Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-17T14:17:48.712Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional streaming flow in confined geometries

Published online by Cambridge University Press:  20 July 2015

Bhargav Rallabandi ,
Alvaro Marin ,
Massimiliano Rossi ,
Christian J. Kähler  and
Sascha Hilgenfeldt
Bhargav Rallabandi*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
Alvaro Marin
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Massimiliano Rossi
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Christian J. Kähler
Affiliation:
Institute for Aerodynamics and Fluid Mechanics, Bundeswehr University Munich, 85577 Neubiberg, Germany
Sascha Hilgenfeldt
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Steady streaming vortex flow from microbubbles has been developed into a versatile tool for microfluidic sample manipulation. For ease of manufacture and quantitative control, set-ups have focused on approximately two-dimensional flow geometries based on semi-cylindrical bubbles. The present work demonstrates how the necessary flow confinement perpendicular to the cylinder axis gives rise to non-trivial three-dimensional flow components. This is an important effect in applications such as sorting and micromixing. Using asymptotic theory and numerical integration of fluid trajectories, it is shown that the two-dimensional flow dynamics is modified in two ways: (i) the vortex motion is punctuated by bursts of strong axial displacement near the bubble, on time scales smaller than the vortex period; and (ii) the vortex trajectories drift over time scales much longer than the vortex period, forcing fluid particles onto three-dimensional paths of toroidal topology. Both effects are verified experimentally by quantitative comparison with astigmatism particle tracking velocimetry (APTV) measurements of streaming flows. It is further shown that the long-time flow patterns obey a Hamiltonian description that is applicable to general confined Stokes flows beyond microstreaming.

JFM classification

Drops and Bubbles: Bubble dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , pp. 408 - 429
Check for updates
Copyright
© 2015 Cambridge University Press 

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

Ahmed, D., Mao, X., Shi, J., Juluri, B. K. & Huang, T. J. 2009 A millisecond micromixer via single-bubble-based acoustic streaming. Lab on a Chip 9 (18), 2738–2741.Google Scholar
Bertelsen, A., Svardal, A. & Tjøtta, S. 1973 Nonlinear streaming effects associated with oscillating cylinders. J. Fluid Mech. 59 (03), 493–511.Google Scholar
Chong, K., Kelly, S. D., Smith, S. & Eldredge, J. D. 2013 Inertial particle trapping in viscous streaming. Phys. Fluids 25 (3), 033602.Google Scholar
Cierpka, C. & Kähler, C. J. 2012 Particle imaging techniques for volumetric three-component (3D3C) velocity measurements in microfluidics. J. Vis. 15 (1), 1–31.CrossRefGoogle Scholar
Cierpka, C., Rossi, M., Segura, R. & Kähler, C. J. 2011 On the calibration of astigmatism particle tracking velocimetry for microflows. Meas. Sci. Technol. 22 (1), 015401.CrossRefGoogle Scholar
Davidson, B. J. & Riley, N. 1971 Cavitation microstreaming. J. Sound Vib. 15 (2), 217–233.Google Scholar
Doinikov, A. A. 1997 Acoustic radiation force on a spherical particle in a viscous heat-conducting fluid. I. General formula. J. Acoust. Soc. Am. 101 (2), 713–721.CrossRefGoogle Scholar
Doinikov, A. A. & Bouakaz, A. 2010 Acoustic microstreaming around a gas bubble. J. Acoust. Soc. Am. 127 (2), 703–709.CrossRefGoogle ScholarPubMed
Gelderblom, H., Zijlstra, A. G., van Wijngaarden, L. & Prosperetti, A. 2012 Oscillations of a gas pocket on a liquid-covered solid surface. Phys. Fluids 24 (12), 122101.CrossRefGoogle Scholar
Holtsmark, J., Johnsen, I., Sikkeland, T. & Skavlem, S. 1954 Boundary layer flow near a cylindrical obstacle in an oscillating, incompressible fluid. J. Acoust. Soc. Am. 26 (1), 26–39.CrossRefGoogle Scholar
Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61 (3), 391–418.Google Scholar
Liu, R. H., Yang, J., Pindera, M. Z., Athavale, M. & Grodzinski, P. 2002 Bubble-induced acoustic micromixing. Lab on a Chip 2 (3), 151–157.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245 (903), 535–581.Google Scholar
Longuet-Higgins, M. S. 1970 Viscous streaming from an oscillating spherical bubble. Proc. R. Soc. Lond. A 454, 725–742.Google Scholar
Lutz, B. R., Chen, J. & Schwartz, D. T. 2005 Microscopic steady streaming eddies created around short cylinders in a channel: flow visualization and stokes layer scaling. Phys. Fluids 17 (2), 1–7.Google Scholar
Lutz, B. R., Chen, J. & Schwartz, D. T. 2006 Hydrodynamic tweezers: 1. Noncontact trapping of single cells using steady streaming microeddies. Analyt. Chem. 78 (15), 5429–5435.CrossRefGoogle ScholarPubMed
Marin, A., Rossi, M., Rallabandi, B., Wang, C., Hilgenfeldt, S. & Kähler, C. J. 2015 Three-dimensional phenomena in microbubble acoustic streaming. Phys. Rev. Appl. 3 (4), 041001.Google Scholar
Marmottant, P. & Hilgenfeldt, S. 2003 Controlled vesicle deformation and lysis by single oscillating bubbles. Nature 423 (6936), 153–156.CrossRefGoogle ScholarPubMed
Marmottant, P. & Hilgenfeldt, S. 2004 A bubble-driven microfludic transport element for bioengineering. Proc. Natl Acad. Sci. USA 101 (26), 9523–9527.Google Scholar
Nyborg, W. L. 1958 Acoustic streaming near a boundary. J. Acoust. Soc. Am. 30 (4), 329–339.Google Scholar
Patel, M. V., Tovar, A. R. & Lee, A. P. 2012 Lateral cavity acoustic transducer as an on-chip cell/particle microfluidic switch. Lab on a Chip 12 (1), 139–145.Google Scholar
Phan, H. V., Şeşen, M., Alan, T. & Neild, A. 2014 Single line particle focusing using a vibrating bubble. Appl. Phys. Lett. 105 (19), 193507.CrossRefGoogle Scholar
Rallabandi, B., Wang, C., Guo, L. & Hilgenfeldt, S.2015 Systematic strategies for open flow mixing with microbubble streaming. Preprint.Google Scholar
Rallabandi, B., Wang, C. & Hilgenfeldt, S. 2014 Two-dimensional streaming flows driven by sessile semicylindrical microbubbles. J. Fluid Mech. 739, 57–71.CrossRefGoogle Scholar
Raney, W. P., Corelli, J. C. & Westervelt, P. J. 1954 Acoustical streaming in the vicinity of a cylinder. J. Acoust. Soc. Am. 26, 1006–1014.CrossRefGoogle Scholar
Riley, N. 1965 Oscillating viscous flows. Mathematika 12 (02), 161–175.Google Scholar
Riley, N. 1966 On a sphere oscillating in a viscous fluid. Q. J. Mech. Appl. Maths 19 (4), 461–472.CrossRefGoogle Scholar
Riley, N. 1967 Oscillatory viscous flows. Review and extension. IMA J. Appl. Maths 3 (4), 419–434.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
Rogers, P. & Neild, A. 2011 Selective particle trapping using an oscillating microbubble. Lab on a Chip 11 (21), 3710–3715.Google Scholar
Rossi, M. & Kähler, C. J. 2014 Optimization of astigmatic particle tracking velocimeters. Exp. Fluids 55 (9), 1–13.Google Scholar
Sadhal, S. S. 2012 Acoustofluidics 16: acoustics streaming near liquid–gas interfaces: drops and bubbles streaming near liquid–gas interfaces: drops and bubbles. Lab on a Chip 12 (16), 2771–2781.Google Scholar
Sanz, A. & Diez, J. 1989 Non-axisymmetric oscillations of liquid bridges. J. Fluid Mech. 205, 503–521.CrossRefGoogle Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24 (4), 673–687.Google Scholar
Thameem, R., Rallabandi, B. & Hilgenfeldt, S.2015 Fast sorting of microparticles in bubble streaming flows. Preprint.Google Scholar
Wang, C.2013 Microbubble streaming flows for non-invasive particle manipulation and liquid mixing. PhD thesis, University of Illinois at Urbana-Champaign.Google Scholar
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2011 Size-sensitive sorting of microparticles through control of flow geometry. Appl. Phys. Lett. 99 (3), 034101.Google Scholar
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2012 Efficient manipulation of microparticles in bubble streaming flows. Biomicrofluidics 6 (1), 012801.Google Scholar
Wang, C., Rallabandi, B. & Hilgenfeldt, S. 2013 Frequency dependence and frequency control of microbubble streaming flows. Phys. Fluids 25, 022002.Google Scholar
Wang, C.-Y. 1968 On high-frequency oscillatory viscous flows. J. Fluid Mech. 32 (01), 55–68.CrossRefGoogle Scholar
Wang, S. S., Jiao, Z. J., Huang, X. Y., Yang, C. & Nguyen, N. T. 2009 Acoustically induced bubbles in a microfluidic channel for mixing enhancement. Microfluid. Nanofluid. 6 (6), 847–852.Google Scholar
Wiklund, M., Green, R. & Ohlin, M. 2012 Acoustofluidics 14: applications of acoustic streaming in microfluidic devices. Lab on a Chip 12 (14), 2438–2451.Google Scholar
Wu, J. & Du, G. 1997 Streaming generated by a bubble in an ultrasound field. J. Acoust. Soc. Am. 101 (4), 1899–1907.Google Scholar
Xie, Y., Ahmed, D., Lapsley, M. I., Lin, S.-C. S., Nawaz, A. A., Wang, L. & Huang, T. J. 2012 Single-shot characterization of enzymatic reaction constants $K_{m}$ and $k_{\mathit{cat}}$ by an acoustic-driven, bubble-based fast micromixer. Analyt. Chem. 84 (17), 7495–7501.CrossRefGoogle Scholar