Lateral vibration of a water drop and its motion on a vibrating surface

The resonant modes of sessile water drops on a hydrophobic substrate subjected to a small-amplitude lateral vibration are investigated using computational fluid dynamic (CFD) modeling. As the substrate is vibrated laterally, its momentum diffuses within the Stokes layer of the drop. Above the Stokes layer, the competition between the inertial and Laplace forces causes the formation of capillary waves on the surface of the drop. In the first part of this paper, the resonant states of water drops are illustrated by investigating the velocity profile and the hydrostatic force using a 3d simulation of the Navier-Stokes equation. The simulation also allows an estimation of the contact angle variation on both sides of the drop. In the second part of the paper, we investigate the effect of vibration on a water drop in contact with a vertical plate. Here, as the plate vibrates parallel to gravity, the contact line oscillates. Each oscillation is, however, rectified by hysteresis, thus inducing a ratcheting motion to the water droplet vertically downward. Maximum rectification occurs at the resonant states of the drop. A comparison between the frequency-dependent motion of these drops and the variation of contact angles on their both sides is made. The paper ends with a discussion on the movements of the drops on a horizontal hydrophobic surface subjected to an asymmetric vibration.     

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)     

Viscosity and electric properties of water aerosols

The flow of water mist in a narrow duct has been studied experimentally. The profile of the velocity of drops has been measured, and the viscosity of the mist has been calculated using the Navier–Stokes equation. It has been found that at low gradients of the rate of shear the viscosity of the mist can exceed that of clean air by tens and even hundreds of times. The electric charge of the drops has been measured. It has been found that the viscosity of the mist differs from that of clean air at gradients of the rate of shear that are less than the frequency of the establishment of electric equilibrium between the drops. A comparative analysis of the viscosities of the mist and a drop cluster has been carried out, and the dependence of the viscosity of the water aerosol on the radius and the charge of the drops has been predicted. The possible role of aerosols that contain submicron drops in the known “clear air turbulence” problem has been shown.     

A level-set continuum method for two-phase flows with insoluble surfactant

A level-set continuum surface force method is presented to compute two-phase flows with insoluble surfactant. Our method recasts the Navier–Stokes equations for a two-phase flow with insoluble surfactant as “one-fluid” formulation. Interfacial transport and interfacial jump conditions are treated using the level-set method and the discrete Dirac function. Based on the density-weighted projection method, a stable semi-implicit scheme is used to decouple the velocity components in solving the regularized Navier–Stokes equations. It allows numerical simulations for a wide range of viscosity ratios and density ratios.Numerical simulations on single drop deformation in a 2D shear flow are presented. Simulations on two drop interaction shows that surfactants can play a critical role in preventing drop coalescence. A fully 3D simulation demonstrating the physical interactions of multiple surfactant-laden drops is presented.     

On the mechanism of noncoalescence in a droplet cluster

Experimental data are presented, from which it follows that the mechanism of noncoalescence in a cluster of drops is not attributable to the electrostatic charging and the presence of surfactants. The Stokes force acting upon drops of the cluster in a convective plume amounts to a fraction of a percent of the drop weight. New effects are described, which provide evidence for a fast proper rotation of drops in the cluster. Estimates show that this rotation is explained in terms of the hypothesis of a thermocapillary nature of the noncoalescence phenomenon.     

Evaporation of Charged Drops

A model of evaporation of a multiply charged liquid drop is developed. The model self-consistently takes into account the main factors influencing the charged drop evaporation, including effects of the drop surface curvature and charge on the saturated vapor pressure, repeated fragmentation of drops during evaporation, and the capability of drops having a unit charge and a certain stabilization radius not to evaporate even in an unsaturated vapor medium. Analytical dependences are derived that can be used to calculate an integral lifetime of a charged drop with allowance for its fragmentation into smaller drops. Our estimates demonstrate that the evaporation time of charged drops is much smaller than that of uncharged drops.     

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.     

On the motion of a uniformly heated drop in a viscous liquid under gravity

The motion of a uniformly heated spherical drop under gravity is theoretically studied within the Stokes approximation. The Stokes and Hadamard-Rybchinsky formulas are generalized so that the temperature dependence of the viscosity can be found in a wide temperature range. Also, the drag force and the velocity of gravity fall are calculated for an arbitrary temperature difference between the surface of the drop and distant points.     

NMR imaging of falling water drops

The falling water drop is a simple model for studying phenomena related to chemical extraction, where two immiscible phases are dynamically blended to promote the transport of solute molecules from one phase to the other. Convective motion inside the drop significantly influences the extraction efficiency. Whereas optical and tracer methods are model bound or invasive, NMR imaging is noninvasive, direct, and applicable to nontransparent media. The first NMR measurements of a water drop falling through air are reported. It is shown that, in drops from pure water, large-scale convection rolls are observed in contrast to drops with the surface tension lowered by surfactants.     

Basic Studies of Electrohydrodynamic Atomization Process using phase Doppler measurement technique

A planar phase Doppler system is used to measure submicron droplets generated by an electrospray. Measured drop dia-meters are correlated with the liquid properties and the condition for transition of the spray from the single-jet mode to the multi-jet mode is introduced. In another set of measurements using a standard phase Doppler system, combined size and velocity data are employed to deduce the drag force on the drops. In a situation where the drag force is balanced primarily by the electric force, the phase Doppler measurements allow to estimate the power-law relationship between the charge on a drop and its diameter and hence, many provide insights into the underlying atomization mechanisms.     

Superhydrophobic wind turbine blade surfaces obtained by a simple deposition of silica nanoparticles embedded in epoxy

Samples of wind turbine blade surface have been covered with a superhydrophobic coating made of silica nanoparticles embedded in commercial epoxy paint. The superhydrophobic surfaces have a water contact angle around 152°, a hysteresis less than 2° and a water drop sliding angle around 0.5°. These surfaces are water repellent so that water drops cannot remain motionless on the surface. Examination of coated and uncoated surfaces with scanning electron microscopy and atomic force microscopy, together with measurements of water contact angles, indicates that the air trapped in the cavity enhances the water repellency similarly to the lotus leaf effect. Moreover, this new coating is stable under UVC irradiation and water pouring. The production of this nanoscale coating film being simple and low cost, it can be considered as a suitable candidate for water protection of different outdoor structures.     

Charge and force acting on a spherical body near a planar electrode in a polarizable conducting medium

A method for calculating electric fields in conducting polarizable media with interface is suggested. An integral equation for the density of surface charge induced at the interface is derived. The value of this density is used to find the field in the volume. The total charge induced at the interface and the force acting on a spherical body touching a planar electrode are calculated. It is found that the total charge and the force are alternating functions of the relative conductivity of the media; that is, both repulsion from and attraction to the electrode are possible depending on the conductivity. The near-electrode force acting on solid particles, bubbles, and drops in an immiscible liquid is studied experimentally.     

Hysteresis effect and surface energy of drops in silicon

We report here the observation of the hysteresis effect of the drop luminescence in silicon at the temperature of 6.6 K. Hysteresis ratios up to 2.1 have been registered. The surface energy σ of drops is deduced from the measurement of the energy shift of the drops luminescence at low pumping level. The results yield: σ = (125±60) × 10^?4ergcm^?2.     

Temperature dependence of the radius of electron-hole drops in Ge

The temperature dependence of the radius of electron-hole drops in Ge is determined from measurements of the number of particles in the drops using the p-n junction technique. The drop radius is found to increase from 5.5μ at 1.7 K to 10μ at 3.2 K for an excitation intensity of 160 mWatt/mm². As a function of excitation level at 1.8 K the drop radius is found to increase from 2.9μ at 8 mWatt/mm² to 6.5μ at 300 mWatt/mm². Our data are compared to results available in this field.     

氩气介质阻挡放电不同放电模式的电学特性研究

采用水电极介质阻挡放电装置，在气压为40kPa的氩气中实现了弥散、流光和斑图三种不同 模式的放电，并对其光电特性进行测量.通过测量测试电容上的电压，从而将气隙电压计算 出来，发现随外加电压增加，放电起始时刻不断提前，放电占空比增加；对应放电时刻，气 隙电压减小、输运电荷突增，使得气隙电压和电量波形都远远偏离正弦.气隙电压与输运电 荷成非线性关系.给出了外加电压零点对应的气隙电压随外加电压峰值的变化关系.讨论了壁 电荷在放电中的作用及对气隙电压和电量波形的影响. 关键词： 介质阻挡放电 气隙电压 自组织斑图 输运电荷     

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.     

倾斜均质表面上等径水滴聚合过程的可视化实验

对倾斜均匀表面上等直径水滴的聚合过程及特性进行了可视化实验研究,获得了水滴直径和表面倾角等参数对液滴聚合过程中液滴液桥半径、接触角和接触线变化特性的影响,分析了水滴聚合对其运动的影响.实验结果表明:表面倾角越大,下滑的临界半径越小;液滴的直径越大,液滴聚合后越容易下滑;液滴聚合可以加快液滴的运动,使下滑临界半径减小.     

Dropwise chains as the elements of water fog spatial structure

Video images of water fog drops were acquired under standard atmospheric conditions with weak turbulence of the environment. Pair correlation functions of the drops were performed and traces of the spatial arrangement of the drops inside the fog determined. The fog structure carriers are the drop chains with a fixed interdroplet distance. The possible influence of the drop chains on the shear viscosity and fog surface tension has been analysed.     

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.     

The wetting angle of very small and large drops

On the basis of Born-Green-Yvon integral equations for the density distribution functions, an approximate integral equation is established for the profile of the surface of the drop. Numerical solutions and analytical solutions for limiting cases are obtained for this profile. Equations relating the angle at the leading edge and in its vicinity to parameters characterizing the interaction forces between the molecules of the liquid and between those of the liquid and solid are derived for large and for very small drops on a horizontal solid surface. One concludes that there is a rapid spatial variation of shape near the leading edge, that for large drops the measured macroscopic wetting angle is reached at a distance of about 20 to 40 Å from the leading edge, and that for very small drops the wetting angle is weakly size dependent. A condition for drop stability is established, which if not satisfied, the liquid will spread over the surface of the solid.