholar
8. Eckart, C. 1948 Vortices and streams caused by sound waves. Phys. Rev. 73, 6876.CrossRefGoogle Scholar
9. Faraday, M. 1831 On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Phil. Trans. R. Soc. Lond. 121, 299340.CrossRefGoogle Scholar
10. Friend, J. R. & Yeo, L. Y. 2009 Fabrication of microfluidics devices using polydimethylsiloxane (PDMS). Biomicrofluidics 4, 026502.CrossRefGoogle Scholar
11. Friend, J. R. & Yeo, L. Y. 2011 Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev. Mod. Phys. 83, 647704.CrossRefGoogle Scholar
12. Girardo, S., Cecchini, M., Beltram, F., Cingolani, R. & Pisignano, D. 2008 Polydimethylsiloxane–LiNbO3 surface acoustic wave micropump devices for fluid control in microchannels. Lab on a Chip 8, 15571563.CrossRefGoogle ScholarPubMed
13. Hamilton, M. 2003 Acoustic streaming generated by standing waves in two-dimensional channels of arbitrary width. J. Acoust. Soc. Am. 113, 153160.CrossRefGoogle ScholarPubMed
14. Hodgson, R. P., Tan, M., Yeo, L. Y. & Friend, J. R. 2009 Transmitting high power rf acoustic radiation via fluid couplants into superstrates for microfluidics. Appl. Phys. Lett. 94, 024102.CrossRefGoogle Scholar
15. Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavl, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am. 26, 2639.CrossRefGoogle Scholar
16. Hutchisson, E. & Morgan, F. B. 1931 An experimental study of Kundt’s tube dust figures. Phys. Rev. 37, 11551163.CrossRefGoogle Scholar
17. Li, H., Friend, J. R. & Yeo, L. Y. 2008 Microfluidic colloidal island formation and erasure induced by surface acoustic wave radiation. Phys. Rev. Lett. 101, 084502.CrossRefGoogle Scholar
18. Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61, 391418.CrossRefGoogle Scholar
19. Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. 245, 535581.CrossRefGoogle Scholar
20. Luong, T.-D., Phan, V.-N. & Nguyen, N.-T. 2011 High-throughput micromixers based on acoustic streaming induced by surface acoustic wave. Microfluid Nanofluid 10, 619625.CrossRefGoogle Scholar
21. Nam, J., Lim, H., Kim, D. & Shin, S. 2011 Separation of platelets from whole blood using standing surface acoustic waves in a microchannel. Lab on a Chip 11, 3361.CrossRefGoogle Scholar
22. Nyborg, W. L. 1952 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25, 18.Google Scholar
23. Qi, A., Yeo, L. Y. & Friend, J. R. 2008 Interfacial destabilization and atomization driven by surface acoustic waves. Phys. Fluids 20, 074103.CrossRefGoogle Scholar
24. Ramos, E., Cuevas, S. & Huelsz, G. 2001 Interaction of Stokes boundary layer flow with sound wave. Phys. Fluids 13, 37093713.CrossRefGoogle Scholar
25. Rayleigh, Lord 1884 On the circulation of air observed in Kundt’s tubes and on some allied acoustical problems. Phil. Trans. R. Soc. Lond. 175, 121.CrossRefGoogle Scholar
26. Riley, N. 1965 Oscillating viscous flows. Mathematika 12, 161175.CrossRefGoogle Scholar
27. Riley, N. 1986 Streaming from a cylinder due to an acoustic source. J. Fluid Mech. 180, 319326.CrossRefGoogle Scholar
28. Riley, N. 1998 Acoustic streaming. Theor. Comput. Fluid Dyn. 10, 349356.CrossRefGoogle Scholar
29. Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 4365.CrossRefGoogle Scholar
30. Rogers, P. P., Friend, J. R. & Yeo, L. Y. 2010 Exploitation of surface acoustic waves to drive size-dependent microparticle concentration within a droplet. Lab on a Chip 10, 29792985.CrossRefGoogle Scholar
31. Rosenhead, L.  (Ed.) 1963 Laminar Boundary Layers. Oxford Engineering: Clarendon.Google Scholar
32. Rudenko, O. V. & Soluyan, S. I. 1977 Theoretical Foundations of Nonlinear Acoustics. Plenum.CrossRefGoogle Scholar
33. Schlichting, H. 1932 Calculation of even periodic barrier currents. Physik. Z. 33, 327335.Google Scholar
34. Secomb, T. W. 1978 Flow in a channel with pulsating walls. J. Fluid Mech. 88, 273288.CrossRefGoogle Scholar
35. Shi, J., Huang, H., Stratton, Z., Huang, Y. & Huang, T. J. 2009 Continuous particle separation in a microfluidic channel via standing surface acoustic waves (SSAW). Lab on a Chip 9, 33543359.CrossRefGoogle Scholar
36. Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673687.CrossRefGoogle Scholar
37. Tan, M. K., Friend, J. R. & Yeo, L. Y. 2007a Direct visualization of surface acoustic waves along substrates using smoke particles. Appl. Phys. Lett. 91, 224101.CrossRefGoogle Scholar
38. Tan, M. K., Friend, J. R. & Yeo, L. Y. 2007b Microparticle collection and concentration via a miniature surface acoustic wave device. Lab on a Chip 7, 618625.CrossRefGoogle Scholar
39. Tan, M. K., Yeo, L. Y. & Friend, J. R. 2009 Rapid fluid flow and mixing induced in microchannels using surface acoustic waves. Eur. Phys. Lett. 87, 16.CrossRefGoogle Scholar
40. Wang, C. Y. 2005 On high-frequency oscillatory viscous flows. J. Fluid Mech. 32, 5568.CrossRefGoogle Scholar
41. Westervelt, P. J. 2004 The theory of steady rotational flow generated by a sound field. J. Acoust. Soc. Am. 25, 6067.CrossRefGoogle Scholar
42. Wixforth, A., Strobl, C., Gauer, C., Toegl, A., Scriba, J. & von Guttenberg, Z. 2004 Acoustic manipulation of small droplets. Anal. Bioanal. Chem. 379, 982991.CrossRefGoogle ScholarPubMed
43. Yeo, L. Y. & Friend, J. R. 2009 Ultrafast microfluidics using surface acoustic waves. Biomicrofluidics 3, 012002.CrossRefGoogle ScholarPubMed
44. Zeng, Q., Chan, H. W. L., Zhao, X. Z. & Chen, Y. 2010 Enhanced particle focusing in microfluidic channels with standing surface acoustic waves. Microelectron. Engng 87, 12041206.CrossRefGoogle Scholar
30
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The appearance of boundary layers and drift flows due to high-frequency surface waves
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

The appearance of boundary layers and drift flows due to high-frequency surface waves
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

The appearance of boundary layers and drift flows due to high-frequency surface waves
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *