Abstract
The nonlinear dynamics of the interface between dielectric fluids in a strong horizontal electric field is studied. It is shown that three-dimensional waves of small but finite amplitude can propagate without shape distortions either in a direction coinciding with the direction of the external field vector or in the direction opposite to this vector, along the interface of the fluids, whose density ratio is directly proportional to the ratio of their dielectric constants. For this particular case, an analytical description of the interaction of counterpropagating weakly nonlinear waves of arbitrary shape is given.
Similar content being viewed by others
References
J. R. Melcher, Field-Coupled Surface Waves (MIT Press, Cambridge, 1963).
J. R. Melcher, “Electrohydrodynamic and Magnetohydrodynamic SurfaceWaves and Instabilities,” Phys. Fluids 4, 1348–1354 (1961).
J. R. Melcher and W. J. Schwarz, “Interfacial Relaxation Overstability in a Tangential Electric Field,” Phys. Fluids 11, 2604–2616 (1968).
M. F. El-Sayed, “Electro-Aerodynamic Instability of a Thin Dielectric Liquid Sheet Sprayed with an Air Stream,” Phys. Rev. E 60, 7588–7591 (1999).
L. L. Barannyk, D. T. Papageorgiou, and P. G. Petropoulos, “Suppression of Rayleigh-Taylor Instability Using Electric Fields,” Math. Comput. Simulat. 82, 1008–1016 (2012).
B. S. Tilley, P. G. Petropoulos, and D. T. Papageorgiou, “Dynamics and Rupture of Planar Electrified Liquid Sheets,” Phys. Fluids 13, 3547–3563 (2001).
D. T. Papageorgiou and J.-M. Vanden-Broeck, “Large-Amplitude Capillary Waves in Electrified Fluid Sheets,” J. Fluid Mech. 508, 71–88 (2004).
O. Ozen, D. T. Papageorgiou, and P. G. Petropoulos, “Nonlinear Stability of a Charged Electrified Viscous Liquid Sheet under the Action of a Horizontal Electric Field,” Phys. Fluids 18, 042102 (2006).
S. Grandison, D. T. Papageorgiou, and J.-M. Vanden-Broeck, “Interfacial Capillary Waves in the Presence of Electric Fields,” Eur. J. Mech., B: Fluids 26, 404–421 (2007).
N. M. Zubarev, “Nonlinear Waves on the Surface of a Dielectric Liquid in a Strong Tangential Electric Field,” Phys. Lett., A 333, 284–288 (2004).
N. M. Zubarev and O. V. Zubareva, “Dispersionless Propagation of Finite-Amplitude Waves on the Surface of a Dielectric Liquid in a Tangential Electric Field,” Pis’ma Zh. Tekh. Fiz. 32(20), 40–44 (2006).
N. M. Zubarev, “Nonlinear Waves on the Surface of a Dielectric Liquid in a Horizontal Electric Field in 3d Geometry: Exact Solutions,” Pis’ma Zh. Tekh. Fiz. 89(6), 317–321 (2009).
N. M. Zubarev and O. V. Zubareva, “Propagation of Large-Amplitude Waves on Dielectric Liquid Sheets in a Tangential Electric Field: Exact Solutions in Three-Dimensional Geometry,” Phys. Rev. E 82, 046301 (2010).
V. E. Zakharov, “Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid,” Prikl. Mekh. Tekh. Fiz. 9(2), 86–94 (1968) [J. Appl. Mech. Tech. Phys. 9 (2), 352–362 (1968)].
E. A. Kuznetsov, M. D. Spector, and V. E. Zakharov, “Surface Singularities of Ideal Fluid,” Phys. Lett., A 182, 387–393 (1993).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N.M. Zubarev, E.A. Kochurin.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 54, No. 2, pp. 52–58, March–April, 2013.
Rights and permissions
About this article
Cite this article
Zubarev, N.M., Kochurin, E.A. Three-dimensional nonlinear waves at the interface between dielectric fluid in an external horizontal electric field. J Appl Mech Tech Phy 54, 212–217 (2013). https://doi.org/10.1134/S0021894413020053
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894413020053