Abstract
It is well known that if either a sinusoidal pressure disturbance or a simple pressure difference is imposed on a simply connected bubble, then the bubble surface will be forced into motion, oscillating nonlinearly about an equilibrium position and surface deformations soon set in. Assuming the departure from sphericity is small we can represent the surface distortion terms by an infinite sum of spherical harmonics. A Lagrangian is formulated to describe the system and then approximated by considering a finite number of modes only. Making use of the symbolic language MAPLE V the approximated system is reduced to a system of nonlinear amplitude equations which are then solved numerically to determine the bubble shape after a finite time evolution. Extensive results associated with these nonlinear oscillations are presented and compared with solutions obtained by a boundary integral numerical method.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benjamin, T.B.: 1987, Hamiltonian theory for motions of bubbles in an infinite fluid, J. Fluid Mech. 181, pp. 29–50
Benjamin, T.B. and Ellis, A.T.: 1990, Self-propulsion of asymmetrically vibrating bubbles, J. Fluid Mech. 212, pp. 65–80.
Holt, R.G., Holzfuss, J., Judt, A., Philip, A. and Horsburgh, S.: 1990, Forced nonlinear oscillations of single air bubbles in water: experimental results, it ISNA Austin
Kucera, A.: 1993, A boundary integral method applied to the growth and collapse of bubbles near a rigid boundary, J. Comput. Phys (submitted)
Landau, L.D. and Liftshifz, E.M.: 1960, Fluid Mechanics, Pergamon Press, Elmsford, NY Miles, J.: 1976, Nonlinear surface waves in closed basins, J. Fluid Mech. 75, pp. 419–448.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Shaw, S.J. (1994). Surface mode deformations on an oscillating bubble. In: Blake, J.R., Boulton-Stone, J.M., Thomas, N.H. (eds) Bubble Dynamics and Interface Phenomena. Fluid Mechanics and Its Applications, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0938-3_33
Download citation
DOI: https://doi.org/10.1007/978-94-011-0938-3_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4404-2
Online ISBN: 978-94-011-0938-3
eBook Packages: Springer Book Archive