Wave flows in a thin layer of a viscous liquid. Influence of a constant electric field

The influence of a constant transverse electric field on the dynamics of longwave, weakly nonlinear flow of a viscous dielectric liquid film down a vertical wall is studied. An amplitude integrodifferential equation in partial derivatives of the Kuramoto-Sivashinskii equation type, which describes the behavior of the free surface of the layer, is derived using the method of multiscale stretching. In the case considered, the potential energy of the electric field is a source of longwave perturbations, but, on the whole, secondary regimes are apparently nonlinearly steady. Probably, the electric polarization effects studied can be used as a factor that governs the dynamics of film flow. Computer Center, Siberian Division, Russian Academy of Sciences, Krasnoyarsk 660036. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 90–97, January–February, 1998.     

The role of external influences in the formation of waves on the surface of a flowing-down film of a viscous fluid

The example of two non-stationary forces is used to study the impact of external influences leading to the occurrence of additional ponderomotive forces on the wave regimes of the film freely flowing down a vertical surface. The first case describes a ferromagnetic fluid film affected by the magnetic field, and the second case touches upon a dielectric fluid film affected by the electric field. For the given forces, in the case of small flow rates, the problem is reduced to the solution of a model equation for the perturbation of the film thickness. The numerical solutions of the problem are obtained, and several characteristic scenarios of evolution of periodical perturbations are considered. It is shown that changes in the boundaries of the region of linear stability of the unperturbed flow with a flat free surface under the influence of ponderomotive forces have a great impact on the flow.     

Stability of conducting liquid flowing down an inclined plane at moderate Reynolds number in the presence of constant electromagnetic field

The stability of a conducting viscous film flowing down an inclined plane at moderate Reynolds number in the presence of electromagnetic field is investigated under induction-free approximation. Using momentum integral method a non-linear evolution equation for the development of the free surface is derived. The linear stability analysis of the evolution equation shows that the magnetic field stabilizes the flow whereas the electric field stabilizes or destabilizes the flow depending on its orientation with the flow. The weakly non-linear study reveals that both the supercritical stability and subcritical instability are possible for this type of thin film flow. The influence of magnetic field on the different zones is very significant, while the impact of electric field is very feeble in comparison.     

Thin liquid film morphology driven by electro-static field

The development of stationary patterns on a thin polymer surface subject to an electric field is studied by means of the hexagonal-planform weakly nonlinear stability analysis and numerical simulations.The time evolution of the interface between the air and the polymer film on the unbounded spatial domain is described by a thin film equation,incorporating the electric driving force and the surface diffusion.The nonlinear interfacial growth includes the amplitude equations and superposition of one-dimensional structures at regular orientations.The pattern selection is driven by the subcritical instability mechanism in which the relative thickness of the polymer film plays a critical role.     

Buoyancy-driven motion of a two-dimensional bubble or drop through a viscous liquid in the presence of a vertical electric field

The effect of an electric field on the buoyancy-driven motion of a two-dimensional gas bubble rising through a quiescent liquid is studied computationally. The dynamics of the bubble is simulated numerically by tracking the gas–liquid interface when an electrostatic field is generated in the vertical gap of the rectangular enclosure. The two phases of the system are assumed to be perfect dielectrics with constant but different permittivities, and in the absence of impressed charges, there is no free charge in the fluid bulk regions or at the interface. Electric stresses are supported at the bubble interface but absent in the bulk and one of the objectives of our computations is to quantify the effect of these Maxwell stresses on the overall bubble dynamics. The numerical algorithm to solve the free-boundary problem relies on the level-set technique coupled with a finite-volume discretization of the Navier–Stokes equations. The sharp interface is numerically approximated by a finite-thickness transition zone over which the material properties vary smoothly, and surface tension and electric field effects are accounted for by employing a continuous surface force approach. A multi-grid solver is applied to the Poisson equation describing the pressure field and the Laplace equation governing the electric field potential. Computational results are presented that address the combined effects of viscosity, surface tension, and electric fields on the dynamics of the bubble motion as a function of the Reynolds number, gravitational Bond number, electric Bond number, density ratio, and viscosity ratio. It is established through extensive computations that the presence of the electric field can have an important effect on the dynamics. We present results that show a substantial increase in the bubble’s rise velocity in the electrified system as compared with the corresponding non-electrified one. In addition, for the electrified system, the bubble shape deformations and oscillations are smaller, and there is a reduction in the propensity of the bubble to break up through increasingly larger oscillations.     

聚变堆相关的液态金属膜流初步实验研究

在磁约束核聚变堆的面对等离子部件设计中,液态金属锂膜流因具有带走杂质、保护面对等离子固壁等优点而被认为是优选方案之一. 然而,如何克服聚变堆中强磁场环境下产生的磁流体力学效应并形成大面积均匀铺展锂膜流动是目前亟需解决的问题.本文通过搭建室温液 态镓铟锡回路和高温液态锂回路,开展了两种不同特性的液态金属膜流实验, 并采用传统可视化方法获得了展向磁场存在时镓铟锡和锂在导电底板形成的液膜流动表面特征.实验结果 表明: 无磁场时,两种液态金属膜流流动表面波动特性与常规流体膜流均一致, 即随着流动雷诺数的增加表面波动变得更为混乱; 而展向磁场存在时,镓铟锡膜流表面波动变得更为规则, 且沿着磁场方向平行排列,表现为拟二维波动的特征; 而锂膜流却产生了明显的磁流体 力学阻力效应,表现为在流动方向局部产生锂滞留现象, 且滞留点随雷诺数增大向下游移动. 最后通过膜流受力分析,进一步阐述了锂膜流受到比镓铟锡膜流更为严重磁流体力学效应影响的原因.      

A theoretical analysis of the breakdown of electrostrictive oxide film on metal

Oxide films that form to protect (passivate) metal substrates from corrosive environments can be severely damaged when they are subjected to sufficient levels of electric potential. A continuum mechanics model is presented that captures the intimate electromechanical coupling of the environment and the film responsible for either growth or dissolution of the oxide. Analytical solutions, obtained for a finite-thick film experiencing a uniform electric field, illustrate the existence of a critical combination of electric field strength, initial film thickness and shape, beyond which the passivating oxide can become thin enough to undergo dielectric breakdown, or the substrate can become exposed to the corrosive environment. An experimental procedure is proposed to measure combinations of material properties required by the theoretical model to predict the lifetime of the oxide or to avoid the critical state. Illustrative numerical examples are provided to describe the morphological evolution of oxide films with a periodically wavy surface.     

Wrinkling of a charged elastic film on a viscous layer

A thin metallic film deposited on a compliant polymeric substrate begins to wrinkle under compression induced in curing process and afterwards cooling of the system. The wrinkle mode depends upon the thin film elasticity, thickness, compressive strain, as well as mechanical properties of the compliant substrate. This paper presents a simple model to study the modulation of the wrinkle mode of thin metallic films bonded on viscous layers in external electric field. During the procedure, linear perturbation analysis was performed for determining the characteristic relation that governs the evolution of the plane-strain wrinkle of the thin films under varying conditions, i.e., the maximally unstable wrinkle mode as a function of the film surface charge, film elasticity and thickness, misfit strain, as well as thickness and viscosity of the viscous layer. It shows that, in proper electric field, thin film may wrinkle subjected to either compression or tension. Therefore, external electric field can be employed to modulate the wrinkle mode of thin films. The present results can be used as the theoretical basis for wrinkling analysis and mode modulation in surface metallic coatings, drying adhesives and paints, and microelectromechanical systems (MEMS), etc.     

Film boiling of an electrically insulating fluid in the presence of an electric field

This paper deals with the experimental and theoretical investigation of the influence of an electric field on the heat transfer rate during stable film boiling of the electrically insulating fluid FC-72. In particular the case of stable saturated film boiling from a horizontal plate is studied. The experiments show that the heat transfer rate increases ±50 when an electric field of 27.3 kV/cm is applied. A new correlation for the heat transfer rate in the presence of an electric field based on the heat transfer model of Klimenko is derived in this paper. Therefore the behavior of the liquid-vapor interface is studied in more detail. This study shows that the electric field has a two fold effect on the interface. On the one hand the distance between adjacent bubbles decreases and on the other hand the bubbles elongate in the presence of the electric field. The new correlation is in good agreement with the experiments. Received on 20 October 1998     

Deformation and buckling of a pre-stretched soft elastic film induced by spatially modulated electric fields

We study mechanical response of a uniaxially pre-stretched soft elastic film to spatially modulated electric fields. The film is adhered onto a rigid, conductive substrate, and the electric field is generated through a periodically patterned electrode over the film. Our work shows that at low applied voltages the deformation of the film follows the pattern of the electrode, allowing for the transfer of the surface morphology of the electrode onto the film surface in opposite sign. However, when the voltage reaches a threshold, the film buckles to form stripped pattern parallel to the tensile direction. This newly resulting deformation is superposed on that before onset of buckling, leading to complicated and ordered topography of the film. The phenomenon may provide a new clue for creating ordered surface structures with the aid of elastic buckling.     

Instability of a liquid layer under periodic influence: Falling film in an alternating electric field

The linear analysis of stability of a plane-parallel time-periodic flow is carried out. The numerical method which makes it possible to reduce the spectral problem for the time-dependent Orr–Sommerfeld equation to an algebraic eigenvalue problem is used. The film of viscous conducting liquid which flows down a vertical wall in the normal electric field is considered and parametric resonances are revealed.     

薄膜润滑中双电层效应的理论分析与实验研究

建立了考虑双电层效应的有限宽组合滑块薄膜润滑数学模型,并利用组合滑块与圆盘的滑动摩擦试验对双电层效应进行研究,利用实验结果修正了润滑过程中双电层效应的计算,给出电粘度的计算公式并进行数值分析.结果表明:在薄膜厚度较薄的情况下,双电层效应使得流体的等效粘度随膜厚减小而迅速增加;随着膜厚增加,双电层的电粘度效应逐渐减弱;随着电场强度增加,双电层的电粘度效应增加,当电场强度达到一定程度时,双电层的电粘度效应开始减弱.     

Liquid crystal model of vesicle deformation in alternating electric fields

Considering the effects of osmotic pressure, elastic bending, Maxwell pressure, surface tension, as well as flexo-electric and dielectric properties of phospholipid membrane, the shape equation for sphere vesicle in alternation (AC) electric field is derived based on the liquid crystal model by minimizing the free energy due to coupled mechanical and AC electrical fields. Besides the effect of elastic bending, the influence of osmotic pressure and surface tension on the frequency dependent behavior of vesicle membrane in AC electric field is also discussed. Our theoretical results for membrane deformation are consistent with corresponding experiments. The present model provides the possibility to further disclose the frequency-depended behavior of biological cells in the coupled AC electric and different mechanical fields.     

生物芯片中周期性电渗驱动液体薄膜的流动特性

研究了二维周期性电渗驱动液体薄膜的流动特性. 以Debye-Hückel 假设近似下线性化的Poisson-Boltzmann方程描述双电层电动势分布和电荷密度的分布关系, 与黏性不可压缩流体Navier-Stokes方程相耦合, 得到流体在自由面与固壁之间的周期电渗流流场的精确解. 结果显示, 薄膜内速度振幅与流体黏性密切相关, 雷诺数越大, 速度振幅就越小. 该文还细致分析了雷诺数和自由面ζ电势对自由面的流速振幅和薄膜内速度相位差的影响.     

Non-linear analysis of creeping flow on the inclined permeable substrate plane subjected to an electric field

The effect of an externally applied electric field on the stability of a thin fluid film over an inclined porous plane is analyzed using linear and non-linear stability analysis in the long wave limit. The principle aim of this study is to illustrate the influence of electric field on the non-linear stability of a thin liquid layer flow down incline substrate when the plane is porous. The driving force for the instability under an electric field is an electrostatic force exerted on the free charges accumulated at the dividing interface. The coupled non-linear evolution equations for the local film thickness and the interfacial charge for two-dimensional disturbances are derived to analyze the effect of long-wave instabilities. The method of multiple scales is applied to obtain approximate solutions and analyze the stability criteria. Numerical simulations of this system of non-linear evolution equations are performed. It is found that the permeability parameter as well as the inclination of the plane plays a destabilizing role in the stability criteria, while the damping influence is observed for increasing of the electrical conductivity in both linear and non-linear behavior.     

Waves on the surface of a falling power-law fluid film

Waves that occur at the surface of a falling film of thin power-law fluid on a vertical plane are investigated. Using the method of integral relations an evolution equation is derived for two types of waves equation which are possible under long wave approximation. This equation reveals the presence of both kinematic and dynamic wave processes which may either act together or singularly dominate the wave field depending on the order of different parameters. It is shown that, at a small flow rate, kinematic waves dominate the flow field and the energy is acquired from the mean flow during the interaction of the waves, while, for high flow rate, inertial waves dominate and the energy comes from the kinematic waves. It is also found that this exchange of energy between kinematic and inertial waves strongly depends on the power-law index n. Linear stability analysis predicts the contribution of different terms in the wave mechanism. Further, it is found that the surface tension plays a double role: for a kinematic wave process, it exerts dissipative effects so that a finite amplitude case may be established, but for a dynamic wave process it yields dispersion. Further, it is shown that the non-Newtonian character n plays a vital role in controlling the role of the term that contains surface tension in the above processes.     

Modification of the elastic properties of nanostructures with surface charges in applied electric fields

The influences of applied electric fields and surface charges on elastic modulus of nanostructures such as nanowires and nanofilms are investigated within the framework of classic continuum mechanics. Under an applied electric field, the surfaces of structures are subjected to the electrostatic forces (negative pressure) along the direction of the electric field, and the resulting surface charges also change the surface mechanical properties due to the Hellman–Feynman (H–F) forces. Through incorporating the surface energy from the negative pressure and the H–F forces into surface free energy, the exact and analytical expressions of the effective elastic modulus of nanowires and nanofilms are addressed by considering the surface energy effects on the elastic modulus of nanostructures, which involves the contribution of the applied electric field and surface charges. The numerical results indicate that applied electric fields parallel to the axis of the nanowire and nanofilms enhance the transverse Young's modulus while reducing axial modulus of nanostructures. The effective modulus of nanowires and nanofilms with lateral surface charges depends on the surface charges density and the sign of the charges. In addition, the effect of electric field and surface charges on Young's moduli of nanowires and nanofilms has been found to be sensitive to structural geometric dimensions such as the thickness of the film and the diameter of the wire.     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Wave regimes on a film of generalized Newtonian fluid flowing down a vertical plane

The flow of a thin film of generalized Newtonian fluid down a vertical wall in the gravity field is considered. For small flow-rates, in the long-wave approximation, an equation describing the evolution of the surface perturbations is obtained. Depending on the signs of the coefficients, this equation is equivalent to one of four equations with solutions significantly different in evolutionary behavior. For the most interesting case, soliton solutions are numerically found.