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Interaction between two laser-induced cavitation bubbles in a quasi-two-dimensional geometry



We report on experimental and numerical studies of pairs of cavitation bubbles growing and collapsing close to each other in a narrow gap. The bubbles are generated with a pulsed and focused laser in a liquid-filled gap of 15 μm height; during their lifetime which is shorter than 14 μs they expand to a maximum radius of up to Rmax = 38 μm. Their motion is recorded with high-speed photography at up to 500000 frames s−1. The separation at which equally sized bubbles are created, d, is varied from d = 46–140 μm which results into a non-dimensional stand-off distance, γ = d/(2Rmax), from 0.65 to 2. For large separation the bubbles shrink almost radially symmetric; for smaller separation the bubbles repulse each other during expansion and during collapse move towards each other. At closer distances we find a flattening of the proximal bubbles walls. Interestingly, due to the short lifetime of the bubbles (≤14 μs), the radial and centroidal motion can be modelled successfully with a two-dimensional potential flow ansatz, i.e. neglecting viscosity. We derive the equations for arbitrary configurations of two-dimensional bubbles. The good agreement between model and experiments supports that the fluid dynamics is essentially a potential flow for the experimental conditions of this study. The interaction force (secondary Bjerknes force) is long ranged dropping off only with 1/d as compared to previously studied three-dimensional geometries where the force is proportional to 1/d2.


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Basset, A. B. 1887 On the motion of two spheres in a liquid. Proc. Lond. Math. Soc. 18, 369378.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bergmann, R., van der Meer, D., Stijnman, M., Sandtke, M., Prosperetti, A. & Lohse, D. 2006 Giant bubble pinch-off. Phys. Rev. Lett. 96, 154505.
Bjerknes, C. A. 1915 Hydrodynamische Fernkraft. Engelmann.
Bjerknes, V. F. K. 1906 Fields of Force. Columbia University Press.
Bremond, N., Arora, M., Dammer, S. M. & Lohse, D. 2006 a Interaction of cavitation bubbles on a wall. Phys. Fluids 18, 121505.
Bremond, N., Arora, M., Ohl, C. D. & Lohse, D. 2006 b Controlled multibubble surface cavitation. Phys. Rev. Lett. 18, 121505.
Crowdy, D. G., Surana, A. & Yick, K.-Y. 2007 The irrotational flow generated by two planar stirrers in inviscid fluid. Phys. Fluids 19, 018103.
Crum, L. A. 1975 Bjerknes forces on bubbles in a stationary sound field. J. Acoust. Soc. Am. 57, 13631370.
Dear, J. P., Field, J. E. & Walton, A. J. 1988 Gas compression and jet formation in cavities collapsed by a shock wave. Nature 332, 505508.
Doinikov, A. 2004 Mathematical model for collective bubble dynamics in strong ultrasound fields. J. Acoust. Soc. Am. 116, 821827.
Harkin, A., Kaper, T. J. & Nadim, A. 2001 Coupled pulsation and translation of two gas bubbles in a liquid. J. Fluid Mech. 445, 377411.
Hilgenfeldt, S., Brenner, M. P., Grossmann, S. & Lohse, D. 1998 Analysis of Rayleigh–Plesset dynamics for sonoluminescing bubbles. J. Fluid Mech. 365, 171204.
Illinskii, Y. A., Hamilton, M. F. & Zabotskaya, E. A. 2007 Bubble interaction dynamics in Lagrangian and Hamiltonian mechanics. J. Acoust. Soc. Am. 121, 786795.
Lamb, H. 1932 Hydrodynamics, 6th edition. Cambridge University Press.
Leighton, T. G. 1994 The Acoustic Bubble. Academic Press.
Lohse, D., Bergmann, R., Mikkelsen, R., Zeilstra, C., van der Meer, D., Versluis, M., van der Weele, K., van der Hoef, M. & Kuipers, H. 2004 Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003.
Luther, S., Mettin, R. & Lauterborn, W. 2000 Modeling acoustic cavitation by a Lagrangian approach. In Nonlinear Acoustics at the Turn of the Milenium, ISNA 15th International Symposium on Nonlinear Acoustics (ed. Lauterborn, W. & Kurz, T.), International Symposia on Nonlinear Acoustics, vol. 524, pp. 351354. AIP.
Nair, S. & Kanso, E. 2007 Hydrodynamically-coupled rigid bodies. J. Fluid Mech. 592, 393411.
Naudé, C. F. & Ellis, A. T. 1961 On the mechanism of cavitation damage by non hemispherical cavities collapsing in contact with a solid boundary. Trans. ASME D.: J. Basic Engng 83, 648656.
Oguz, H. N. & Prosperetti, A. 1993 Dynamics of bubble growth and detachment from a needle. J. Fluid. Mech. 257, 111145.
Quinto-Su, P. A., Venugopalan, V. & Ohl, C. D. 2008 Generation of laser-induced cavitation bubbles with a digital hologram. Opt. Exp. 16, 1896418969.
Rayleigh, L. 1917 On the pressure developed in a liquid during the collapse of a spherical cavity. Phil. Mag. 34, 9498.
Wang, Q. X. 2004 Interaction of two circular cylinders in inviscid fluid. Phys. Fluids 16, 44124425.
Zwaan, E., Gac, S.Le Tsuji, K. & Ohl, C. D. 2007 Controlled cavitation in microfluidic systems. Phys. Rev. Lett. 98, 254501.
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Interaction between two laser-induced cavitation bubbles in a quasi-two-dimensional geometry



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