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Register a new userSufficient integral criteria for instability of the free charged surface of an ideal liquid
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Applying the method of integral estimates to the analysis of three-wave processes we derive the sufficient criteria for the hard loss of stability of the charged plane surface of liquids with different physical properties. The influence of higher-order wave interactions on the instability dynamics is also discussed.
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The nonlinear dynamics of charged-surface instability development was investigated for liquid helium far above the critical point. It is found that, if the surface charge completely screens the field above the surface, the equations of three-dimensional (3D) potential motion of a fluid are reduced to the well-known equations describing the 3D Laplacian growth process. The integrability of these equations in 2D geometry allows the analytic description of the free-surface evolution up to the formation of cuspidal singularities at the surface.
We analyze nonlinear dynamics of the Kelvin-Helmholtz quantum instability of the He-II free surface, which evolves during counterpropagation of the normal and superfluid components of liquid helium. It is shown that in the vicinity of the linear stability threshold, the evolution of the boundary is described by the $|phi|^4$ Klein-Gordon equation for the complex amplitude of the excited wave with cubic nonlinearity. It is important that for any ratio of the densities of the helium component, the nonlinearity plays a destabilizing role, accelerating the linear instability evolution of the boundary. The conditions for explosive growth of perturbations of the free surface are formulated using the integral inequality approach. Analogy between the Kelvin-Helmholtz quantum instability and electrohydrodynamic instability of the free surface of liquid helium charged by electrons is considered.
The dynamics of the development of instability of the free surface of liquid helium, which is charged by electrons localized above it, is studied. It is shown that, if the charge completely screens the electric field above the surface and its magnitude is much larger then the instability threshold, the asymptotic behavior of the system can be described by the well-known 3D Laplacian growth equations. The integrability of these equations in 2D geometry makes it possible to described the evolution of the surface up to the formation of singularities, viz., cuspidal point at which the electric field strength, the velocity of the liquid, and the curvature of its surface assume infinitely large values. The exact solutions obtained for the problem of the electrocapillary wave profile at the boundary of liquid helium indicate the tendency to a charge in the surface topology as a result of formation of charged bubbles.
We report the generation of a dynamic labyrinthine pattern in an active alcohol film. A dynamic labyrinthine pattern is formed along the contact line of air/pentanol/aqueous three phases. The contact line shows a clear time-dependent change with regard to both perimeter and area of a domain. An autocorrelation analysis of time-development of the dynamics of the perimeter and area revealed a strong geometric correlation between neighboring patterns. The pattern showed autoregressive behavior. The behavior of the dynamic pattern is strikingly different from those of stationary labyrinthine patterns. The essential aspects of the observed dynamic pattern are reproduced by a diffusion-controlled geometric model.
The problem of determining equilibrium configurations of the free surface of a conducting liquid is considered with allowance for a finite interelectrode distance. The analogy is established between this electrostatic problem and that of finding the profile of a progressive capillary wave on the free surface of a liquid layer of a finite depth, which was solved by Kinnersley. This analogy allowed exact solutions to be obtained for the geometry of liquid electrodes, which expand the existing notions about the possible stationary states of the system.
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