Skip to main content Accessibility help

Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications

  • C.-T. Hsiao (a1), J.-K. Choi (a1), S. Singh (a1), G. L. Chahine (a1), T. A. Hay (a2), Yu. A. Ilinskii (a2), E. A. Zabolotskaya (a2), M. F. Hamilton (a2), G. Sankin (a3), F. Yuan (a3) and P. Zhong (a3)...


Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.


Corresponding author

Email address for correspondence:


Hide All
Arndt, R. E. A 1981 Cavitation in fluid machinery and hydraulic structure. Annu. Rev. Fluid Mech. 13, 273328.
Blake, J. R. & Gibson, D. C. 1987 Cavitation bubbles near boundaries. Annu. Rev. Fluid Mech. 19, 99123.
Brennen, C. E. 1995 Cavitation and Bubble Dynamics. Oxford University Press.
Calvisi, M. L., Iloreta, J. I. & Szeri, A. J 2008 Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies nonspherical cavitation collapse. J. Fluid Mech. 616, 6397.
Chahine, G. L. 1982 Experimental and asymptotic study of nonspherical bubble collapse. Appl. Sci. Res. 38, 187197.
Chahine, G. L. 1991 Dynamics of the interaction of non-spherical cavities. In Mathematical Approaches in Hydrodynamics (ed. Miloh, T.). SIAM.
Chahine, G. L. 1993 Cavitation dynamics at microscale level. J. Heart Valve Disease 3, 102116.
Chahine, G. L. 1994 Strong interactions bubble/bubble and bubble/flow. In Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.). Kluwer.
Chahine, G. L. 1995 Bubble interactions with vortices. In Vortex Flows (ed. Green, S.), chap. 18, Kluwer.
Chahine, G. L. 1996 Scaling of mechanical heart valves for cavitation inception observation and acoustic detection. J. Heart Valve Disease 5, 207215.
Chahine, G. L. 2005 Numerical studies of the interaction of multiple explosion bubbles (limited distribution). Crit. Technol. Shock Vib. 3 (1), 113.
Chahine, G. L. & Duraiswami, R. 1993 Method for calculating 2-D and 3-D underwater explosion bubble behavior in free water and near structure. NSWC Dahlgren Div. Rep. NSWCDD/TR-93/44.
Chahine, G. L., Duraiswami, R. & Kalumuck, K. M 1997 Boundary element method for calculating 2-D and 3-D underwater explosion bubble loading on nearby structures including fluid-structure interaction effects. NSWC Dahlgren Div. Rep. NSWCDD/TR-93/46.
Chahine, G. L., Duraiswami, R. & Rebut, M. 1992 Analytical and numerical study of large bubble/bubble and bubble/flow interactions, In 19th ONR Symposium of Naval Hydrodynamics, Seoul S. Korea, 679–699.
Chahine, G. L. & Liu, H. L. 1985 A singular perturbation theory of the growth of a bubble cluster in a superheated liquid. J. Fluid Mech 156, 257279.
Chahine, G. L. & Morine, A. K. 1980 The influence of polymer additives on the collapse of a bubble between two solid walls. ASME Cavitation and Polyphase Flow Forum, New Orleans, Louisiana.
Chahine, G. L., Perdue, T. O. & Tucker, C. B. 1989 Interaction between underwater explosion bubble and a solid submerged body. Dynaflow Inc. Tech. Rep. 89001-1.
Chen, H., Brayman, A. A., Bailey, M. R. & Matula, T. J. 2010 Blood vessel rupture by cavitation. Urol Res. 39, 321326.
Chen, H., Brayman, A. A., Bailey, M. R. & Matula, T. J. 2011 Observations of translation and jetting of ultrasound-activated microbubbles in mesenteric microvessel. Ultraso. Med. Biol. 37, 21392148.
Cui, J., Hamilton, M. F., Wilson, P. S. & Zabolotskaya, E. A. 2006 Bubble pulsations between parallel plates. J. Acoust. Soc. Am. 119 (4), 20672072.
Darrozes, J. S. & Chahine, G. L. 1983 Les Recherches sur le Phenomne de Cavitation Effectues L’Ecole Nationale Suprieure de Techniques Avances. Sciences et Techniques de L’Armement, Memorial de l’Artillerie Francaise, 11–183.
Gonzalez-Avila, S. L., Klaseboer, E., Khoo, B. C. & Ohl, C.-D. 2011 Cavitation bubble dynamics in a liquid gap of variable height. J. Fluid Mech. 682, 241260.
Gracewski, S. M., Miao, H. & Dalecki, D. 2005 Ultrasonic excitation of a bubble near a rigid or deformable sphere: implications for ultrasonically induced hemolysis. J. Acoust. Soc. Am. 117 (3), 18.
Haines, J. R., Riemer, B. W., Felde, D. K., Hunn, J. D., Pawel, S. J. & Tsai, C. C. 2005 Summary of cavitation erosion investigations for the SNS mercury target. J. Nucl. Mater. 343 (1–3), 5869.
Haubold, A. D., Ely, J. L. & Chahine, G. L. 1994 Effect of cavitation on pyrolytic carbon in vitro. J. Heart Valve Dis. 3, 318323.
Hay, T. A., Ilinskii, Yu. A., Zabolotskaya, E. A. & Hamilton, M. F. 2012 Model for bubble pulsation in liquid between parallel viscoelastic layers. J. Acoust. Soc. Am. 132 (1), 124137.
Hsiao, C.-T. & Chahine, G. L. 2010 3DynaFS ©A Three-dimensional Free Surface and Bubble Dynamics Code. Dynaflow, Inc., User Manual 7.085.
Hsiao, C.-T., Lu, X. & Chahine, G. L. 2010 Three-dimensional modelling of the dynamics of therapeutic ultrasound contrast agent. Ultraso. Med. Biol. 36 (12), 20652079.
Ilinskii, Y. A., Zabolotskaya, E. A., Hay, T. A. & Hamilton, M. F. 2012 Models of cylindrical bubble pulsations. J. Acoust. Soc. Am. 133 (3), 13461357.
Iloreta, J. I., Fung, N. & Szeri, A. J 2008 Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 1. Consequences of interference between incident and reflected waves. J. Fluid Mech. 616, 4361.
Knapp, R. T., Daily, J. W. & Hammitt, F. G. 1970 Cavitation. McGraw-Hill.
Krieger, J. & Chahine, G. L. 2005 Acoustic signals of underwater explosions Near surfaces. J. Acoust. Soc. Am. 118 (5), 29612974.
Kroninger, D., Kohler, K., Kurz, T. & Lauterborn, W. 2010 Particle tracking velocimetry of the flow field around a collapsing cavitation bubble. Exp. Fluids 48 (3), 395408.
Lauterborn, W. & Bolle, H. 1975 Experimental investigations of cavitation-bubble collapse in the neighbourhood of a solid boundary. J. Fluid Mech. 72, 391399.
Leighton, T. 2012 The inertial terms in equations of motion for bubbles in tubular vessels or between plates. J. Acoust. Soc. Am. 130, 33333338.
Lim, K. Y., Quinto-Su, P. A., Klaseboer, E. & Khoo, B. C. 2010 Nonspherical laser-induced cavitation bubbles. Phys. Rev. E 81, 016308.
Miao, H., Gracewski, S. M. & Dalecki, D. 2008 Ultrasonic excitation of a bubble inside a deformable tube: implications for ultrasonically induced hemorrhage. J. Acoust. Soc. Am. 124 (4), 23742384.
Miller, D. L 1987 A review of ultrasonic bioeffects of microsonation, gas-body activation, and related cavitation-like phenomena. Ultraso. Med. Biol. 13, 443470.
Mitragotri, S. 2005 Innovation healing sound: the use of ultrasound in drug delivery and other therapeutic applications. Nature Rev. Drug Dis. 4 (3), 255260.
Overvelde, M., Garbin, V., Dollet, B., Cojoc, D., Ferrari, E., de Jong, N., Fabrizio, E. D., Lohse, D. & Versluis, M. 2007 3D optical micromanipulation of ultrasound contrast agents: bubble-wall and bubble–bubble interactions. In Proceedings of the 19th International Congress on Acoustics, Paper NLA-02-005-IP.
Pishchalnikov, Y. A., Sapozhnikov, O. A., Bailey, M. R., Williams, J. C., Cleveland, R. O., Colonius, T., Crum, L. A., Evan, A. P. & McAteer, J. A. 2003 Cavitation bubble cluster activity in the breakage of kidney stones by lithotripter shockwaves. J. Endourol. 17, 435446.
Plesset, M. S. & Chapman, R. B. 1971 Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary. J. Fluid Mech. 47 (2), 283290.
Plesset, M. S. & Prosperetti, A. 1977 Bubble dynamics and cavitation. Annu. Rev. Fluid Mech. 9, 145185.
Sankin, G. N., Yuan, F. & Zhong, P 2010 Pulsating tandem microbubble for localized and directional single cell membrane poration. Phys. Rev. Lett. 105 (7), 078101.
Shima, A. & Sato, Y 1980 The behaviour of a bubble between narrow parallel plates. Z. Angew. Math. Phys. 31, 691704.
Shima, A & Tomita, Y 1981 The behavior of a spherical bubble near a solid wall in a compressible liquid. Ing.-Arch. 51, 243255.
Tomita, Y., Robinson, P. B., Tong, R. P. & Blake, J. R. 2002 Growth and collapse of cavitation bubbles near a curved rigid boundary. J. Fluid Mech. 466, 259283.
Tomita, Y., Sato, K. & Shima, A 1994 Interaction of two laser-produced cavitation bubbles near boundaries. In Bubble Dynamics and Interface Phenomena (ed. Blake, J. R., Boulton-Stone, J. M. & Thomas, N. H.), Kluwer.
Wilson, S. K. 2010 Dynamics of a two-dimensional vapour bubble confined between superheated or subcooled parallel plates. Phys. Rev. E 81, 046314.
Yuan, F., Sankin, G. N. & Zhong, P. 2011 Dynamics of tandem bubble interaction in a microfluidic channel. J. Acoust. Soc. Am. 130, 3339.
Zhang, J., Duncan, J. H. & Chahine, G. L. 1993 The final stage of the collapse of a cavitation bubble near a rigid wall. J. Fluid Mech. 257, 147181.
Zhong, P., Cocks, F. H., Cioanta, I. & Preminger, G. M. 1997 Controlled, forced collapse of cavitation bubbles for improved stone fragmentation during shock wave lithotripsy. J. Urol.: Invest. Urol. 158, 23232328.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications

  • C.-T. Hsiao (a1), J.-K. Choi (a1), S. Singh (a1), G. L. Chahine (a1), T. A. Hay (a2), Yu. A. Ilinskii (a2), E. A. Zabolotskaya (a2), M. F. Hamilton (a2), G. Sankin (a3), F. Yuan (a3) and P. Zhong (a3)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed