Experimental Analysis of the Response of a Laser/Phase Doppler Anemometer System to a Partially Atomized Spray

This work describes a systematic approach adopted to establish Laser and Phase Doppler Anemometry, LDA/PDA, experimental techniques that would allow velocity and dropsize measurements to be made over wide velocity and size ranges with confidence in partially atomized sprays. The analysis considers the sprays generated by different gasoline direct injection (GDI) systems injecting into air under atmospheric conditions. The upper limit to the dropsize range in the fuel sprays was confirmed using (a) an Oxford Lasers' VisiSizer and (b) droplets of a known size produced by a mono‐dispersed droplet generator. GDI fuel sprays are highly transient, optically dense and provide a high degree of penetration and atomization. The measurement problem is therefore one of the detection of small, high speed droplets inside a dense cloud of surrounding droplets. Furthermore, under the transients found at the start and end of injection and during high fuel loads, fuel elements in the form of sheets, ligaments and filaments are also injected. These liquid fuel elements subsequently break‐up, downstream from the nozzle, to form droplets of a much larger size class but with a much lower number density [1]. The co‐existence of these liquid fuel elements and the widely different size classes in the spray are considered to pose a problem for dropsize measurements by the PDA technique. In particular: the wide dynamic range of light intensities scattered by the fuel elements and droplets; the trajectory of large drops through the edges of the PDA measurement volume with its Gaussian intensity distribution [2] and the high probability of non spherical droplets. The work concludes that the LDA/PDA measurement technique, as applied here, is robust. It can discriminate between partially and fully atomized sprays, has a high probability of accurately measuring dropsizes larger than the measurement volume and give a realistic indication of ‘sizes’ for non spherical droplets. However, specification of the PDA system parameters must be strictly compatible with the measurement task to yield unambiguous results.     

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.     

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.     

Application of the Maximum Entropy Formalism on Sprays Produced by Ultrasonic Atomizers

A recent application of the Maximum Entropy Formalism on liquid atomization problems led to the development of a mathematical volume‐based drop‐size distribution. This function, which depends on three parameters, is a reduction of the four‐parameter generalized Gamma function. The aim of the present work is to investigate the relevance of the three parameters in the characterization of liquid atomization processes. To achieve this, a variety of experimental drop‐size distributions of ultrasonic sprays were analyzed with the mathematical function. Firstly, it is found that the mathematical drop‐size distribution is very suitable to represent the volume‐based drop‐size distribution of ultrasonic sprays. Furthermore, it is seen that when considering the three parameters introduced by the function, one of them is constant for all the situations investigated, and the other two are linked to a non‐dimensional group that includes the main parameters controlling the drop production. These results are very important, since they suggest a possible development of physical models of primary atomization based on the M.E.F., which would allow for the prediction of the spray drop‐size distribution. Thusfar, such a model does not exist.     

纳米结构表面上部分润湿液滴合并诱导弹跳的理论研究

部分润湿液滴是适宜纳米结构表面上滴状冷凝传热的主要载体,研究纳米结构参数与部分润湿液滴合并弹跳之间的关系有重要意义,本文依据冷凝液滴生长过程中能量增加最小的原理来判断其是否为部分润湿状态,并根据液滴合并前后的体积和界面自由能守恒,确定了合并液滴的初始形状,进而对合并液滴变形过程的动力学方程进行了求解,结果表明:部分润湿冷凝液滴仅在纳米柱具有一定高度、直径间距比较大的表面上形成,而当纳米柱高度过低、直径间距比小于0.1时则形成完全润湿的冷凝液滴;液滴合并后能否弹跳与纳米结构参数紧密相关,仅在纳米柱较高、直径间距比适宜的表面上,部分润湿液滴合并后才能诱发弹跳;液滴尺度及待合并液滴间的尺度比对合并弹跳也有重要影响;多个部分润湿液滴合并后由于具有更多的过剩界面自由能而比两个液滴合并更容易诱发弹跳,本模型对纳米结构表面上冷凝液滴是否合并诱发弹跳的计算结果与绝大部分实测结果相一致,准确率达到95%。     

Global Rainbow Thermometry for Mean Temperature and Size Measurement of Spray Droplets

Global rainbow thermometry is a new technique for measuring the average size and temperature of spray droplets. For data inversion a global rainbow pattern is employed, which is formed by constructive interference of laser light scattered by an ensemble of spherical droplets. The non‐spherical droplets and liquid ligaments provide a uniform background and hence do not influence the interference pattern from which average size and temperature are derived. This is a large improvement with respect to standard rainbow thermometry, investigated since 1988, which is strongly influenced by particle shape. Moreover, the technique is applicable to smaller droplets than the standard technique because the global pattern is not spoiled by a ripple structure. Data inversion schemes based on inflection points, minima and maxima are discussed with respect to spray dispersion and droplet flux. The temperature derivation from inflection points appears to be independent of spray dispersion. Preliminary measurements in a heated water spray are reported. The mean diameter obtained from the rainbow pattern is smaller than the arithmetic mean diameter measured by phase‐Doppler anemometry. The accuracy of the temperature measurement by global rainbow thermometry is shown to be a few degrees Celsius.     

电控聚合物分散液晶变焦全息透镜制作

介绍了相位型全息聚合物分散液晶(PDLC)材料全息透镜,在电场作用下液晶微滴折射率逐渐与聚合物折射率匹配,实现透镜电控变焦。研究了微米尺寸和纳米尺寸液晶微滴聚合物分散液晶材料配方特性和微观结构。采用优化纳米尺寸材料配方制作5~6μm聚合物分散液晶盒,采用离轴式平面波和球面波干涉全息写入光路,成功制作电控变焦聚合物分散液晶全息透镜样品。该透镜样品焦距为20 mm,能够正一级衍射放大成像。实现“0”,“1”变焦的驱动电压阈值为60 V。并进一步提出了基于聚合物分散液晶电控变焦元件集成叠加技术实现电控变焦光学成像系统的技术思路。     

Nonlinear analysis of the equilibrium shape of a charged drop in the tornado funnel wall

From the pressure balance condition on the free surface of a conducting liquid charged drop, an expression is derived for the equilibrium shape of the drop placed in the field of centrifugal forces acting in the tornado wall. The analysis is carried out in an approximation quadratic in small parameter (the ratio of the deformation amplitude to the radius of the initially spherical drop). In the linear approximation, the drop is a spheroid oblate in the direction normal to the tornado axis. The eccentricity of the spheroid squared is proportional to the angular velocity squared and the radius of the drop cubed. In the quadratic approximation, the equilibrium shape of the drop is other than spheroidal.     

On the time evolution of the surface shape of a charged viscous liquid drop deformed at zero time

The problem of capillary oscillations of the equilibrium spherical shape of a charged viscous incompressible liquid drop is solved in an approximation linear in amplitude of the initial deformation that is represented by a finite sum of axisymmetric modes. In this approximation, the shape of the drop as a function of time, as well as the velocity and pressure fields of the liquid in it, may be represented by infinite series in roots of the dispersion relation and by finite sums in numbers of the initially excited modes. In the cases of low, moderate, and high viscosity, the infinite series in roots of the dispersion relation can be asymptotically correctly replaced by a finite number of terms to find compact analytical expressions that are convenient for further analysis. These expressions can be used for finding higher order approximations in amplitude of the initial deformation.     

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.     

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.     

Droplet suction on porous media

We study the forced aspiration of small ( mm) and large ( cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected “sponge-like”. Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a “locked” regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing () to finite receding () contact angle; 2) an “unlocked” regime, where the contour line recedes with a constant contact angle closed to . In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat “gravity pancake” for large ones. Received 19 January 2000     

液滴低速撞击润湿球面现象观测分析

采用高速摄像仪以10000 帧/s的拍摄速度对液滴低速撞击润湿球体表面过程进行了实验观测, 分析了液滴撞击后的反弹、局部反弹和铺展等现象, 考察了黏度对撞击过程的影响; 在此基础上, 定量讨论了液滴铺展特征参数随撞击速度、球体直径和黏度的变化规律. 观测发现: 黏度较大且撞击速度较低时, 撞击后可能出现反弹和局部反弹, 黏度较小时则不发生; 铺展面积随撞击速度的增大而增大; 黏度增大时, 铺展因子减小; 在球体直径为4–20 mm范围内, 随着球体直径的增加, 铺展因子呈上升趋势. 关键词： 液滴撞击 润湿球面 铺展 黏度     

Angular structure of radiation scattered by monolayer of polydisperse droplets of nematic liquid crystal

We considered light scattering by a polydisperse ensemble of droplets of a nematic liquid crystal. To model light scattering by a monolayer of polymer-dispersed spherical droplets of a nematic liquid crystal with cylindrical symmetry of its internal structure, we proposed a semianalytical modeling method. The method is based on interference approximation of the theory of multiple wave scattering, anomalous diffraction approximation, and effective-medium approximation. The method takes into account cooperative optical effects in concentrated, partially ordered layers and can be used to analyze the small-angle structure of the intensity of scattered radiation in relation to the concentration, size, polydispersity of liquid crystal droplets, orientation of their optical axes, and refractive indices of the liquid crystal and polymer. The obtained relations can be applied to solving direct and inverse problems of light scattering in composite liquid crystal materials using data of polarization measurements. We present graphical results of solving the direct problem for components of the polarization vector of scattered wave. These results illustrate the formation of an angular structure for monolayers with a high concentration of polydisperse droplets of the liquid crystal in the range of small scattering angles (0 < θ _s ≤ 8°).     

A New Formulation of the Maximum Entropy Formalism to Model Liquid Spray Drop‐Size Distribution

Considering the differences and disagreements involving the previous application of the Maximum Entropy Formalism to modeling the drop‐size distribution of liquid sprays, a new formulation is suggested. The constraints introduced in this formulation are based on characteristic features common to any liquid atomization process, i. e., the production of large and small drops is always limited. These limitations are a consequence of the action of both destabilizing and stabilizing forces such as aerodynamic and surface tension forces, respectively. The solution resulting from this approach, which makes use of statistical mechanics, is a three‐parameter Generalized Gamma Distribution, which can treat any type of distribution. It is shown that this solution is identical to a Nukiyama‐Tanasawa distribution that should no longer be regarded as an empirical distribution. Although this new formulation clearly answers the question concerning the amount of information required to describe a spray drop‐size distribution, it raises the problem of the mathematical form to be given to this information, and is discussed here.     

The interface shape of the double-liquid lens

In this article, a differential equation, which describes the shape of the liquid interface in a cylindrical chamber when the density difference of two liquids is zero, is provided. And an analytical solution is found for the differential equation which indicates the interface shape is spherical. And such a result is not independent on the vessel size. In experiment, by means of measuring the focal lengths of liquid lenses with different vessel size, the results show that the focal lengths ratio is quite approximate to the inner radius ratio of the cylindrical chamber, which can inversely verifies that the interface shape of liquid lens with two same density liquids is spherical.     

Interaction of shock waves with bubble-liquid drops

The regular reflection of an air shock wave from a spherical drop of a bubble liquid is studied. In the framework of an extended equilibrium model, the effect of the shock waves on single drops of various shapes and on drop ensembles (drop screens) is numerically investigated. It is shown that, when subjected to shock waves, bubble-liquid drops and drops of a bubble-free liquid collapse in a radically different way.     

Use of Video Enhanced Microscopy for Characterization of Solid‐Liquid‐Liquid Mixtures

Although some particle sizing devices have gained a lot of popularity, none of them is able to distinguish between drops and solids and few are able to handle viscous oily samples. This paper discusses the use of the optical microscopy, enhanced by the use of digital video capabilities and image analysis software, to characterize oil production wastes. Several thousands of particles were counted and their projected areas were measured. A discussion is given about the different corrections required in order to extract the most reliable information from the image analysis, overcoming some of the drawbacks of this kind of measurements. The technique developed here offers unique features like the determination of the fraction of droplets that exist in the form of non‐coalesced agglomerates. When cross‐linked with the results obtained by standard ASTM procedures, it allows to infer the amount of disperse phase that exists in the form of submicron droplets or large free water drops that are usually not sampled for microscope slides.     

Delayed coalescence of droplets with miscible liquids: Lubrication and phase field theories

Mixing of droplets with a body of different liquids shows an interesting behavior for small contact angles at solid substrate. The droplets interact with each other, a liquid exchange appears between the approaching drops owing to surface tension gradients at the droplets interface. But the drops remain separated for some seconds (up to minutes), until the merging into a single drop occurs (Langmuir 24, 6395 (2008)). We investigate this phenomenon using lubrication approximation and phase field approach. For both methods, 2D quantitative computer simulations for delayed fusion of perfectly miscible thin liquid films/droplets with low contact angles are reported.     

Dynamic aspect of solid solution cathodes by method of integral transform

A mathematical model is presented for a thin film, spherical and cylindrical particles electrodes under galvanostatic discharge. The model available to simulate the electrochemical behavior is discussed considering not only their electrochemical representation (transport phenomena), but also the mathematical techniques, i.e. Integral transform that have been used for solving the equations. We examine the non-homogeneous material balance equation in the rectangular, spherical and cylindrical coordinate system; determine the elementary solutions, the norms and the eigenvalues of the problems for galvanostatic boundary conditions and systematically tabulate the resulting expressions. Expressions are developed for plane, cylindrical and spherical particles giving the relation between battery load and the amount of cathode material utilized. The particle shape and a single parameter Q is used to describe cathode performance.