The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is establish that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time.
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that singular points are formed at the fluid boundary in a finite time; at these points, the boundary curvature significantly increases and undergoes a discontinuity. The amplitude and slope angles of the boundary remain small. The singular behavior of the system is demonstrated by spectral functions of the fluid surface - they acquire a power dependence. Near the…
We study experimentally and numerically the thinning of a Newtonian leaky-dielectric filament subject to an axial electric field. We consider moderately viscous liquids with high permittivity. The experiments show that satellite droplets are produced from the breakup of the filaments with high electrical permittivity due to the action of the electric field. Two electrified filaments with the same minimum radius thin at the same speed regardless of when the voltage was applied. The numerical simulations show that the polarization stress is responsible for the pinching delay observed in the expe…
We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates …
Development of strongly nonlinear structures at the charged boundary of a non-conducting liquid in an electric field
Institute of Electrophysics, Russian Academy of Sciences（俄罗斯科学院电物理研究所）；Lebedev Physical Institute, RAS（俄罗斯科学院列别杰夫物理研究所）；Institute of Electrophysics, Ural Division, Russian Academy of Sciences（俄罗斯科学院乌拉尔分院电物理研究所）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术学院）
The properties and structure of electrically-stressed ionic liquid menisci experiencing ion evaporation are simulated using an electrohydrodynamic model with field-enhanced thermionic emission in steady state for an axially-symmetric geometry. Solutions are explored as a function of the external background field, meniscus dimension, hydraulic impedance and liquid temperature. Statically stable solutions for emitting menisci are found to be constrained to a set of conditions: a minimum hydraulic impedance, a maximum current output, and a narrow range of background fields that maximizes at menis…
Liquid metal ion sources (LMIS) are widely used in applications ranging from local ion implantation in semiconductors, to focused ion beam systems for milling and nanolithography, to space micropropulsion devices being developed by NASA. Above a critically large field strength, an electrically stressed liquid metal develops one or more cuspidal protrusions which undergo accelerated conic tip sharpening with runaway field self-enhancement. Zubarev (2001) first predicted from an inviscid model that the electric stresses at the liquid apex undergo self-similar divergent growth in finite time. The…
A direct numerical simulation of the interaction of plane capillary waves on the surface of a liquid dielectric in an external tangential electric field taking into account viscous forces has been performed. It has been shown that the interaction of counter-propagating nonlinear waves can generate a direct energy cascade. In the quasistationary energy dissipation regime, probability density functions for angles of inclination of the boundary tend to a Gaussian distribution and the shape of the boundary becomes complex and chaotic. The spectrum of the surface perturbations in this regime is des…
Experimental studies were carried out on the motions and transformations of liquid metal in ionic liquid under applied electric field. The induced vortex rings and flows of ionic liquid were determined via the photographs taken sequentially over the experiments. The polarization of electric double layer of liquid metals was employed to explain the flow of ionic liquid with the presence of liquid metal. Unlike former observation of liquid metal machine in conventional solution, no gas bubble was generated throughout the whole experiments, which makes it possible to encapsulate the liquid system…
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 counter-propagating waves interaction 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…
The weakly nonlinear dynamics of the free surface of a dielectric liquid in an electric field directed tangentially to the unperturbed boundary is investigated numerically. Within the framework of the strong field model, when the effects of capillarity and gravity are not taken into account, it is shown that nonlinear surface waves have a tendency to break. In result of the collapse of the surface waves, the curvature of the boundary and the gradient of the local electric field undergo infinite discontinuity on the surface of the liquid. The angles of the boundary inclination remain small. The…
Nonlinear dynamics of the free surface of an ideal incompressible non-conducting fluid with high dielectric constant subjected by strong horizontal electric field is simulated on the base of the method of conformal transformations. It is demonstrated that interaction of counter-propagating waves leads to formation of regions with steep wave front at the fluid surface; angles of the boundary inclination tend to π/2, and the curvature of surface extremely increases. A significant concentration of the energy of the system occurs at these points. From the physical point of view, the appearance of …
In the present study, we have studied the electro-hydrodynamic of a physical system where a Newtonian dielectric liquid column or droplet suspended in another Newtonian dielectric liquid medium in presence of a simple shear flow. Taking both the phases as leaky dielectric and perfect dielectric in to consideration, we have performed 2D numerical solution for capturing the essential features of droplet deformation in between the parallel plate configuration. For a perfect dielectric system, this study shows that the deformation characteristic follows a monotonic as well as non-monotonic variati…
