Abstract
Nonlinear shape oscillations of 2D incompressible bubbles in an inviscid fluid, subject to a forced vibration in microgravity, have been studied numerically. Forced vibration induces an oscillatory translational motion as well as shape oscillations. It is shown that for large enough oscillation amplitudes, the coupling between the shape oscillation and the translational motion of a bubble results in a chaotic behaviour. For two-bubble systems, the bubbles may attract each other. The attraction force is stronger at higher Bond numbers. Higher Bond numbers also yield larger bubble deformation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akhatov, I.S., Konovalova, S.I.: Regular and chaotic dynamics of a spherical bubble. J. Appl. Math. Mech. 69, 575–584 (2005)
Alexander, I.: Impulse, vibrations and random disturbances: concequences for convective diffusive transport and fluid interfaces in low gravity experiments. AIAA 96–2073, presented at 27th Fluid Dynamics Conference, New Orleans, LA, 17–20 June (1996)
Azuma, H., Yoshihara, S.: Three-dimensional large-amplitude drop oscillations: experiments and theoretical analysis. J. Fluid Mech. 393, 309–332 (1999)
Barbat, T. Ashgriz, N., Liu, C.: Dynamics of two interacting bubbles in an acoustic field. J. Fluid Mech. 389, 137–168 (1999)
Basaran, O.A.: Nonlinear oscillations of viscous liquid drops. J. Fluid Mech. 241, 169–198 (1992)
Benjamin, T.B., Ellis, A.T.: Self-propulsion of asymmetrically vibrating bubbles. J. Fluid Mech. 212, 65–80 (1990)
Bjerknes, V.: Fields of Force. Columbia University Press (1906)
Bussmann, M., Mostaghimi, J., Chandra, S.: On a three dimensional volume tracking model of droplet impact. Phys. Fluids 11, 1408–1417 (1999)
Cummins, S., Francois, M., Kothe, D.: Estimating curvature from volume fractions. Comput. Struct. 83, 425–434 (2005)
Doinikov, A.A.: Translational motion of a bubble undergoing shape oscillations. J. Fluid Mech. 501, 1–24 (2004)
Eller, A., Crum, L.: Instability of the motion of a pulsating bubble in a sound field. J. Acoust. Soc. Am. 47, 762–767 (1970)
Farris, S.C., Bugg, D.J., Gabriel, K.S.: The motion of bubbles in a sinusoidally oscillating liquid in microgravity. Microgravity Sci. Technol. XV/3, 28–35 (2004)
Feng, Z.C., Su, Y.H.: Numerical simulations of the translational and shape oscillations of a liquid drop in an acoustic field. Phys. Fluids 9(3), 519–529 (1997)
Francois, M., Cummins, S., Dendy, E., Kothe, D., Sicilian, J., Williams, M.: A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework. J. Comput. Phys. 213, 141–173 (2006)
Friesen, T.J., Takahira, H., Allegro, L., Yasuda, Y., Kawaji, M.: Numerical simulations of bubble motion in a vibrated cell under microgravity using level set and VOF algorithms. Ann. N.Y. Acad. Sci. 974, 288–305 (2002)
Golpaygan, A., Ashgriz, N.: Multiphase flow model to study channel flow dynamics of PEM fuel cell: deformation and detachment of water droplets. Int. J. Comput. Fluid Dyn. 22, 85–95 (2008)
Golpaygan, A., Hsu, N., Ahgriz, N.: Numerical investigation of impact and penetration of a droplet onto a porous substrate. J. Porous Media 11(4), 323–341 (2008)
Ishikawa, M., Nakamura, T., Yoda, S., Samejima, H., Goshozono, T.: Responsive motion of bubbles to periodic g-jitter. Microgravity Sci. Technol. VII/2, 164–168. (1994)
Kang, M., Fedkiw, R.P., Liu, X.: A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15(3), 323–360 (2000)
Lamb, H.: Hydrodynamics. Cambridge University Press (1930)
Lauterborn, W., Kurz, T.: Physics of bubble oscillations. Rep. Prog. Phys. 73, 1–88 (2010)
Lundgren, T.S., Mansour, N.N.: Oscillation of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479–510 (1988)
Miller, C.A., Scriven, L.E.: The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–435 (1968)
Monti, R.: Gravity jitters: effect on typical fluid science experiments, in low gravity fluid dynamics and transport phenomena. AIAA Progr. Aeronaut. Astronaut. 130, 275–307 (1990)
Patzek, T.W., Benner, R.E., Bassaran, O.A., Scriven, L.E.: Nonlinear oscillations of inviscid free drops. J. Comput. Phys. 97, 489–515 (1991)
Pelekasis, N.A., Tsamopoulos, J.A.: Bjerknes forces between two bubbles. Part 2. Response to an oscillatory pressure field. J. Fluid Mech. 254, 500–527 (1993)
Press, W.H.: Numerical recipes in FORTRAN: the art of scientific computing. Cambridge University Press (1992)
Rayleigh, L.: On the capillary phenomena of jets. Proc. R. Soc. Lond. 29, 71–97 (1879)
Trinh, E., Wang, T.G.: Large-amplitude free and driven drop-shape oscillations: experimental observations. J. Fluid Mech. 122, 315–338 (1982)
Trinh, E.H., Holt, R.G., Thiessen, D.B.: The dynamics of ultrasonically levitated drops in an electric field. Phys. Fluids 8(1), 43–61 (1996)
Trinh, E.H., Thiessen, D.B., Holt, R.G.: Driven and freely decaying nonlinear shape oscillations of drops and bubbles immersed in a liquid: experimental results. J. Fluid Mech. 364, 253–272 (1998)
Tryggvason, B.V.: Acceleration levels and operation of the microgravity vibration isolation mount (MIM) on the shuttle and the MIR space station. AIAA 99–0578, 37th AIAA Aerospace Sciences Meeting and Exhibition, Jan. 11–14, Reno, Nevada (1999)
Watanabe, T., Kukita, Y.: Translational and radial motions of a bubble in an acoustic standing wave field. Phys. Fluids A 5, 2682–2688 (1993)
Yoshikawa, H.N., Zoueshtiagh, F., Caps, H., Kurowski, P., Petitjeans, P.: Bubble splitting on oscillatory flows on ground and in reduced gravity. Eur. Phys. J. E. 31, 191–199 (2010)
Youngs, D.L.: An Interface Tracking Method for a 3D Eulerian Hydrodynamics Code, Technical Report 44/92/35, AWRE (1984)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Movassat, M., Ashgriz, N. & Bussmann, M. Chaotic Shape and Translational Dynamics of 2D Incompressible Bubbles under Forced Vibration in Microgravity. Microgravity Sci. Technol. 24, 39–51 (2012). https://doi.org/10.1007/s12217-011-9289-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12217-011-9289-y