Equilibrium shape and stability of a charged drop in an air flow under an electric field

The pressure balance on the surface of a charged liquid drop moving along a uniform electrostatic field is analyzed. The liquid is assumed to be nonviscous and incompressible. In the approximation linear in deformation amplitude, the equilibrium shape of the drop as a function of the charge, field strength, and velocity of travel can be both a prolate and an oblate spheroid. Critical conditions for the surface instability of such a drop are obtained analytically in the form of a relationship between the charge, field strength, and velocity of travel. An instability criterion is found by extrapolating to large Reynolds numbers. This makes it possible to fit the earlier model of a corona-initiated lightning in the vicinity of large charged water drops or hailstones to the charges of the drops, field strengths, and velocities of travel (relative to the medium) typical of thunderclouds.     

Electrical properties of water drops inside the dropwise cluster

The Letter shows that inside a dropwise cluster formed over the heated water surface, water drops are electrically charged. The charge of a separate drop reaches 10³ units of an elementary charge. The drops are positioned from each other at the distance of double Debye radius length. It is fixed up that drops levitate over the water surface in consequence of the Stokes force acting from the side of gas-vapor flow rising from water surface. The Stokes force thousand times exceeds the Coulomb drop repulsion force from the water surface.     

Theoretical modeling of laser fragmentation of nanoparticles in liquid media

A physical model of metal nanoparticle fragmentation in liquid media upon exposure to femtosecond laser pulses is proposed by the example of gold nanoparticle fragmentation in water. The model is based on electrolyzing the metal nanoparticles heated by laser pulses and their fragmentation during development of the instability of charged liquid metal drops. The nanoparticle charge gained upon exposure to laser radiation in water is estimated and the nanoparticle fragmentation parameter is determined.     

Formation of structures from amorphous metallic nanoparticles by dispersing metal drops continuously charging in an electron beam

The formation of amorphous metal nanoparticles by the method of electrohydrodynamic dispersion is studied. In this method, fine liquid metal drops are generated, charged in an electron beam to an unstable state, and dispersed into nanometer droplets. Rapid cooling of these nanometer droplets results in the formation of amorphous metal nanoparticles. The chief problem in the formation of such particles is that it is difficult to charge molten metal drops to an unstable state, since the bombardment of the drop by an electron beam may cause intense emission of electrons. To overcome this difficulty, the drops are charged by a beam of slow electrons. Charging proceeds in such a way that the electron energy rises with the drop’s charge. It is shown that this method makes it possible to obtain granulated films made up of amorphous metal particles. Copper films with a nanoparticle mean size of 2 nm and a small dimensional variation are prepared.     

Modeling of multicomponent-fuel drop-laden mixing layers having a multitude of species

A formulation representing multicomponent-fuel (MC-fuel) composition as a probability distribution function (PDF) depending on the molar mass is used to construct a model of a large number of MC-fuel drops evaporating in a gas flow, so as to assess the extent of fuel specificity on the vapor composition. The PDF is a combination of two Gamma PDFs, which was previously shown to duplicate the behavior of a fuel composed of many species during single drop evaporation. The conservation equations are Eulerian for the flow and Lagrangian for the physical drops, all of which are individually followed. The gas conservation equations for mass, momentum, species, and energy are complemented by differential conservation equations for the first four moments of the gas-composition PDF; all coupled to the perfect gas equation of state. Source terms in all conservation equations couple the gas phase to the drops. The drop conservation equations for mass, position, momentum, and energy are complemented by differential equations for four moments of the liquid-composition PDF. The simulations are performed for a three-dimensional mixing layer whose lower stream is initially laden with drops. Initial perturbations excite the layer to promote the double pairing of its four initial spanwise vortices to an ultimate vortex. The drop temperature is initially lower than that of the surrounding gas, initiating drop heating and evaporation. The results focus on both evolution and the state of the drops and gas when layers reach a momentum-thickness maximum past the double vortex pairing; particular emphasis is on the gas composition. Comparisons between simulations with n-decane, diesel, and three kerosenes show that at same initial Reynolds number and Stokes number distribution, a single-component fuel cannot represent MC fuels. Substantial differences among the MC-fuel vapor composition indicate that fuel specificity must be captured for the prediction of combustion.     

Influence of the accommodation coefficient on the water drop evaporation process in a radiation field

The process of water drop evaporation in a field of intense laser radiation is examined on the basis of the hydro-thermodynamics equations under the assumption of quasistationarity in the conditions in the surrounding medium and in the radius. The influence of the accommodation coefficient on heating of the drops on the magnitude of the surface jump in water vapor density and on the position of the upper bound of the convective evaporation region is analyzed. It is shown that the surface jump in the vapor does not alter the rate of convective evaporation of the drop in practice, but can result in substantially different time dependences of the radius of a diffusely evaporating drop as compared with those found without it. The solution obtained is compared with the solution of the problem of evaporation in a Stefan approximation.     

Energy analysis of possible channels for decomposition of a charged drop into two parts

Based on numerical analysis of the mathematical expression for potential energy of an isolated charged spheroidal drop and two approximate spheroidal daughter drops, mechanisms for decomposition of a multiply charged drop in two nearly equal parts were studied taking into account the electrostatic interaction of the daughter drops. It was shown that, as the distance between the daughter drops increased, both the probability of spontaneous decomposition of a multiply charged drop in two daughter drops and the decomposition symmetry degree increase at the moment of breaking the connection between the daughter drops.     

Electrostatic instability of a heavily charged conducting liquid jet

The effect of electric charge on the jet surface on the capillary instability of the jet and its disintegration into drops is analyzed. A theoretical explanation is given for the electrostatic mechanism of instability development and jet disintegration that is akin to the mechanisms behind the instability of a heavily charged drop (Rayleigh instability) and flat uniformly charged liquid surface (Tonks-Frenkel instability) but differs qualitatively from the conventional capillary mechanism of instability and disintegration.     

Simulations of coulombic fission of charged inviscid drops

We present boundary-integral simulations of the evolution of critically charged droplets. For such droplets, small perturbations are unstable and eventually lead to the formation of a lemon-shaped drop with very sharp tips. For perfectly conducting drops, the tip forms a self-similar cone shape with a subtended angle identical to that of a Taylor cone, and quantities such as pressure and velocity diverge in time with power-law scaling. In contrast, when charge transport is described by a finite conductivity, we find that small progeny drops are formed at the tips, whose size decreases as the conductivity is increased. These small progeny drops are of nearly critical charge, and are precursors to the emission of a sustained flow of liquid from the tips as observed in experiments of isolated charged drops.     

蒸汽爆炸粗混合过程中的蒸发阻力模型

在蒸汽爆炸的粗混合过程中,由于液体的快速蒸发,高温金属液滴的周围会产生一层很薄的蒸汽膜,此时液滴周围的边界层流动与没有液体蒸发时有很大的不同,因此,常温情况下的小球在连续液体中运动时的通用阻力模型在这种情况下是不适用的．本文通过受力分析,考虑了高温小球受力的分布和表面蒸发对小球周围力的影响,从阻力的基本机理上分析了蒸发状态下小球的运动阻力,分别提出了高温颗粒穿过自由表面时与其在液体中运动时的蒸发阻力模型．分析表明,当小球温度高于2500 K,特别是在靠近自由表面的区域,由于小球表面液体蒸发而产生的蒸发阻力作用非常明显．分析指出,小球的入水初速、小球表面的液体蒸发速率以及汽膜厚度都是影响小球运动阻力大小的重要因素．     

On the appearance of ions near the charged surface of an intensely evaporating electrolyte

Two mechanisms behind the appearance of ions in the vapor-gas sheath around a hot electrode immersed in an electrolyte, electrolyte surface instability against the surface charge and field evaporation, are considered. It is shown that the concept of the thermally activated field evaporation of ions provides a better approximation to experimental conditions. A dispersion relation for capillary-barogravity waves at the electrolyte-saturated vapor charged interface is derived. Critical conditions for the instability of these waves are found.     

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.     

Wetting and evaporation behaviors of molten Mg on partially oxidized SiC substrates

The wetting and evaporation behaviors of molten Mg drops on pressureless-sintered SiC surfaces were studied in a flowing Ar atmosphere at 973-1173 K by an improved sessile drop method. The initial contact angles are between 83° and 76°, only mildly depending on temperature. The formation of a ridge at the triple junction as a result of reaction between molten Mg and the SiO₂ film on the SiC surface pins the triple line and leads to a constant contact diameter mode during the entire evaporation process. Moreover, the diffusion coefficients of the Mg vapor at different temperatures were evaluated based on a simple model.     

On the absence of charge symmetry in electrostatic interaction between charged drops and hard particles

It is shown that the analytical expressions for the energy and force of electrostatic interaction between charged conducting particles (drops), a point charge, and a finite-size particle, as well as between a particle (a drop or a point charge) and a conducting plane, are asymmetric with respect to the sign of one of the charges. This is because the polarization interaction is always attractive irrespective of the signs of interacting particles. The absence of this symmetry leads to the self-constriction of charged aerodispersed systems containing a condensed phase, for example, plasma or liquid-droplet systems.     

Nonlinear oscillations of an uncharged conducting drop in an external uniform electrostatic field

The problem of nonlinear oscillations of the finite amplitude of an uncharged drop of an ideal incompressible conducting liquid in an external uniform electrostatic field is solved for the first time by analytical asymptotic methods. The problem is solved in an approximation quadratic in amplitude of the initial deformation of the equilibrium shape of the drop and in eccentricity of its equilibrium spheroidal deformation. Compared with the case of nonlinear oscillations of charged drops in the absence of the field, the curvature of the vertices of uncharged drops nonlinearly oscillating in the field is noticeably higher, whereas the number of resonant situations (in the sense of internal resonant interaction of modes) is much smaller.     

Nonlinear analysis of the equilibrium shape of a charged conducting drop in an electrostatic suspension

An analytical asymptotic expression is derived that describes the equilibrium shape of a charged drop of an ideal incompressible conducting liquid suspended in superposed collinear uniform electrostatic and gravitational fields. The expression is obtained in an approximation quadratic in the small amplitude of deviation of the equilibrium drop from a sphere, with the electrostatic field dimensionless strength taken as a measure of the deviation amplitude. With allowance for the gravitational and electrostatic fields and interaction between the drop self-charge and external electrostatic field, the equilibrium shape of the drop is found to be very close to a spheroid when the charge and the electrostatic field strength are far from their critical values. The analysis is carried out with a refined procedure of calculation of the equilibrium shape of drops placed in external force fields.     

Relationship between the diffusiophoresis rate, evaporation coefficient, and size of a large volatile drop

A new theory of diffusiophoresis of large volatile spherical aerosol drops that is an extension of investigations [1–8] is developed. The influence of the radius of the drop, the surface tension coefficient varying over the surface of the drop, the evaporation coefficient α of the liquid, and the flows inside the drop on the diffusiophoresis rate are taken into account. Expressions obtained allow for direct determination of the velocity of large individual aerosol drops in a binary gas mixture nonuniform in component concentration. It is shown that both the magnitude and the direction of the diffusiophoresis velocity depend on α and the size of the drop. It is assumed that the size of the drop varies but remains considerably greater than the mean free path of gas molecules.     

Some effects of the electrostatic interaction of water drops in the atmosphere

The electric field at the surface of two conducting spherical charged particles and their interaction force are calculated. It is shown that as particles carrying like charge approach each other, the force changes sign and becomes attractive. The case where the charge on each particle varies as the square of its radius is an exception (repulsion at any distance between the particles). Self-similar asymptotic solutions for the interaction force and energy are found for particles of identical size. For a pair of charged water drops falling simultaneously in the atmosphere, a numerical simulation shows that a drop formed by coalescence of the pair may be subject to the Rayleigh instability. Zh. Tekh. Fiz. 69, 12–17 (December 1999)     

密立根油滴实验中运动速度的分析简

通过对带电全程推导分析,而只是选取油滴匀速运动的区域进行测量。通过对带电全程推导分析,得到结果发现油滴在极短时间内就近似达到了极限速度,因此对于匀速区域的选取并不需要特别说明,实验本身的设计是十分合理。     

Description of evaporation of a spherical liquid drop by a non-Markovian random process based on integral stochastic equations

Processes of evaporation (condensation) of vapor particles from the surface of a spherical drop and processes of their diffusion into surrounding volume are considered. Special features of evaporation are investigated taking into account vapor particle fluctuations caused by random changes in the temperature, concentration, etc. Statistical characteristics of fluctuations of the corresponding quantities, including the mass flow through the liquid-vapor boundary and concentration on the liquid surface, are presented. The distribution of completely evaporated drop number versus time is presented.