Formation of curvature singularities on the interface between dielectric liquids in a strong vertical electric field

Kochurin, E. A.; Зубарев, Н. М.; Zubareva, O. V.

doi:10.1103/physreve.88.023014

Cited by 22 publications

(17 citation statements)

References 36 publications

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“…[23,24], there is a tendency for the formation of the sign-definite singularities of the type of η xx ∼ |x − x c | −1/2 on the boundary of a conducting liquid at the nonlinear stage of the Tonks-Frenkel instability. Note also that similar properties are demonstrated by the interface between two ideal dielectric fluids in a strong vertical electric field [25].…”

Section: Discussionsupporting

confidence: 60%

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Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

Зубарев

Kuznetsov

2014

J. Exp. Theor. Phys.

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The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small interface angle approximation (gravity and capillary forces are neglected) admit exact solutions in the implicit form. The analysis of these solutions shows that, in the general case, weak root singularities are formed on the interface in a finite time for which the curvature becomes infinite, while the slope angles remain small. For Atwood numbers close to unity in absolute values, the surface curvature has a definite sign correlated with the boundary deformation directed towards the light fluid. For fluids with comparable densities, the curvature changes its sign in a singular point. In the particular case of fluids with equal densities, the obtained results are consistent with those obtained by Moore based on the Birkhoff-Rott equation analysis.

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Section: Discussionsupporting

confidence: 60%

“…where n is an integer number. Substituting this expression into (25), we find that the branch points of the function V move over the lower half-plane of the complex variable x towards the real axis along the straight lines parallel to the imaginary axis,…”

Section: Evolution Of Periodic Perturbations Of the Interfacementioning

confidence: 99%

Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

Зубарев

Kuznetsov

2014

J. Exp. Theor. Phys.

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“…It is important that the phenomenon of the phase shift cannot be described in the framework of the analytical solution (7). This is probably related with the fact that the solution (7) was obtained for the spatially localized functions; in the present study the periodicity can affect sufficiently on the system evolution. As it is seen from the figure 2 (b), the effect is inversely proportional to the fluid depth τ − τ l ∼ d −1 , i.e., it is very sensitive to variation of d. It is interesting to note that the similar phenomenon of phase shift is demonstrated by the soliton solutions of the Korteweg-de Vries equation [27].…”

Section: Simulation Of Waves Interactionmentioning

confidence: 77%

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

Kochurin¹,

Зубарев²

2018

J. Phys.: Conf. Ser.

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Abstract. Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

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“…IT is well known [1] that an external electric field directed tangentially to the unperturbed free or contact surfaces of dielectric liquids has a stabilizing effect on the boundary. On the contrary, the normal field results in an aperiodic growth of the boundary perturbations [2][3][4]. In recent years, new experimental results concerning the influence of electric field on dynamics of capillary waves on the surface of dielectric liquids have been obtained [5,6].…”

Section: Introductionmentioning

confidence: 99%

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

Kochurin

Зубарев

2018

IEEE Trans. Dielect. Electr. Insul.

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Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The computational method is based on the time-dependent conformal transformation of the region occupied by the fluid into a half-plane. In the limit of a strong electric field, when the gravitational and capillary forces are negligibly small, there exists an exact analytical solution of the electro-hydrodynamic equations describing propagation without distortions of nonlinear surface waves along (or against) the electric field direction. In the situation where gravity and capillarity are taken into account, the results of numerical simulations indeed show that, for large external field, the waves traveling in a given direction tend to preserve their shape. In the limit of a strong electric field, the interaction of counter-propagating waves leads to the formation of regions, where the electrostatic and dynamic pressures undergo a discontinuity, and the curvature of the surface increases infinitely. The Fourier spectrum of the surface perturbations tends to the power-law distribution (k -2 ). In the case of a finite electric field, the wave interaction results in a radiation of massive cascade of small-scale capillary waves that causes the chaotic behavior of the system. The investigated mechanism of interaction between oppositely-traveling waves can enhance development of the capillary turbulence of the fluid surface.

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Formation of curvature singularities on the interface between dielectric liquids in a strong vertical electric field

Cited by 22 publications

References 36 publications

Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

Singularity formation on a fluid interface during the Kelvin-Helmholtz instability development

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

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