Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

Z. C. FENG

doi:10.1017/S0022112096004156

Abstract

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By examining the modal interaction between two non-resonant shape oscillation modes of a charged liquid drop, we have identified a new route to instability via nonlinear coupling. We present numerical simulation results to show that when shape perturbation of a high-mode number Legendre mode is applied to the drop, the prolate–oblate mode of the drop may grow unbounded. Using multiple-scale analysis, we derive amplitude equations for the high-mode-number shape mode and the prolate–oblate mode to show the nonlinear coupling between the two modes.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Gong, Zaisheng Chen, Honghan and Sun, Yongchuan 2000. Coupling processes between self-oscillation of formation pressure and periodic migration-accumulation of natural gases in Yinggehai Basin, South China Sea. Science in China Series D: Earth Sciences, Vol. 43, Issue. 5, p. 494.

Belonozhko, D. F. and Grigor’ev, A. I. 2000. Nonlinear capillary oscillation of a charged drop. Technical Physics, Vol. 45, Issue. 8, p. 1001.

Shiryaeva, S. O. Grigor’ev, A. I. Belonozhko, D. F. and Golovanov, A. S. 2001. Electromagnetic radiation of a nonlinearly oscillating charged drop. Technical Physics Letters, Vol. 27, Issue. 10, p. 875.

Shiryaeva, S. O. 2001. Nonlinear capillary vibrations and stability of a highly charged drop under single-mode initial deformation of large amplitude. Technical Physics, Vol. 46, Issue. 2, p. 158.

Shiryaeva, S. O. 2002. Nonlinear vibrations of a charged drop due to the initial excitation of neighboring modes. Technical Physics, Vol. 47, Issue. 4, p. 389.

Koromyslov, V. A. Shiryaeva, S. O. and Grigor’ev, A. I. 2003. Nonlinear capillary vibrations of a charged drop placed in a dielectric medium: Single-mode initial deformation of the drop shape. Technical Physics, Vol. 48, Issue. 9, p. 1124.

Shiryaeva, S. O. Grigor’ev, A. I. Koromyslov, V. A. and Zharov, A. N. 2003. On the calculation of the translational mode amplitude for a drop nonlinearly vibrating in an environment. Technical Physics, Vol. 48, Issue. 9, p. 1141.

Shiryaeva, S. O. 2003. On internal mode resonance in a nonlinearly vibrating volumetrically charged dielectric drop. Technical Physics, Vol. 48, Issue. 2, p. 152.

Zharov, A. N. Grigor’ev, A. I. and Shiryaeva, S. O. 2003. Internal nonlinear four-mode interactions of capillary oscillations of a charged drop. Technical Physics Letters, Vol. 29, Issue. 5, p. 388.

Rybakova, M. V. Shiryaeva, S. O. and Grigor’ev, A. I. 2004. Internal nonlinear resonance of charged drop capillary oscillations in a dielectric medium at multimode initial deformation of the interface. Technical Physics, Vol. 49, Issue. 1, p. 22.

Zharov, A. N. 2005. Nonlinear Oscillations of the Free Surface of a Charged Drop of a Highly Viscous Liquid. Technical Physics Letters, Vol. 31, Issue. 8, p. 635.

Shiryaeva, S. O. Grigor’ev, A. I. and Volkova, M. V. 2005. On the possibility of corona initiation near a conducting drop nonlinearly vibrating in an external electrostatic field. Technical Physics, Vol. 50, Issue. 7, p. 856.

Zharov, A. N. Grigor’ev, A. I. and Shiryaeva, S. O. 2005. Properties of expansions in Legendre polynomial derivatives that show up in analysis of nonlinear vibrations of a viscous liquid drop. Technical Physics, Vol. 50, Issue. 9, p. 1124.

Shiryaeva, S. O. Belonozhko, D. F. and Grigor’ev, A. I. 2005. On the internal nonlinear resonant three-mode interaction of charged drop oscillations. Technical Physics, Vol. 50, Issue. 2, p. 185.

Zharov, A. N. Grigor’ev, A. I. and Shiryaeva, S. O. 2005. Analytical study of nonlinear vibrations of a charged viscous liquid drop. Technical Physics, Vol. 50, Issue. 12, p. 1568.

Shiryaeva, S. O. Volkova, M. V. and Grigor’ev, A. I. 2005. Nonlinear oscillations of an uncharged conducting drop in an external uniform electrostatic field. Technical Physics, Vol. 50, Issue. 3, p. 321.

Grigor’ev, A. I. Zharov, A. N. and Shiryaeva, S. O. 2005. Effect of the initial deformation of a charged drop on nonlinear corrections to critical conditions for instability. Technical Physics, Vol. 50, Issue. 8, p. 1006.

Shiryaeva, S. O. 2006. Nonlinear vibrations of a charged drop in an electrostatic suspension. Technical Physics, Vol. 51, Issue. 3, p. 385.

Zharov, A. N. Grigor’ev, A. I. and Zharova, I. G. 2006. Evolution of the shape of a bubble deformed at the zero time in a viscous fluid. Technical Physics, Vol. 51, Issue. 3, p. 307.

Su, Y. H. 2006. A numerical study of electrostatic interactions between two charged conducting droplets. Physics of Fluids, Vol. 18, Issue. 4,

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Instability caused by the coupling between non-resonant shape oscillation modes of a charged conducting drop

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