Nonlinear electrohydrodynamic instability conditions of an interface between two fluids under the effect of a normal periodic electric field. III

A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal periodic electric field is subjected to nonlinear deformations. We use the method of multiple scales in order to solve the nonlinear equations. In the first-order problem we obtained Mathieu's differential equation. For the second order, we obtain the nonhomogeneous Mathieu equation and we use the method of multiple scales to obtain a sequence of equations. In the third order we obtain the second-order differential equation of periodic coefficients. Also, we obtain a formula for surface elevation. The stability conditions are determined.     

Effect of heat transfer on the penetration of an electromagnetic pulse into a plasma layer and the inverse skin effect

Penetration of a heating pulse into a plasma layer was studied using the system of coupled nonlinear equations for electric field, electron, and ion temperatures. Numerical calculations of field structure and temperature evolution are performed both in the absence and in the presence of heat transfer. It is established that heat transfer leads to a more rapid penetration of the field near the illuminated surface of the layer and impairs penetration in regions of the layer far from this surface. We found that heat transfer promotes the creation of more favourable conditions for manifestation of the inverse skin effect.     

Formation of singularities on the charged surface of a liquid-helium layer with a finite depth

The dynamics of the development of an instability of a charged surface of a liquid-helium layer with a finite depth is investigated. The equations describing the evolution of the free surface are derived with the use of conformal variables for the case in which the charge completely screens the electric field above the liquid. A model of the evolution of a spatially localized perturbation of a liquid-helium surface is proposed for the strong-field limit where the dynamics of the liquid is predominantly determined by the effect of electrostatic forces. This model describes the development of an instability of the initially planar boundary to the point of the formation of cuspidal dimples. The limit of an infinitely deep liquid is considered. The stability of the previously revealed liquid flow regime described by the Laplacian growth equations is proved without significant constraints on the surface geometry.     

Nonlinear electrohydrodynamic Rayleigh-Taylor instability with mass and heat transfer subject to a vertical oscillating force and a horizontal electric field

Weakly nonlinear stability of interfacial waves propagating between two electrified inviscid fluids influenced by a vertical periodic forcing and a constant horizontal electric field is studied. Based on the method of multiple-scale expansion for a small-amplitude periodic force, two parametric nonlinear Schrödinger equations with complex coefficients are derived in the resonance cases. A standard nonlinear Schrödinger equation with complex coefficients is derived in the nonresonance case. A temporal solution is carried out for the parametric nonlinear Schrödinger equation. The stability analysis is discussed both analytically and numerically.     

Effect of the processes of orientation of nonlinear optical fragments of a side chain in comb-shaped polymers of the methacrylic series on the second-harmonic generation in thin films

New comblike copolymers of methacrylic acid esters with an optically nonlinear chromophore—a derivative of the 4′-(4-nitrobenzylideneamino)phenol—in a side chain were obtained. Processes of forced orientation of nonlinear optical chromophores covalently bonded with the main chains in an electric field and the effects of the conditions of orientation on the nonlinear second-order optical activity of the polymer films were studied in some detail. The existence of a correlation between the chemical structure and the composition of the copolymers with the magnitude and the stability of the surface electron potential of the corresponding films was shown. It was established that a maximum extent of orientation of chromophores in the bulk of the polymer and, as a consequence, a high intensity of the second-harmonic signal were achieved when the thickness of the region of the uniform electric field maximally approached the thickness of the sample.     

Physical states and properties of barium titanate films in a plane electric field

The influence of a plane electric field on the phase states of barium titanate thin films under the conditions of forced deformation has been studied. The field dependence of a complete set of material constants has been taken in the region of the c-phase, where polarization losses are absent. The material constants are calculated using equations of the piezoelectric effect derived by linearizing the nonlinear equations of state from the phenomenological; theory for barium titanate. It has been shown that there is a critical value of the field at which the electromechanical coupling coefficient reaches a maximum.     

固体表面液滴铺展与润湿接触线的移动分析

液滴在固体表面上的铺展行为与润湿特性对许多工业生产过程的研究具有重要意义.根据液滴在光滑表面上的受力情况,建立了液滴平壁铺展的动力学模型.应用润滑近似方法和二维Navier-Stokes方程,建立了液滴沿理想表面铺展的动量和连续性方程.根据建立的方程,应用数值解法求解并详细分析了液滴在铺展过程中膜厚、接触线铺展半径以及铺展速度随时间的变化关系.研究结果表明:液滴的铺展过程可分为扩展和收缩两个阶段,铺展过程伴随着表面能、动能以及各种势能的相互转化,液滴最终的铺展半径大小由固体基面固有的润湿特性所决定;液滴在铺展过程中出现的"坍塌效应"与弯曲液面处的Laplace压力差有关;铺展半径随时间变化的标定律近似满足"1/7"次方标度律.     

An electrohydrodynamics model for non-equilibrium electron and phonon transport in metal films after ultra-short pulse laser heating

The electrons and phonons in metal films after ultra-short pulse laser heating are in highly non-equilibrium states not only between the electrons and the phonons but also within the electrons. An electrohydrodynamics model consisting of the balance equations of electron density, energy density of electrons, and energy density of phonons is derived from the coupled non-equilibrium electron and phonon Boltzmann transport equations to study the nonlinear thermal transport by considering the electron density fluctuation and the transient electric current in metal films, after ultra-short pulse laser heating. The temperature evolution is calculated by the coupled electron and phonon Boltzmann transport equations, the electrohydrodynamics model derived in this work, and the two-temperature model. Different laser pulse durations, film thicknesses, and laser fluences are considered. We find that the two-temperature model overestimates the electron temperature at the front surface of the film and underestimates the damage threshold when the nonlinear thermal transport of electrons is important. The electrohydrodynamics model proposed in this work could be a more accurate prediction tool to study the non-equilibrium electron and phonon transport process than the two-temperature model and it is much easier to be solved than the Boltzmann transport equations.     

Surface morphological response of crystalline solids to mechanical stresses and electric fields

Surface morphological evolution under the action of external fields is a fascinating topic that has attracted considerable attention within the surface science community over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. In this report, we review theoretical progress in modeling the surface morphological response of stressed elastic solids under conditions that promote surface diffusion and of electrically conducting solids under surface electromigration conditions. A self-consistent model of surface transport and morphological evolution is presented that has provided the basis for the theoretical and computational work that is reviewed. According to this model, the surface morphological response of electrically conducting elastic solids to the simultaneous action of mechanical stresses and electric fields is analyzed. Emphasis is placed on metallic surfaces, including surfaces of voids in metallic thin films.Surfaces of stressed elastic solids are known to undergo morphological instabilities, such as the Asaro–Tiller or Grinfeld (ATG) instability that leads to emanation of crack-like features from the surface and their fast propagation into the bulk of the solid material. This instability is analyzed theoretically, simulated numerically, and compared with experimental measurements. The surface morphological evolution of electrically conducting, single-crystalline, stressed elastic solids under surface electromigration conditions is also examined. We demonstrate that, through surface electromigration, a properly applied and sufficiently strong electric field can stabilize the surface morphology of the stressed solid against both crack-like ATG instabilities and newly discovered secondary rippling instabilities; the effects of important parameters, such as surface crystallographic orientation, on the surface morphological response to the simultaneous action of an electric field and mechanical stress also are reviewed. In addition, electromigration-driven surface morphological response is analyzed systematically, focusing on the current-driven surface morphological evolution of voids in metallic thin films; this analysis has been motivated largely by the crucial role of void dynamics in determining the reliability of metallic interconnects in integrated circuits and has led to the interpretation of a large body of experimental observations and measurements. The electromigration-driven translational motion of morphologically stable voids, effects of current-driven void dynamics on the evolution of the electrical resistance of metallic thin films, and current-driven void–void interactions also are reviewed. Furthermore, theoretical studies are reviewed that demonstrated very interesting current-driven nonlinear void dynamics in stressed metallic thin films, including the inhibition of electromigration-induced instabilities due to the action of biaxial tensile stress, and stress effects on the electromigration-driven translational motion of morphologically stable voids.Complex, oscillatory surface states under surface electromigration conditions have been observed in numerical studies. In this report, emphasis is placed on void surfaces in metallic thin films, for which stable time-periodic states have been demonstrated. It is shown that increasing parameters such as the electric-field strength or the void size past certain critical values leads to morphological transitions from steady to time-periodic states; the latter states are characterized by wave propagation on the surface of a void that migrates along the metallic film at constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy as determined by the crystallographic orientation of the film plane. It is also shown that, in the case where the Hopf bifurcation is subcritical, the simultaneous action of mechanical stress leads the current-driven void morphological response to the stabilization of chaotic attractors; in such cases, as the applied stress level increases, the void dynamics is set on a route to chaos through a sequence of period-doubling bifurcations. The observation of current-driven chaotic dynamics in homoepitaxial islands also is discussed.     

Nonlinear evolution of two-magnetofluid instability

The nonlinear surface instability of a horizontal interface separating two magnetic fluids of different densities, magnetic permeabilities, and velocities, including surface tension effects, is investigated. The magnetic field is applied along the direction of streaming. It is shown that the evolution of the amplitude is governed by a nonlinear Ginzburg-Landau equation with the use of the multiple scale method. When the influence of streaming is neglected, the nonlinear diffusion equation is obtained. Further, it is shown that a nonlinear Schrödinger equation is obtained in the absence of gravity. The various stability criteria are discussed from these equations, of both Rayleigh-Taylor and Kelvin-Helmholtz problems, both analytically and numerically and the stability diagrams are obtained. Obtained also are the stability properties of solitary solutions to the Ginzburg-Landau equation in the case of constant surface tension.     

Current-induced stabilization of surface morphology in stressed solids

We examine the surface morphological evolution of a conducting crystalline solid under the simultaneous action of an electric field and mechanical stress based on a fully nonlinear model and combining linear stability theory with self-consistent dynamical simulations. We demonstrate that electric current, through surface electromigration, can stabilize the surface morphology of the stressed solid against cracklike surface instabilities. The results also have more general implications for the morphological response of solid surfaces under the simultaneous action of multiple external forces.     

On the time evolution of the liquid meniscus at the end of a capillary placed in an external electric field

Using a linearized set of equations of electrodynamics, the stability of the uniformly charged meniscus of a viscous conducting incompressible liquid at the end of a capillary is investigated and analytical expressions are derived for the electric field outside the meniscus, velocity fields in the liquid flow and meniscus, and generatrix of the meniscus shape. It is found that, if an external electric field near the meniscus exceeds that at which the free liquid surface becomes unstable against the surface charge, a finite number of longest waves become unstable with their instability growth rates nonmonotonically depending on the wavenumber. Analysis of the time evolution of the meniscus shape under various initial conditions shows that cylindrical waves with the highest instability growth rates play a decisive role in this process, while the influence of the initial deformation amplitude is insignificant.     

Equilibrium configurations of uncharged conducting liquid jets in a transverse electric field

Solutions for the problem on the equilibrium configurations of uncharged conducting liquid jets in a transverse electric field are obtained. These solutions correspond to finite-amplitude non-axisymmetric azimuthal deformations of the surface of a round jet: the jet is stretched along the field in its cross-section. The range of electric fields is determined for which solutions of the problem exist. If the electric field strength is over some critical value, the electrostatic equations have no solution, and the jet splits. The obtained solutions are qualitatively examined for stability under small azimuthal perturbations.     

Self-Interacting Electromagnetic Fields and a Classical Discussion on the Stability of the Electric Charge

The present work proposes a discussion on the self-energy of charged particles in the framework of nonlinear electrodynamics. We seek magnetically stable solutions generated by purely electric charges whose electric and magnetic fields are computed as solutions to the Born-Infeld equations. The approach yields rich internal structures that can be described in terms of the physical fields with explicit analytic solutions. This suggests that the anomalous field probably originates from a magnetic excitation in the vacuum due to the presence of the very intense electric field. In addition, the magnetic contribution has been found to exert a negative pressure on the charge. This, in turn, balances the electric repulsion, in such a way that the self-interaction of the field appears as a simple and natural classical mechanism that is able to account for the stability of the electron charge.     

Soliton regimes of surface magnetostatic wave propagation in a magnet-semiconductor structure

The nonlinear properties of exchange-free surface magnetostatic spin waves in a layered structure containing films of a ferromagnet and a semiconductor are investigated theoretically. The stability of nonlinear surface magnetostatic waves relative to longitudinal disturbances is investigated using the envelope evolution equation in the weak-nonlinearity approximation. It is shown that, under certain conditions, a surface spin-wave pulse propagates in the form of an envelope soliton. Calculations are performed for the case of an yttrium iron-garnet-indium antimonide structure. Fiz. Tverd. Tela (St. Petersburg) 41, 1272–1275 (July 1999)     

非平整基底上受热液膜流动稳定性研究

本文研究了二维黏性流体薄膜沿非平整不均匀加热基底流动时非线性表面波的演化及其流动稳定性.利用长波摄动法推导出非平整线性加热基底上非线性表面波的零阶和一阶演化方程,基于所得演化方程,绘制出正弦波纹基底上液膜的表面波形图,并研究液膜流动的线性稳定性,分析了各无量纲参数对液膜线性稳定性的影响.分析结果表明:在正弦波纹基底上,液膜自由表面随同壁面作相同频率的正弦型波动,且液膜厚度沿流动方向逐渐变小;Marangoni数为稳定影响因素,随Marangoni数的增大,液膜稳定区域增大;Peclet数和倾角θ均为不稳定影响因素,随Peclet数和倾角θ的增大,液膜稳定区域减小;在非平整基底的波峰和波谷处,Peclet数、Marangoni数和倾角θ对稳定性的影响趋势一致,但基底波谷处的液膜稳定区域小于波峰处区域,流动更易失稳.     

Cylindrical electromagnetic waves in a nonlinear nondispersive medium: Exact solutions of the Maxwell equations

The excitation and propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium are analyzed. It is assumed that the medium lacks a center of symmetry and that the dependence of the electric displacement on the electric field can be approximated by an exponential function. For this case, a method for integrating the system of the Maxwell equations is proposed. Exact solutions to a set of nonlinear electromagnetic field equations are obtained by this method. It is shown that nonlinear effects described by these solutions can become apparent under experimental conditions.     

Rosenzweig instability in a thin layer of a magnetic fluid

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.     

Formation of root singularities on the free surface of a conducting fluid in an electric field

The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.     

Spectral broadening of a few-cycle laser pulse propagating in fused quartz

Results of theoretical study of nonlinear propagation of a few-cycle laser pulse in a fused quartz are presented. With use of the finite-difference technique we have integrated numerically the system of the nonlinear Maxwell equations describing the propagation of a linearly polarized pulse at the central wavelength in the range of zero dispersion (λ₀ = 1.27 μm) and duration 20 fs. The evolution of the laser pulse spectrum is calculated and the dependences of the shift of the spectral peak on both the strength of electric field and medium length are obtained.