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Acoustic microstreaming near a plane wall due to a pulsating free or coated bubble: velocity, vorticity and closed streamlines

Published online by Cambridge University Press:  25 July 2019

Nima Mobadersany  and
Kausik Sarkar Open the ORCID record for Kausik Sarkar [Opens in a new window]
Nima Mobadersany
Affiliation:
Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052, USA
Kausik Sarkar*
Affiliation:
Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052, USA
*
†Email address for correspondence: [email protected]
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Abstract

Acoustic microstreaming due to an oscillating microbubble, either coated or free, is analytically investigated. The detailed flow field is obtained and the closed streamlines of the ring vortex generated by microstreaming are plotted in both Eulerian and Lagrangian descriptions. Analytical expressions are found for the ring vortex showing that its length depends only on the separation of the microbubble from the wall and the dependence is linear. The circulation as a scalar measure of the vortex is computed quantitatively identifying its spatial location. The functional dependence of circulation on bubble separation and coating parameters is shown to be similar to that of the shear stress.

JFM classification

Drops and Bubbles: Bubble dynamics Drops and Bubbles: Cavitation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 781 - 806
Copyright
© 2019 Cambridge University Press 

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References

Aliabouzar, M., Lee, S. J., Zhou, X., Zhang, G. L. J. & Sarkar, K. 2018 Effects of scaffold microstructure and low intensity pulsed ultrasound on chondrogenic differentiation of human mesenchymal stem cells. Biotechnol. Bioengng 115 (2), 495–506.Google Scholar
Aliabouzar, M., Zhang, L. G. & Sarkar, K. 2016 Lipid coated microbubbles and low intensity pulsed ultrasound enhance chondrogenesis of human mesenchymal stem cells in 3D printed scaffolds. Sci. Rep. 6, 37728.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.Google Scholar
Chatterjee, D. & Sarkar, K. 2003 A Newtonian rheological model for the interface of microbubble contrast agents. Ultrasound Med. Biol. 29 (12), 1749–1757.Google Scholar
Church, C. C. 1995 The effects of an elastic solid-surface layer on the radial pulsations of gas-bubbles. J. Acoust. Soc. Am. 97 (3), 1510–1521.Google Scholar
Collis, J., Manasseh, R., Liovic, P., Tho, P., Ooi, A., Petkovic-Duran, K. & Zhu, Y. 2010 Cavitation microstreaming and stress fields created by microbubbles. Ultrasonics 50 (2), 273–279.Google Scholar
Davidson, B. J. & Riley, N. 1971 Cavitation microstreaming. J. Sound Vib. 15 (2), 217–233.Google Scholar
Doinikov, A. A. & Bouakaz, A. 2010a Acoustic microstreaming around a gas bubble. J. Acoust. Soc. Am. 127 (2), 703–709.Google Scholar
Doinikov, A. A. & Bouakaz, A. 2010b Theoretical investigation of shear stress generated by a contrast microbubble on the cell membrane as a mechanism for sonoporation. J. Acoust. Soc. Am. 128 (1), 11–19.Google Scholar
Doinikov, A. A. & Bouakaz, A. 2014 Effect of a distant rigid wall on microstreaming generated by an acoustically driven gas bubble. J. Fluid Mech. 742, 425–445.Google Scholar
Doinikov, A. A. & Bouakaz, A. 2016 Microstreaming generated by two acoustically induced gas bubbles. J. Fluid Mech. 796, 318–339.Google Scholar
Elder, S. A. 1959 Cavitation microstreaming. J. Acoust. Soc. Am. 31 (1), 54–64.Google Scholar
Fabre, D., Jalal, J., Leontini, J. S. & Manasseh, R. 2017 Acoustic streaming and the induced forces between two spheres. J. Fluid Mech. 810, 378–391.Google Scholar
Fan, Z., Kumon, R. E. & Deng, C. X. 2014 Mechanisms of microbubble-facilitated sonoporation for drug and gene delivery. Therapeutic Deliv. 5 (4), 467–486.Google Scholar
Forbes, M. M. & O’Brien, W. D. Jr 2012 Development of a theoretical model describing sonoporation activity of cells exposed to ultrasound in the presence of contrast agents. J. Acoust. Soc. Am. 131 (4), 2723–2729.Google Scholar
Goldberg, B. B., Raichlen, J. S. & Forsberg, F. 2001 Ultrasound Contrast Agents: Basic Principles and Clinical Applications. Martin Dunitz.Google Scholar
Hoff, L., Sontum, P. C. & Hovem, J. M. 2000 Oscillations of polymeric microbubbles: effect of the encapsulating shell. J. Acoust. Soc. Am. 107 (4), 2272–2280.Google Scholar
de Jong, N., Cornet, R. & Lancee, C. T. 1994 Higher harmonics of vibrating gas-filled microspheres. 1. Simulations. Ultrasonics 32 (6), 447–453.Google Scholar
de Jong, N., Hoff, L., Skotland, T. & Bom, N. 1992 Absorption and scatter of encapsulated gas filled microspheres – theoretical considerations and some measurements. Ultrasonics 30 (2), 95–103.Google Scholar
Katiyar, A., Duncan, R. L. & Sarkar, K. 2014 Ultrasound stimulation increases proliferation of MC3T3-E1 preosteoblast-like cells. J. Theor. Ultrasound 2, 1.Google Scholar
Katiyar, A. & Sarkar, K. 2011 Excitation threshold for subharmonic generation from contrast microbubbles. J. Acoust. Soc. Am. 130 (5), 3137–3147.Google Scholar
Katiyar, A., Sarkar, K. & Jain, P. 2009 Effects of encapsulation elasticity on the stability of an encapsulated microbubble. J. Colloid Interface Sci. 336, 519–525.Google Scholar
Kolb, J. & Nyborg, W. L. 1956 Small-scale acoustic streaming in liquids. J. Acoust. Soc. Am. 28 (6), 1237–1242.Google Scholar
Krasovitski, B. & Kimmel, E. 2004 Shear stress induced by a gas bubble pulsating in an ultrasonic field near a wall. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51 (8), 973–979.Google Scholar
Kumar, K. N. & Sarkar, K. 2015 Effects of ambient hydrostatic pressure on the material properties of the encapsulation of an ultrasound contrast microbubble. J. Acoust. Soc. Am. 138 (2), 624–634.Google Scholar
Kumar, K. N. & Sarkar, K. 2016 Interfacial rheological properties of contrast microbubble Targestar P as a function of ambient pressure. Ultrasound Med. Biol. 42 (4), 1010–1017.Google Scholar
Lajoinie, G., Luan, Y., Gelderblom, E., Dollet, B., Mastik, F., Dewitte, H., Lentacker, I., de Jong, N. & Versluis, M. 2018 Non-spherical oscillations drive the ultrasound-mediated release from targeted microbubbles. Commun. Phys. 1 (1), 22.Google Scholar
Lentacker, I., De Smedt, S. C. & Sanders, N. N. 2009 Drug loaded microbubble design for ultrasound triggered delivery. Soft Matt. 5 (11), 2161–2170.Google Scholar
Lewin, P. A. & Bjorno, L. 1982 Acoustically induced shear stresses in the vicinity of microbubbles in tissue. J. Acoust. Soc. Am. 71 (3), 728–734.Google Scholar
Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61 (3), 391–418.Google Scholar
Liu, X. & Wu, J. 2009 Acoustic microstreaming around an isolated encapsulated microbubble. J. Acoust. Soc. Am. 125 (3), 1319–1330.Google Scholar
Marmottant, P. & Hilgenfeldt, S. 2003 Controlled vesicle deformation and lysis by single oscillating bubbles. Nature 423 (6936), 153–156.Google Scholar
Marmottant, P., van der Meer, S., Emmer, M., Versluis, M., de Jong, N., Hilgenfeldt, S. & Lohse, D. 2005 A model for large amplitude oscillations of coated bubbles accounting for buckling and rupture. J. Acoust. Soc. Am. 118 (6), 3499–3505.Google Scholar
Miller, D. L. 1988 Particle gathering and microstreaming near ultrasonically activated gas-filled micropores. J. Acoust. Soc. Am. 84 (4), 1378–1387.Google Scholar
Mobadersany, N. & Sarkar, K. 2018 Collapse and jet formation of ultrasound contrast microbubbles near a membrane for sonoporation. In 10th International Cavitation Symposium, Baltimore, MD, USA. ASME.Google Scholar
Najjari, M. R. & Plesniak, M. W. 2016 Evolution of vortical structures in a curved artery model with non-Newtonian blood-analog fluid under pulsatile inflow conditions. Exp. Fluids 57 (6), 100.Google Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25 (1), 68–75.Google Scholar
Nyborg, W. L. 1958 Acoustic streaming near a boundary. J. Acoust. Soc. Am. 30 (4), 329–339.Google Scholar
Orbay, S., Ozcelik, A., Lata, J., Kaynak, M., Wu, M. & Huang, T. J. 2016 Mixing high-viscosity fluids via acoustically driven bubbles. J. Micromech. Microengng 27 (1), 015008.Google Scholar
Paul, S., Katiyar, A., Sarkar, K., Chatterjee, D., Shi, W. T. & Forsberg, F. 2010 Material characterization of the encapsulation of an ultrasound contrast microbubble and its subharmonic response: strain-softening interfacial elasticity model. J. Acoust. Soc. Am. 127 (6), 3846–3857.Google Scholar
Paul, S., Nahire, R., Mallik, S. & Sarkar, K. 2014 Encapsulated microbubbles and echogenic liposomes for contrast ultrasound imaging and targeted drug delivery. Comput. Mech. 53 (3), 413–435.Google Scholar
Paul, S., Russakow, D., Rodgers, T., Sarkar, K., Cochran, M. & Wheatley, M. A. 2013 Determination of the interfacial rheological properties of a poly(DL-lactic acid)-encapsulated contrast agent using in vitro attenuation and scattering. Ultrasound Med. Biol. 39 (7), 1277–1291.Google Scholar
Pommella, A., Brooks, N. J., Seddon, J. M. & Garbin, V. 2015 Selective flow-induced vesicle rupture to sort by membrane mechanical properties. Sci. Rep. 5, 13163.Google Scholar
Rallabandi, B., Marin, A., Rossi, M., Kahler, C. J. & Hilgenfeldt, S. 2015 Three-dimensional streaming flow in confined geometries. J. Fluid Mech. 777, 408–429.Google Scholar
Rallabandi, B., Wang, C. & Hilgenfeldt, S. 2014 Two-dimensional streaming flows driven by sessile semicylindrical microbubbles. J. Fluid Mech. 739, 57–71.Google Scholar
Raney, W. P., Corelli, J. C. & Westervelt, P. J. 1954 Acoustical streaming in the vicinity of a cylinder. J. Acoust. Soc. Am. 26 (6), 1006–1014.Google Scholar
Rayleigh, L. 1945 Theory of Sound. Dover.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33 (1), 43–65.Google Scholar
Rooney, J. A. 1970 Hemolysis near an ultrasonically pulsating gas bubble. Science 169 (3948), 869–871.Google Scholar
Sarkar, K., Katiyar, A. & Jain, P. 2009 Growth and dissolution of an encapsulated contrast microbubble. Ultrasound Med. Biol. 35 (8), 1385–1396.Google Scholar
Sarkar, K., Shi, W. T., Chatterjee, D. & Forsberg, F. 2005 Characterization of ultrasound contrast microbubbles using in vitro experiments and viscous and viscoelastic interface models for encapsulation. J. Acoust. Soc. Am. 118 (1), 539–550.Google Scholar
Schlicting, H. 1979 Boundary Layer Theory. McGraw-Hill.Google Scholar
Sontum, P. C. 2008 Physicochemical characteristics of Sonazoid™, a new contrast agent for ultrasound imaging. Ultrasound Med. Biol. 34 (5), 824–833.Google Scholar
Sontum, P. C., Ostensen, J., Dyrstad, K. & Hoff, L. 1999 Acoustic properties of NC100100 and their relation with the microbubble size distribution. Investigative Radiol. 34 (4), 268–275.Google Scholar
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673–687.Google Scholar
Thameem, R., Rallabandi, B. & Hilgenfeldt, S. 2016 Particle migration and sorting in microbubble streaming flows. Biomicrofluidics 10 (1), 014124.Google Scholar
Tho, P., Manasseh, R. & Ooi, A. 2007 Cavitation microstreaming patterns in single and multiple bubble systems. J. Fluid Mech. 576, 191–233.Google Scholar
Tsiglifis, K. & Pelekasis, N. A. 2008 Nonlinear radial oscillations of encapsulated microbubbles subject to ultrasound: the effect of membrane constitutive law. J. Acoust. Soc. Am. 123 (6), 4059–4070.Google Scholar
Vollmers, H. 2001 Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data. Meas. Sci. Technol. 12 (8), 1199–1207.Google Scholar
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2012 Efficient manipulation of microparticles in bubble streaming flows. Biomicrofluidics 6 (1), 012801.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
Wu, J. & Du, G. 1997 Streaming generated by a bubble in an ultrasound field. J. Acoust. Soc. Am. 101 (4), 1899–1907.Google Scholar
Wu, J. R. 2002 Theoretical study on shear stress generated by microstreaming surrounding contrast agents attached to living cells. Ultrasound Med. Biol. 28 (1), 125–129.Google Scholar
Xia, L., Porter, T. M. & Sarkar, K. 2015 Interpreting attenuation at different excitation amplitudes to estimate strain-dependent interfacial rheological properties of lipid-coated monodisperse microbubbles. J. Acoust. Soc. Am. 138 (6), 3994–4003.Google Scholar
Zhou, X., Castro, N. J., Zhu, W., Cui, H. T., Aliabouzar, M., Sarkar, K. & Zhang, L. G. 2016 Improved human bone marrow mesenchymal stem cell osteogenesis in 3D bioprinted tissue scaffolds with low intensity pulsed ultrasound stimulation. Sci. Rep. 6, 23876.Google Scholar