increasing the height-to-width ratio. In contrast, by replacing
water by a 50% glycerol-in-water mixture, we demonstrated how
to enhance the streaming effects. The former study may form a
good starting point for designing streaming-free devices for
handling of sub-micrometer particles, such as small cells,
bacteria, and viruses, and thus supporting concurrent experimental
efforts to suppress streaming, e.g., through averaging
over alternating actuation frequencies.43 The latter study is
pointing in the direction of developing devices with improved
mixing capabilities by enhancing streaming.44,45 We have thus
shown that our simulation tool has a great potential for enabling
improved design of acoustofluidic devices.
An important next step is to obtain a direct experimental
verification of our numerical simulation. As the relative
uncertainty of measured acoustophoretic particle velocities in
current experimental acoustofluidics is 5% or better,8 it is within
reach to obtain such an experimental verification. A problem is
of course that the streaming fields calculated in this work are in
the vertical plane, which is perpendicular to the usual horizontal
viewing plane, and thus specialized 3-dimensional visualization
techniques are required such as stereoscopic micro particle–
image velocimetry42,46 or astigmatism particle tracking velocimetry.
47 But even if such 3D-methods are complex to carry out,
it would be worth the effort given the great use of having a wellverified
numerical model of acoustophoretic particle motion.
Given a successful experimental verification, it would clearly be
valuable to extend the numerical model. One obvious step, which
is not conceptually difficult, but which would require significant
computational resources, would be to make a full 3D-model
taking the elastic properties of the chip surrounding the
microchannel into account. The relevance of such an extension
lies in the sensitivity of the acoustic streaming on the boundary
conditions. Only a full acousto-elastic theory would supply
realistic and accurate boundary conditions. Another class of
obvious model extensions deals with the modeling of the particle
suspension. A trivial extension would be to include gravity and
buoyancy, but more importantly and much more difficult would
be the inclusion of particle–particle and particle–wall interactions
that are neglected in the present work. These many-particle effects
include, e.g., the generation of streaming flow in the boundary
layer of each particle48 and not just the boundary layer of the wall.
After such an extension, our model could be used together with
high-precision experiments as a new and better research tool to
study and clarify the many yet unsolved problems with particle–
particle and particle–wall interactions in acoustofluidics.
The above-mentioned applications all demonstrate that our
numerical model is both timely and has a huge potential within
device design and studies of basic physical aspects of acoustophoresis.
Acknowledgements
This research was supported by the Danish Council for
Independent Research, Technology and Production Sciences,
Grants No. 274-09-0342 and No. 11-107021.
References
1 J. Friend and L. Y. Yeo, Rev. Mod. Phys., 2011, 83, 647–704.
2 H. Bruus, J. Dual, J. Hawkes, M. Hill, T. Laurell, J. Nilsson, S.
Radel, S. Sadhal and M. Wiklund, Lab Chip, 2011, 11, 3579–3580.
3 A. Lenshof, C. Magnusson and T. Laurell, Lab Chip, 2012, 12,
1210–1223.
4 M. Gedge and M. Hill, Lab Chip, 2012, 12, 2998–3007.
5 H. Bruus, Lab Chip, 2012, 12, 1014–1021.
6 M. Wiklund, R. Green and M. Ohlin, Lab Chip, 2012, 12, 2438–2451.
7 R. Barnkob, P. Augustsson, T. Laurell and H. Bruus, Lab Chip, 2010,
10, 563–570.
8 P. Augustsson, R. Barnkob, S. T. Wereley, H. Bruus and T. Laurell,
Lab Chip, 2011, 11, 4152–4164.
9 K. Yosioka and Y. Kawasima, Acustica, 1955, 5, 167–173.
10 L. P. Gorkov, Soviet Physics – Doklady, 1962, 6, 773–775.
11 M. Settnes and H. Bruus, Phys. Rev. E, 2012, 85, 016327.
12 K. Frampton, S. Martin and K. Minor, Appl. Acoust., 2003, 64,
681–692.
13 M. Hamilton, Y. Ilinskii and E. Zabolotskaya, J. Acoust. Soc. Am.,
2003, 113, 153–160.
14 J. F. Spengler, W. T. Coakley and K. T. Christensen, AIChE J., 2003,
49, 2773–2782.
15 S. M. Hagsa¨ ter, T. G. Jensen, H. Bruus and J. P. Kutter, Lab Chip,
2007, 7, 1336–1344.
16 H. Bruus, Lab Chip, 2012, 12, 1578–1586.
17 L. Rayleigh, Philos. Trans. R. Soc. London, 1884, 175, 1–21.
18 H. Schlichting, Physik Z, 1932, 33, 327–335.
19 J. Lighthill, J. Sound Vib., 1978, 61, 391–418.
20 L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Pergamon Press,
Oxford, 2nd edn, 1993, vol. 6, Course of Theoretical Physics.
21 H. Lei, D. Henry and H. BenHadid, Appl. Acoust., 2011, 72, 754–759.
22 M. K. Aktas and B. Farouk, J. Acoust. Soc. Am., 2004, 116,
2822–2831.
23 P. M. Morse and K. U. Ingard, Theoretical Acoustics, Princeton
University Press, Princeton NJ, 1986.
24 A. D. Pierce, Acoustics, Acoustical Society of America, Woodbury,
1991.
25 D. T. Blackstock, Physical acoustics, John Wiley and Sons, Hoboken
NJ, 2000.
26 L. D. Landau and E. M. Lifshitz, Statistical physics, Part 1,
Butterworth-Heinemann, Oxford, 3rd edn, 1980, vol. 5.
27 W. L. Nyborg, J. Acoust. Soc. Am., 1953, 25, 68–75.
28 M. Koklu, A. C. Sabuncu and A. Beskok, J. Colloid Interface Sci.,
2010, 351, 407–414.
29 COMSOL Multiphysics 4.2a, www.comsol.com, 2012.
30 CRCnetBASE Product, CRC Handbook of Chemistry and Physics,
Taylor and Francis Group, www.hbcpnetbase.com/, 92nd edn, 2012.
31 L. Bergmann, Der Ultraschall und seine Anwendung in Wissenschaft
und Technik, S. Hirzel Verlag, Stuttgart, 6th edn, 1954.
32 P. H. Mott, J. R. Dorgan and C. M. Roland, J. Sound Vib., 2008,
312, 572–575.
33 L. D. Landau and E. M. Lifshitz, Theory of Elasticity. Course of
Theoretical Physics, Pergamon Press, Oxford, 3rd edn, 1986, vol. 7.
34 N.-S. Cheng, Ind. Eng. Chem. Res., 2008, 47, 3285–3288.
35 F. Fergusson, E. Guptill and A. MacDonald, J. Acoust. Soc. Am.,
1954, 26, 67–69.
36 O. Bates, Ind. Eng. Chem., 1936, 28, 494–498.
37 F. Gucker and G. Marsh, Ind. Eng. Chem., 1948, 40, 908–915.
38 J. Dual and T. Schwarz, Lab Chip, 2012, 12, 244–252.
39 M. Wiklund, P. Spe´gel, S. Nilsson and H. M. Hertz, Ultrasonics,
2003, 41, 329–333.
40 J. Hultstro¨m, O. Manneberg, K. Dopf, H. M. Hertz, H. Brismar and
M. Wiklund, Ultrasound Med. Biol., 2007, 33, 145–151.
41 R. Barnkob, I. Iranmanesh, M. Wiklund and H. Bruus, Lab Chip,
2012, 12, 2337–2344.
42 M. Raffel, C. E. Willert, S. T. Wereley and J. Kompenhans, Particle
Image Velocimetry, Springer, New York, 2007.
43 M. Ohlin, A. Christakou, T. Frisk, B. O¨
nfelt and M. Wiklund, Proc.
15th MicroTAS, 2 - 6 October 2011, Seattle (WA), USA, 2011, pp.
1612–1614.
44 K. Sritharan, C. Strobl, M. Schneider, A. Wixforth and Z.
Guttenberg, Appl. Phys. Lett., 2006, 88, 054102.
45 T. Frommelt, M. Kostur, M. Wenzel-Schaefer, P. Talkner, P.
Haenggi and A. Wixforth, Phys. Rev. Lett., 2008, 100, 034502.
46 R. Lindken, M. Rossi, S. Grosse and J. Westerweel, Lab Chip, 2009,
9, 2551–2567.
47 C. Cierpka, M. Rossi, R. Segura and C. J. Kaehler, Meas. Sci.
Technol., 2011, 22, 015401.
48 S. Sadhal, Lab Chip, 2012, 12, 2600–2611.
This journal is The Royal Society of Chemistry 2012 Lab Chip, 2012, 12, 4617–4627 | 4627
Downloaded by DTU Library on 27 February 2013
Published on 23 July 2012 on http://pubs.rsc.org | doi:10.1039/C2LC40612H
View Article Online