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On the influence of viscosity and caustics on acoustic streaming in sessile droplets: an experimental and a numerical study with a cost-effective method

Published online by Cambridge University Press:  25 May 2017

A. Riaud Open the ORCID record for A. Riaud [Opens in a new window] ,
M. Baudoin ,
O. Bou Matar ,
J.-L. Thomas  and
P. Brunet
A. Riaud
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520, International Laboratory LEMAC/LICS - IEMN, F-59000 Lille, France Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7588, Institut des NanoSciences de Paris, 4 place Jussieu, 75005 Paris, France
M. Baudoin*
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520, International Laboratory LEMAC/LICS - IEMN, F-59000 Lille, France
O. Bou Matar
Affiliation:
Univ. Lille, CNRS, Centrale Lille, ISEN, Univ. Valenciennes, UMR 8520, International Laboratory LEMAC/LICS - IEMN, F-59000 Lille, France
J.-L. Thomas
Affiliation:
Sorbonne Universités, UPMC Univ Paris 06, CNRS UMR 7588, Institut des NanoSciences de Paris, 4 place Jussieu, 75005 Paris, France
P. Brunet
Affiliation:
Laboratoire Matière et Systèmes Complexes, UMR CNRS 7057, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris CEDEX 13, France
*
†Email address for correspondence: michael.baudoin@univ-lille1.fr
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Abstract

When an acoustic wave travels in a lossy medium such as a liquid, it progressively transfers its pseudo-momentum to the fluid, which results in a steady flow called acoustic streaming. This phenomenon involves a balance between sound attenuation and shear, such that the streaming flow does not vanish in the limit of vanishing viscosity. Hence, the effect of viscosity has long been ignored in acoustic streaming experiments. Here, we investigate the acoustic streaming in sessile droplets exposed to surface acoustic waves. According to experimental data, the flow structure and velocity magnitude are both strongly influenced by the fluid viscosity. We compute the sound wave propagation and hydrodynamic flow motion using a numerical method that reduces memory requirements via a spatial filtering of the acoustic streaming momentum source terms. These calculations agree qualitatively well with experiments and reveal how the acoustic field in the droplet, which is dominated by a few caustics, controls the flow pattern. We evidence that chaotic acoustic fields in droplets are dominated by a few caustics. It appears that the caustics drive the flow, which allows for qualitative prediction of the flow structure. Finally, we apply our numerical method to a broader span of fluids and frequencies. We show that the canonical case of the acoustic streaming in a hemispherical sessile droplet resting on a lithium niobate substrate only depends on two dimensionless numbers related to the surface and bulk wave attenuation. Even in such a baseline configuration, we observe and characterize four distinct flow regimes.

JFM classification

Acoustics: Acoustics Mathematical Foundations: Mathematical Foundations Micro-/Nano-fluid dynamics: Microfluidics

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Papers
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Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 384 - 420
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© 2017 Cambridge University Press 

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References

Alghane, M., Chen, B. X., Fu, Y. Q., Li, Y., Desmulliez, M. P. Y., Mohammed, M. I. & Walton, A. J. 2012 Nonlinear hydrodynamic effects induced by Rayleigh surface acoustic wave in sessile droplets. Phys. Rev. E 86, 056304.Google Scholar
Alghane, M., Chen, B. X., Fu, Y. Q., Li, Y., Luo, J. K. & Walton, A. J. 2011 Experimental and numerical investigation of acoustic streaming excited by using a surface acoustic wave device on a 128° YX-LiNbO3 substrate. J. Micromech. Microeng. 21 (1), 015005.CrossRefGoogle Scholar
Alzuaga, S., Manceau, J.-F. & Bastien, F. 2005 Motion of droplets on solid surface using acoustic radiation pressure. J. Sound. Vib. 282 (1–2), 151–162.CrossRefGoogle Scholar
Baudoin, M., Brunet, P., Bou Matar, O. & Herth, E. 2012 Low energy droplet actuation via modulated surface acoustic waves. Appl. Phys. Lett. 100, 154102.CrossRefGoogle Scholar
Berry, M. V. 1976 Waves and Thom’s theorem. Adv. Phys. 25 (1), 1–26.CrossRefGoogle Scholar
Beyssen, D., Le Brizoual, L., Elmazria, O., Alnot, P., Perry, I. & Maillet, D. 2006 6i-2 droplet heating system based on saw/liquid interaction. In IEEE Ultras. Symp., vol. 1–5, pp. 949–952.Google Scholar
Blamey, J., Yeo, L. Y. & Friend, J. R. 2013 Microscale capillary wave turbulence excited by high frequency vibration. Langmuir 29, 3835–3845.CrossRefGoogle ScholarPubMed
Bou-Zeid, E. 2015 Challenging the large eddy simulation technique with advanced a posteriori tests. J. Fluid Mech. 764, 1–4.Google Scholar
Bourquin, Y., Reboud, J., Wilson, R. & Cooper, J. M. 2010 Tuneable surface acoustic waves for fluid and particle manipulations on disposable chips. Lab on a Chip 10, 1898–1901.CrossRefGoogle ScholarPubMed
Brunet, P., Baudoin, M., Bou Matar, O. & Zoueshtiagh, F. 2010 Droplet displacement and oscillations induced by ultrasonic surface acoustic waves: a quantitative study. Phys. Rev. E 81, 036315.Google Scholar
Bühler, O. 2009 Waves and Mean Flows. Cambridge University Press.Google Scholar
Campbell, J. J. & Jones, W. R. 1970 Propagation of surface waves at the boundary between a piezoelectric crystal and a fluid medium. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 17 (2), 71–76.Google Scholar
Cheeke, J. D. N. 2002 Fundamental and Applications of Ultrasonic Waves, p. 8.3. CRC Press LLC.Google Scholar
Cheng, N.-S. 2008 Formula for the viscosity of a glycerol-water mixture. Ind. Engng Chem. Res. 47 (9), 3285–3288.Google Scholar
Collignon, S., Friend, J. & Yeo, L. 2015 Planar microfluidic drop splitting and merging. Lab on a Chip 15, 1942–1951.Google Scholar
Coulouvrat, F. 1992 On the equations of nonlinear acoustics. J. Acoust. 5, 321–359.Google Scholar
De Gennes, P.-G., Brochard-Wyart, F. & Quéré, D. 2013 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer Science & Business Media.Google Scholar
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453–480.CrossRefGoogle Scholar
Du, X. Y., Swanwick, M. E., Fu, Y. Q., Luo, J. K., Flewitt, A. J., Lee, D. S., Maeng, S. & Milne, W. I. 2009 Surface acoustic wave induced streaming and pumping in 128° Y-cut LiNbO3 for microfluidic applications. J. Micromech. Microengng 19 (3), 035016.Google Scholar
Eckart, C. 1948 Vortices and streams caused by sound waves. Phys. Rev. 73, 68–76.Google Scholar
Friend, J. R. & Yeo, L. Y. 2011 Microscale acoustofluidics: microfluidics driven via acoustics and ultrasonics. Rev. Mod. Phys. 83, 647–704.Google Scholar
Frommelt, T., Kostur, M., Wenzel-Schäfer, M., Talkner, P., Hänggi, P. & Wixforth, A. 2008 Microfluidic mixing via acoustically driven chaotic advection. Phys. Rev. Lett. 100, 034502.Google Scholar
Fukaya, T. & Kondoh, J. 2015 Experimental consideration of droplet manipulation mechanism using surface acoustic wave. Japan. J. Appl. Phys. 54 (7S1), 07HE06.Google Scholar
Gusev, V. E. & Rudenko, O. V. 1979 Nonstready quasi-one-dimensional acoustic streaming in unbounded volumes with hydrodynamic nonlinearity. Sov. Phys. Acoust. 25, 493–497.Google Scholar
Hertz, G. & Mende, H. 1939 Der strahlungsdrunk in flüssigkeiten. Z. Phys. 114, 354–367.CrossRefGoogle Scholar
Ito, S., Sugimoto, Y., Matsui, Y. & Kondoh, J. 2007 Study of surface acoustic wave streaming phenomenon based on temperature measurement and observation of streaming in liquids. Japan. J. Appl. Phys. 46, 4718.CrossRefGoogle Scholar
Kondoh, J., Shimizu, N., Matsui, Y., Sugimoto, M. & Shiokawa, S. 2005 Development of saw thermocycler for small liquid droplets. IEEE Ultrason. Symp. 2, 1023–1027.Google Scholar
Kondoh, J., Shimizu, N., Matsui, Y., Sugimoto, M. & Shiokawa, S. 2009 Development of temperature control system for liquid droplet using surface acoustic wave device. Sensors Actuators A 149, 292–297.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
Kuznetsov, V. P. 1970 Equations of nonlinear acoustics. Sov. Phys. Acoust. 16, 467–470.Google Scholar
Liebermann, L. N. 1949 The second viscosity of liquids. Phys. Rev. 75, 1415–1422.Google Scholar
Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61 (3), 391–418.Google Scholar
Masanori, S. & Toshitaka, F. 2001 Quantum mechanical representation of acoustic streaming and acoustic radiation pressure. Phys. Rev. E 64, 026311.Google Scholar
Mitome, H. 1998 The mechanism of generation of acoustic streaming. Electron. Commun. Japan. III 81 (10), 1–8.Google Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25 (1), 68–75.Google Scholar
Pope, S. B. 2004 Ten questions concerning the large-eddy simulation of turbulent flows. New J. Phys. 6 (1), 35.Google Scholar
Qi, A., Yeo, L. Y. & Friend, J. R. 2008 Interfacial destabilization and atomization driven by surface acoustic waves. Phys. Fluids 20 (7), 074103.Google Scholar
Quintero, R. & Simonetti, F. 2013 Rayleigh wave scattering from sessile droplets. Phys. Rev. E 88, 043011.Google Scholar
Raghavan, R. V., Friend, J. R. & Yeo, L. Y. 2010 Particle concentration via acoustically driven microcentrifugation: micropiv flow visualization and numerical modelling studies. Microfluid Nanofluid 8 (1), 73–84.Google Scholar
Rayleigh, Lord 1884 On the circuclation of air observed in Kundt’s tubes, ans some allied acoustical problems. Phil. Trans. R. Soc. Lond. 175, 1–21.Google Scholar
Rayleigh, Lord 1915 The principle of similitude. Nature 95, 66–68.CrossRefGoogle Scholar
Reboud, J., Bourquin, Y., Wilson, G. S., Pall, G. S., Jiwaji, M., Pitt, A. R., Graham, A., Waters, A. P. & Cooper, J. M. 2012 Shaping acoustic fields as a toolset for microfluidic manipulations in diagnostic technologies. Proc. Natl Acad. Sci. USA 109, 15162.Google Scholar
Rednikov, A. Y. & Sadhal, S. S. 2011 Acoustic/steady streaming from a motionless boundary and related phenomena: generalized treatment of the inner streaming and examples. J. Fluid Mech. 667, 426–462.Google Scholar
Renaudin, A., Tabourier, P., Zang, V., Camart, J. C. & Druon, C. 2006 Saw nanopump for handling droplets in view of biological applications. Sensors Actuators B 113, 389–397.Google Scholar
Rezk, A. R., Yeo, L. Y. & Friend, J. R. 2014 Poloidal flow and toroidal particle ring formation in a sessile drop driven by megahertz order vibration. Langmuir 30 (37), 11243–11247.Google Scholar
Riaud, A., Baudoin, M., Thomas, J. L. & Bou Matar, O. 2016 SAW synthesis with IDTs array and the inverse filter: toward a versatile saw toolbox for microfluidics and biological applications. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 63, 1601–1607.Google Scholar
Riley, N. 1998 Acoustic streaming. Theor. Comput. Fluid Dyn. 10 (1–4), 349–356.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
Rooney, J. A., Smith, C. W. & Carey, R. F. 1982 Acoustic streaming in superfluid helium. J. Acoust. Soc. Am. 72 (1), 245–249.CrossRefGoogle Scholar
Roux-Marchand, T., Beyssen, D., Sarry, F. & Elmazria, O. 2015 Rayleigh surface acoustic waves as an efficient heating system for biological reactions: investigation of microdroplet temperature uniformity. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62 (4), 729–735.Google Scholar
Roux-Marchand, T., Beyssen, D., Sarry, F., Grandemange, S. & Elmazria, O. 2012 Microfluidic heater assisted by rayleigh surface acoustic wave on AlN/128° Y-X LiNbO3 multilayer structure. IEEE Intl Ultrason. Symp. pp. 1706–1709.Google Scholar
Royer, D. & Dieulesaint, E. 1996 Elastic Waves in Solids 1. Springer.Google Scholar
Royer, D. & Dieulesaint, E. 1999 Elastic Waves in Solids 2. Springer.Google Scholar
Schindler, M., Talkner, P. & Hänggi, P. 2006 Computing stationary free-surface shapes in microfluidics. Phys. Fluids 18 (10), 103303.Google Scholar
Shilton, R. J., Mattoli, V., Travagliati, M., Agostini, M., Desii, A., Beltram, F. & Cecchini, M. 2015 Rapid and controllable digital microfluidic heating by surface acoustic waves. Adv. Funct. Mater. 25, 5895–5901.Google Scholar
Shiokawa, S., Matsui, Y. & Toyosaka, M. 1988 Water streaming due to c-6 saw (surface acoustic wave). In Symposium Ultrasonic Electronics, vol. 9, pp. 83–84 (In japanese).Google Scholar
Shiokawa, S., Matsui, Y. & Ueda, T. 1990 Study on SAW streaming and its application to fluid device. Japan. J. Appl. Phys. 29 (Sup. 29-1), 137–139.Google Scholar
Slie, W. M., Donfor, A. R. & Litovitz, T. A. 1966 Ultrasonic shear and longitudinal measurements in aqueous glycerol. J. Chem. Phys. 44 (10), 3712–3718.Google Scholar
Sritharan, K., Strobl, C. J., Schneider, M. F. & Wixforth, A. 2006 Acoustic mixing at low reynolds numbers. Appl. Phys. Lett. 054102.Google Scholar
Stanzial, D., Bonsi, D. & Schiffrer, G. 2003 Four-dimensional treatment of linear acoustic fields and radiation pressure. Acta Acust. United. Ac. 89 (2), 213–224.Google Scholar
Tan, M. K., Friend, J. R. & Yeo, L. Y. 2009 Interfacial jetting phenomena induced by focused surface vibrations. Phys. Rev. Lett. 103 (2), 024501.CrossRefGoogle ScholarPubMed
Tan, M. K., Friend, J. R., Matar, O. K. & Yeo, L. Y 2010 Capillary wave motion excited by high frequency surface acoustic waves. Phys. Fluids 22 (11), 112112.Google Scholar
Tanter, M., Thomas, J. L., Coulouvrat, F. & Fink, M. 2001 Breaking of the time reversal invariance in nonlinear acoustics. Phys. Rev. E 64, 016602.CrossRefGoogle ScholarPubMed
Vanneste, J. & Bühler, O. 2011 Streaming by leaky surface acoustic waves. Phil. Trans. R. Soc. Lond. A 467 (2130), 1779–1800.Google Scholar
Westervelt, P. J. 1953 The theory of steady rotational flow generated by a sound field. J. Acoust. Soc. Am. 25 (1), 60–67.Google Scholar
Wiklund, M. 2012 Acoustofluidics 14: applications of acoustic streaming in microfluidic devices. Lab on a Chip 12, 2438–2451.Google Scholar
Wixforth, A., Strobl, C., Gauer, C., Toegl, A., Scriba, J. & Guttenberg, Z. 2004 Acoustic manipulation of small droplets. Anal. Bioanal. Chem. 379 (7), 982–991.Google Scholar
Zhang, A., Zha, Y. & Fu, X. 2013 Splitting a droplet with oil encapsulation using surface acoustic wave excited by electric signal with low power. AIP Advances 3 (7), 072119.Google Scholar
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