Skip to main content Accessibility help
Hostname: page-component-747cfc64b6-db5sh Total loading time: 0.29 Render date: 2021-06-12T15:26:17.745Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true }

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
Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052, USA
Kausik Sarkar
Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052, USA
E-mail address:


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 Papers
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.


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), 495506.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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, 189214.CrossRefGoogle Scholar
Chatterjee, D. & Sarkar, K. 2003 A Newtonian rheological model for the interface of microbubble contrast agents. Ultrasound Med. Biol. 29 (12), 17491757.CrossRefGoogle ScholarPubMed
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), 15101521.CrossRefGoogle 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), 273279.CrossRefGoogle ScholarPubMed
Davidson, B. J. & Riley, N. 1971 Cavitation microstreaming. J. Sound Vib. 15 (2), 217233.CrossRefGoogle Scholar
Doinikov, A. A. & Bouakaz, A. 2010a Acoustic microstreaming around a gas bubble. J. Acoust. Soc. Am. 127 (2), 703709.CrossRefGoogle 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), 1119.CrossRefGoogle 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, 425445.CrossRefGoogle Scholar
Doinikov, A. A. & Bouakaz, A. 2016 Microstreaming generated by two acoustically induced gas bubbles. J. Fluid Mech. 796, 318339.CrossRefGoogle Scholar
Elder, S. A. 1959 Cavitation microstreaming. J. Acoust. Soc. Am. 31 (1), 5464.CrossRefGoogle Scholar
Fabre, D., Jalal, J., Leontini, J. S. & Manasseh, R. 2017 Acoustic streaming and the induced forces between two spheres. J. Fluid Mech. 810, 378391.CrossRefGoogle Scholar
Fan, Z., Kumon, R. E. & Deng, C. X. 2014 Mechanisms of microbubble-facilitated sonoporation for drug and gene delivery. Therapeutic Deliv. 5 (4), 467486.CrossRefGoogle ScholarPubMed
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), 27232729.CrossRefGoogle ScholarPubMed
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), 22722280.CrossRefGoogle ScholarPubMed
de Jong, N., Cornet, R. & Lancee, C. T. 1994 Higher harmonics of vibrating gas-filled microspheres. 1. Simulations. Ultrasonics 32 (6), 447453.CrossRefGoogle 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), 95103.CrossRefGoogle ScholarPubMed
Katiyar, A., Duncan, R. L. & Sarkar, K. 2014 Ultrasound stimulation increases proliferation of MC3T3-E1 preosteoblast-like cells. J. Theor. Ultrasound 2, 1.Google ScholarPubMed
Katiyar, A. & Sarkar, K. 2011 Excitation threshold for subharmonic generation from contrast microbubbles. J. Acoust. Soc. Am. 130 (5), 31373147.CrossRefGoogle ScholarPubMed
Katiyar, A., Sarkar, K. & Jain, P. 2009 Effects of encapsulation elasticity on the stability of an encapsulated microbubble. J. Colloid Interface Sci. 336, 519525.CrossRefGoogle ScholarPubMed
Kolb, J. & Nyborg, W. L. 1956 Small-scale acoustic streaming in liquids. J. Acoust. Soc. Am. 28 (6), 12371242.CrossRefGoogle 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), 973979.CrossRefGoogle 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), 624634.CrossRefGoogle ScholarPubMed
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), 10101017.CrossRefGoogle 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.CrossRefGoogle Scholar
Lentacker, I., De Smedt, S. C. & Sanders, N. N. 2009 Drug loaded microbubble design for ultrasound triggered delivery. Soft Matt. 5 (11), 21612170.CrossRefGoogle Scholar
Lewin, P. A. & Bjorno, L. 1982 Acoustically induced shear stresses in the vicinity of microbubbles in tissue. J. Acoust. Soc. Am. 71 (3), 728734.CrossRefGoogle Scholar
Lighthill, J. 1978 Acoustic streaming. J. Sound Vib. 61 (3), 391418.CrossRefGoogle Scholar
Liu, X. & Wu, J. 2009 Acoustic microstreaming around an isolated encapsulated microbubble. J. Acoust. Soc. Am. 125 (3), 13191330.CrossRefGoogle ScholarPubMed
Marmottant, P. & Hilgenfeldt, S. 2003 Controlled vesicle deformation and lysis by single oscillating bubbles. Nature 423 (6936), 153156.CrossRefGoogle ScholarPubMed
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), 34993505.CrossRefGoogle Scholar
Miller, D. L. 1988 Particle gathering and microstreaming near ultrasonically activated gas-filled micropores. J. Acoust. Soc. Am. 84 (4), 13781387.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Nyborg, W. L. 1953 Acoustic streaming due to attenuated plane waves. J. Acoust. Soc. Am. 25 (1), 6875.CrossRefGoogle Scholar
Nyborg, W. L. 1958 Acoustic streaming near a boundary. J. Acoust. Soc. Am. 30 (4), 329339.CrossRefGoogle 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 ScholarPubMed
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), 38463857.CrossRefGoogle ScholarPubMed
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), 413435.CrossRefGoogle ScholarPubMed
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), 12771291.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Rallabandi, B., Marin, A., Rossi, M., Kahler, C. J. & Hilgenfeldt, S. 2015 Three-dimensional streaming flow in confined geometries. J. Fluid Mech. 777, 408429.CrossRefGoogle Scholar
Rallabandi, B., Wang, C. & Hilgenfeldt, S. 2014 Two-dimensional streaming flows driven by sessile semicylindrical microbubbles. J. Fluid Mech. 739, 5771.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 (6), 10061014.CrossRefGoogle Scholar
Rayleigh, L. 1945 Theory of Sound. Dover.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33 (1), 4365.CrossRefGoogle Scholar
Rooney, J. A. 1970 Hemolysis near an ultrasonically pulsating gas bubble. Science 169 (3948), 869871.CrossRefGoogle ScholarPubMed
Sarkar, K., Katiyar, A. & Jain, P. 2009 Growth and dissolution of an encapsulated contrast microbubble. Ultrasound Med. Biol. 35 (8), 13851396.CrossRefGoogle ScholarPubMed
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), 539550.CrossRefGoogle ScholarPubMed
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), 824833.CrossRefGoogle 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), 268275.CrossRefGoogle ScholarPubMed
Stuart, J. T. 1966 Double boundary layers in oscillatory viscous flow. J. Fluid Mech. 24, 673687.CrossRefGoogle Scholar
Thameem, R., Rallabandi, B. & Hilgenfeldt, S. 2016 Particle migration and sorting in microbubble streaming flows. Biomicrofluidics 10 (1), 014124.CrossRefGoogle ScholarPubMed
Tho, P., Manasseh, R. & Ooi, A. 2007 Cavitation microstreaming patterns in single and multiple bubble systems. J. Fluid Mech. 576, 191233.CrossRefGoogle 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), 40594070.CrossRefGoogle ScholarPubMed
Vollmers, H. 2001 Detection of vortices and quantitative evaluation of their main parameters from experimental velocity data. Meas. Sci. Technol. 12 (8), 11991207.CrossRefGoogle Scholar
Wang, C., Jalikop, S. V. & Hilgenfeldt, S. 2012 Efficient manipulation of microparticles in bubble streaming flows. Biomicrofluidics 6 (1), 012801.CrossRefGoogle ScholarPubMed
Westervelt, P. J. 1953 The theory of steady rotational flow generated by a sound field. J. Acoust. Soc. Am. 25 (1), 6067.CrossRefGoogle Scholar
Wu, J. & Du, G. 1997 Streaming generated by a bubble in an ultrasound field. J. Acoust. Soc. Am. 101 (4), 18991907.CrossRefGoogle 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), 125129.CrossRefGoogle ScholarPubMed
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), 39944003.CrossRefGoogle ScholarPubMed
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 ScholarPubMed
Cited by

Send article to Kindle

To send this article to your Kindle, first ensure 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 sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ 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.

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

Send article to Dropbox

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

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

Send article to Google Drive

To send 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 use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

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