Deformation and instability of nematic drops in an external electric field

The behavior of nematic liquid-crystal drops freely suspended in an isotropic liquid polymer exposed to an external electric field was studied. A giant deformation was observed for the drop. As the field intensity increased, its equilibrium shape took the form of a prolate ellipsoid. The dependences of the shape and critical fields on the concentration of ions in the polymer liquid were established. A plausible theoretical explanation is suggested for the observed effect. The experimental dependence of drop size on the electric-field strength is analyzed, and the conditions for the loss of drop stability are determined.     

The shape of a drop in a constant electric field

The variation of the shape of a drop immersed in an immiscible liquid under the action of an electric field is calculated. The charge is transferred both by ohmic current through the interface and by the convective component over the interface. A solution quadratic in the parameter that is the ratio of the electric pressure to the capillary pressure is analyzed. Conditions where the drop transforms into a spheroid that is prolate or oblate along the electric field vector are found. An experimental study of the drop deformation by electric forces is carried out.     

Investigation on dynamics of double emulsion droplet in a uniform electric field

Phase field method based on Cahn–Hilliard free energy formulation is adopted for predicting the behavior of double emulsion droplet suspended in a continuous phase under the influence of a uniform electric field. The role played by the inner droplet on the electric-field-driven fluid flow, and also on deformation of the outer droplet is predicted by present numerical simulation. Three different kind of deformation type of outer and inner droplet (prolate–oblate, prolate–prolate and oblate–prolate) has been observed. With increase in the volume fraction of inner drop, transition in the deformation of outer drop from prolate to oblate occurs at lower value of fluid permittivity ratio.     

Nonlinear oscillations of a charged drop accelerated in an electrostatic field

An analytical asymptotic solution to the problem of nonlinear oscillations of a charged drop moving with acceleration through a vacuum in a uniform electrostatic field is found. The solution is based on a quadratic approximation in two small parameters: the eccentricity of the equilibrium spheroidal shape of the drop and the amplitude of the initial deformation of the equilibrium shape. In the calculations carried out in an inertial frame of reference with the origin at the center of mass of the drop, expansions in fractional powers of the small parameter are used. Corrections to the vibration frequencies are always negative and appear even in the second order of smallness. They depend on the stationary deformation of the drop in the electric field and nonlinearly reduce the surface charge critical for development of the drops’s instability. It is found that the evolutions of the shapes of nonlinearly vibrating unlike-charged drops differ slightly owing to inertial forces.     

Forces and charges on a slightly deformed droplet in the DC field of a plate condenser

A conducting drop in partial wetting on the lower electrode of a plate condenser and surrounded by a dielectric fluid is considered. When a DC field is applied the drop, acquiring electric charges, is subjected to an electrostatic force normal to the electrode. The force exerted on undeformable drops was previously calculated. In this paper, the distortion from a spherical shape is asymptotically calculated at low electric Bond numbers to generalize previous developments. A mechanism is proposed to explain the drop detachment, leading to an electrical field strength threshold. Some experiments were performed confirming the mechanism.     

Nonlinear vibrations of a charged drop in an electrostatic suspension

The problem of nonlinear vibrations of a charged drop of an ideal incompressible conducting fluid in an electrostatic suspension is analytically solved in an approximation quadratic in two small parameters: vibration amplitude and equilibrium deformation of the shape of the drop in an electrostatic field. To solve the problem analytically, the desired quantities are expanded in semiinteger powers of the small parameters. It is shown that the charge of the drop and the gravitational field influence the shape of the drop, nonlinear corrections to the vibration frequencies, and critical conditions for instability of the drop against the surface charge. At near-critical values of the charge, the shape of the nonlinearly vibrating drop falls far short of being a sphere or a spheroid, which should be taken into account in treating experimental data.     

On the equilibrium shapes of a conducting drop in a uniform and nonuniform electric field

The equilibrium shape of a drop in the electrostatic field of a point charge and a point dipole is asymptotically calculated in terms of the dimensionless deformation of the shape and a ratio between the drop’s radius and the distance to the point charge (dipole). Irrespective of the degree of nonuniformity of the field, the prolate spheroidal deformation (typical of the uniform field) is shown to be the main reason for the change in the equilibrium shape of the spherical drop. When the nonuniformity of the field grows, the equilibrium shape becomes more and more asymmetric and different from the spheroidal one. This, all other things being equal, may influence the critical conditions for the instability of the drop’s surface against an induced charge. It follows from the aforesaid that the drop in the field of the dipole will be the first to undergo instability with the electrostatic pressure on the drop being the same.     

Numerical simulation of an uncharged droplet in a uniform electric field

The deformations of a real dielectric droplet subjected to a uniform alternating electric field and immersed in an insulating fluid are numerically studied by the Boundary Element Method. The alternating electric field time scale is taken much smaller than the hydrodynamic time scale of the droplet shape deformation. The influence of the frequency and the conductivity of the droplet upon the critical electric field, beyond which instabilities develop, are compared with the experimental measurements. Numerical results well account for experimental data while an unexpected good correspondence with Taylor's theory is found.     

Numerical investigation of the deformation mechanism of a bubble or a drop rising or falling in another fluid

A numerical method for simulating the motion and deformation of an axisymmetric bubble or drop rising or falling in another infinite and initially stationary fluid is developed based on the volume of fluid （VOF） method in the frame of two incompressible and immiscible viscous fluids under the action of gravity, taking into consideration of surface tension effects. A comparison of the numerical results by this method with those by other works indicates the validity of the method. In the frame of inviseid and incompressible fluids without taking into consideration of surface tension effects, the mechanisms of the generation of the liquid jet and the transition from spherical shape to toroidal shape during the bubble or drop deformation, the increase of the ring diameter of the toroidal bubble or drop and the decrease of its cross-section area during its motion, and the effects of the density ratio of the two fluids on the deformation of the bubble or drop are analysed both theoretically and numerically.     

Stability of charged metal clusters in the vicinity of an ionic charge

Stability of highly charged metal clusters in the electric field of an external ion is investigated with the classical liquid drop model. We study the optimum shape of the cluster which has a local minimum of the total energy, taking account of the effects of the surface charge polarization on the Coulomb energy and the cluster deformation on the surface energy. We find that the cluster deformation greatly affects the total energy of the system and that a cluster with a fissility larger than some critical value 0.7-0.8 can become unstable against deformation. We investigate the local competition between the Coulomb force and the surface tension at the cluster surface and show that the surface charge polarization which is induced by the external electric field significantly affects the shape of the cluster and its stability. Received 5 November 2002 / Received in final form 27 January 2003 Published online 11 March 2003 RID="a" ID="a"e-mail: hamada@konan-u.ac.jp     

On the possibility of corona initiation near a conducting drop nonlinearly vibrating in an external electrostatic field

An analytical asymptotic expression for the field strength near an ideal incompressible electrically conducting liquid drop nonlinearly vibrating in external electrostatic field E ₀ is found in an order of 5/2 in a small parameter. The small parameter here is the amplitude of deformation of the spherical shape of the drop. It is found that the strength of the electric field resulting at the tops of the drop exceeds the corona-initiating field even if E ₀ is one order of magnitude lower than the value at which the drop becomes unstable against the induced charge (that is, at such values of E ₀ as are observed in storm clouds in full-scale experiments).     

真空绝缘子脉冲表面电场在线测量系统的实现

基于Kerr电光效应,建立了用以对纳秒脉冲高电压作用下的真空绝缘子表面电场进行在线测量的实验系统。该测量系统由快脉冲高电压源、YAG激光器、同步控制系统、被测中空薄壁绝缘子及Kerr效应单元、光学相位差检测系统等部分构成。利用YAG激光器输出的激光脉冲,触发导通快脉冲高压源中的高压气体开关,使其给被测绝缘子试品上施加一个脉宽100ns的高压脉冲方波。利用同步控制,使得探测激光在试品上的脉冲方波达到幅值后,入射到Kerr腔体中对Kerr效应进行探测。从而实现了对绝缘子表面电场的在线测量,并给出了初步的测量结果。     

Two-parametric family of exact solutions for the profile of the surface of a conducting liquid in a nonuniform electric field

Possible equilibrium configurations of the free surface of a conducting liquid in an external nonuniform electric field are investigated. The liquid is at the tip of a wedge-shaped electrode, and the counter-elecrode is a thin straight conducting filament parallel to the edge of the wedge. The conformal mapping method is used to obtain a two-parametric family of exact solutions for the shape of the surface. The solutions describe the deformation of the surface right to separation of a drop from the electrode.     

汽泡在电场作用下的变形

为探明外加电场对汽泡形状的影响规律,本文采用人工注射汽泡的方式,对均匀电场作用下单个汽泡的形状进行了可视化试验研究,计算了汽-液两相系统中的电场分布及汽泡所受的电应力。结果表明:电场作用下汽泡表面所受电应力分布的不均匀性导致汽泡沿与电场相平行的方向拉长,变成扁长椭球形。随着场强的增加,汽泡变形量加剧,汽泡与壁面的接触角逐渐变大。此外,讨论了汽泡变形对电场强化沸腾换热的影响。     

Modification of the boundary layer theory for calculating viscous drop oscillations in a uniform electrostatic field

Capillary oscillations on the free surface of a viscous conductive liquid drop placed in an electrostatic field are calculated. In an approximation linear in stationary deformation amplitude, the drop in this field has the shape of a spheroid extended along the field. The initial problem is modified and simplified in terms of the boundary layer theory by applying an approximation that is linear in the oscillation amplitude and quadratic in the eccentricity of the drop. The accuracy of the approximate solution relative to an exact one is estimated. It is shown that, with a rise in the electrostatic field strength (with an increase in the eccentricity of the drop) and in the viscosity of the liquid, the boundary layer at the free surface of the drop becomes thicker.     

Switching kinetics of ferroelastic ferroelectrics

Switching kinetics of uniaxial ferroelastic ferroelectrics (FFs) in external electric and stress fields is studied using classical theory of nucleation and growth. The stage in which the polarization and deformation reversal involves the main body of the FF and the final stage (Ostwald ripening) of the FF switching are studied with allowance for the change in the repolarization and redeformation during the phase transition. The time dependences of the repolarization and redeformation are found, and equations are derived from which the polarization current and the deformation flux, as well as their time dependence, can be calculated. The calculated main characteristics of the FF switching are compared with the experimental data for switching of Rochelle salt single crystals.     

Local enhancement of a uniform electrostatic field near the tip of a spheroidal drop

The enhancement in a uniform electrostatic field at the tip of a spheroidal drop is shown to depend on the dielectric constant of the drop material, its initial radius, and the external electric field and to become greater as these increase. The loss of stability of a drop in an external electrostatic field that is accompanied by a very rapid growth in the magnitude of the spheroidal deformation causes a rapid, transient enhancement of the field at its tip. Zh. Tekh. Fiz. 69, 49–54 (August 1999)     

Nonlinear analytical calculation of the equilibrium shape of a charged drop uniformly accelerated in an electrostatic field

An analytical asymptotic expression for the equilibrium shape of a charged drop of an ideal incompressible conducting liquid uniformly accelerated in collinear electrostatic and gravitational fields is derived in an approximation quadratic with respect to the deviation of the equilibrium shape of the drop from a sphere. It is found that the equilibrium shape of the drop is close to a prolate spheroid when its self-charge and the external electric field strength are far from their values critical in terms of instability against the self-charge and induced charge. This spheroid experiences an insignificant pear-shaped distortion even when the charge of the drop and the electrostatic field strength are high.     

Shape oscillations of a droplet in an Oldroyd-B fluid

We present a Navier-Stokes/Oldroyd-B immersed boundary algorithm that captures the interaction of a flexible structure with a viscoelastic fluid. In particular, we study the effects of bulk viscoelasticity on freely decaying shape oscillations of an Oldroyd-B fluid droplet suspended in an Oldroyd-B matrix. Our numerical data indicate that if the fluid viscosity is low, viscoelasticity plays a modulating role in the drop shape relaxation; specifically, it increases the oscillation frequency and decreases the decay rate when the fluid relaxation time is above a critical value. In the high viscosity limit, i.e., when a Newtonian droplet is expected to return to a spherical shape with an aperiodic decay, an increase in the relaxation time eventually results in the reappearance of the oscillations. Both these results are in line with the prediction of small deformation theory for viscoelastic droplet oscillations. The algorithm was also validated by direct comparison with linear asymptotics.     

On the structure of the velocity field under the free spheroidal surface of a viscous liquid drop oscillating in an electrostatic field

An asymptotic analytical solution to an initial boundary-value problem considering (i) the time evolution of the capillary oscillation amplitude as applied to a viscous spheroidal liquid drop placed in a uniform electrostatic field and (ii) the liquid flow velocity field inside the drop is found. The problem is solved in an approximation that is linear in two small parameters: the dimensionless oscillation amplitude and the dimensionless field-induced constant deformation of the equilibrium (spherical) shape of the drop. Terms proportional to the product of the small parameters are retained. In this approximation, interaction between oscillation modes is revealed. It is shown that the intensity of the eddy component of the oscillation-related velocity field depends on the liquid viscosity and the external uniform electrostatic field strength. The intensity of the eddy component decays rapidly with distance from the free surface. The depth to which the eddy flow (which is caused by periodical flows on the free surface) penetrates into the drop is a nonmonotonic function of the polar angle and increases with dimensionless viscosity and field strength.