Development of a Three-parameter Volume-based Spray Drop Size Distribution through the Application of the Maximum Entropy Formalism

This work is an extension of a previous investigation on the determination of mathematical volume-spray drop size distributions by the application of the maximum entropy formalism. A two-parameter drop size distribution was derived and was found to give reasonable fits with experimental distributions obtained under different experimental conditions. However, as it is discussed, this two-parameter distribution shows critical limitations and cannot be applied in any situations of interest as far as drop size distributions in liquid sprays are concerned. To overcome this problem, a third parameter, equivalent to a drop diameter, is introduced into the procedure. This correction leads to a three-parameter drop size distribution with independent mean, width and symmetry. This function is a generalized gamma distribution and it can cover more practical situations than the previous two-parameter distribution. Furthermore, it is found that, contrary to the two-parameter distribution, the new volume-based drop size distribution shows a corresponding number-based drop size distribution with a physical behavior as the drop diameter decreases. This last result shows the importance of using three parameters to describe spray drop size distributions and that one of these parameters must represent the population of small drops.     

Drop-Size Distributions Produced by Flat-Spray Nozzles

This study deals with measurements of the drop-size distributions of different types of fan spray atomisers using a scattered-light particle size counting analyser. The drop-size distributions were determined at various locations in the spray cone. These local distributions change systematically from the fan's axis to its border. Superimposing these local distributions, adequately weighted, one acquires the entire distribution of all the drops. A comparison of the experimental results is made with those yielded by mathematical equations.     

振动斜板上下落液体薄膜的数值模拟

用Galerkin有限元法数值模拟了振动斜板上的下落液体薄膜流动,研究了流场中不同强迫频率和初始扰动频率的影响.结果表明由于它们之间的相互作用,流场中出现低频信号,其在流场中的非线性效应使得表面波发生合并,加速了表面波的发展.对较高的强迫频率,这种效应更明显,且可观察到孤立包的产生.     

Correlations to predict droplet size in ultrasonic atomisation.

In conventional two fluid nozzles, the high velocity air imparts its energy to the liquid and disrupts the liquid sheet into droplets. If the energy for liquid sheet fragmentation can be supplied by the use of ultrasonic energy, finer droplets with high sphericity and uniform size distribution can be achieved. The other advantage of ultrasound induced atomisation process is the lower momentum associated with ejected droplets compared to the momentum carried by the droplets formed using conventional nozzles. This has advantage in coating and granulation processes. An ultrasonic probe sonicator was designed with a facility for liquid feed arrangement and was used to atomise the liquid into droplets. An ingenious method of droplet measurement was attempted by capturing the droplets on a filter paper (size variation with regard to wicking was uniform in all cases) and these are subjected to image analysis to obtain the droplet sizes. This procedure was evaluated by high-speed photography of droplets ejected at one particular experimental condition and these were image analysed. The correlations proposed in the literature to predict droplet sizes using ultrasound do not take into account all the relevant parameters. In this work, a truly universal correlation is proposed which accounts for the effects of physico-chemical properties of the liquid (flow rate, viscosity, density and surface tension), and ultrasonic properties like amplitude, frequency and the area of vibrating surface. The significant contribution of this work is to define dimensionless numbers incorporating ultrasonic parameters, taking cue from the conventional numbers that define the significance of different forces involved in droplet formation. The universal correlations proposed are robust and can be used for designing ultrasonic atomisers for different applications. Among the correlations proposed here, those ones that are based on the dimensionless numbers and Davies approach predict droplet sizes within acceptable limits of deviation. Also, an empirical correlation from experimental data has been proposed in this work.     

Controlled exfoliation of molybdenum disulfide for developing thin film humidity sensor

We report a facile, size-controllable exfoliation process using an ultrasound-assisted liquid method to fabricate few-layer molybdenum disulfide (MoS₂) nanosheets. The morphology, structure and size distribution of the nanosheets processed with different ultrasonic powers were examined by atomic force microscopy, Raman spectroscopy and dynamic light scattering. It was revealed that the size of nanosheets reduces and final yield increases with elevating ultrasonic power. Bulk and exfoliated MoS₂ based thin film sensors are fabricated by a simple drop casting method on alumina substrates. Our sensors exhibit excellent sensitivity with very quick response and recovery speed to humidity gas. Comparative studies are carried out to draw up the size or ultrasonic power dependent sensing behavior.     

Electrowetting-induced oil film entrapment and instability

We investigate the spreading at variable rate of a water drop on a smooth hydrophobic substrate in an ambient oil bath driven by electrowetting. We find that a thin film of oil is entrapped under the drop. Its thickness is described by an extension of the Landau-Levich law of dip coating that includes the electrostatic pressure contribution. Once trapped, the thin film becomes unstable under the competing effects of the electrostatic pressure and surface tension and dewets into microscopic droplets, in agreement with a linear stability analysis. Our results recommend electrowetting as an efficient experimental approach to the fundamental problem of dynamic wetting in the presence of a tunable substrate-liquid interaction.     

Deconvolution with Maximum Entropy Solution to Determine Local Extinction Coefficient and Local Volume Concentration Values from Laser Diffraction Data

The traditional use of the laser diffraction technique provides line‐of‐sight liquid spray drop‐size distribution. However, deconvolution of the measurements can be performed for axisymmetric spray in order to determine local spray characteristics. In a previous publication, a new deconvolution technique making use of the maximum entropy principle was established and applied to determine the local drop‐size distributions. The entire approach was experimentally validated. In this work, the technique is employed to determine local extinction coefficient values. As in the previous investigation, the measurement procedure consists of scanning a laser beam through the spray cross‐section from the center to the edge of the spray. By use of the transmittance theory, the local extinction coefficients allow the local volume concentrations to be calculated. This theory introduces the mean scattering coefficient. The results show that this coefficient must be determined as a function of the Sauter mean diameter in order to avoid overestimation of the volume concentration. Although no proper validation is presented, the coherence of the overall approach is discussed in detail and solutions for improving the spatial resolution are presented. Finally, the local volume concentrations are combined with the local drop‐size distribution to provide local volume‐weighted, drop‐size distributions. These distributions provide information on the localization of the drops according to their diameter as well as on the spatial liquid distribution. This work illustrates applications and performances of laser diffraction technique that are rarely used.     

Spray impingement wall film breakup by wave entrainment

Fuel spray impingement on engine wall and piston in the spark-ignition direct-injection (SIDI) setting has been considered a major concern in the aspect of engine emission and combustion efficiency. Excess wall film will result in deterioration of engine friction, incomplete combustion, and substantial cycle-to-cycle variations. These effects are more pronounced during engine cold-start process. Therefore, the formation of wall film on engine wall/piston and the dynamic process of the wall film interacting with impinging spray and spray-induced gas flow are of great significance for reducing wall film mass. However, the dynamic process of wall film was not investigated thoroughly in existing literatures. This work will present a high-speed, simultaneous measurement of a single-hole spray structure, as well as wall film geometry and thickness, via Mie scattering and volumetric laser-induced fluorescence, respectively. Quantitative film thickness measurement was achieved via fluorescence intensity signal calibration with a known, wedge-shape liquid film apparatus. Remarkable wall film droplet entrainment at the leading edge of the liquid film waves was revealed in the measurement, which has not been adequately depicted or analyzed in existing spray impingement studies. A considerable amount of liquid droplets detaches from the liquid film via liquid film fingering, during which process the quantity of liquid mass on the wall is decreased. Quantitative analysis of such phenomenon is performed and we estimated that a liquid mass equivalent to 30–40% of the residual liquid film mass is detached from the liquid film via wave entrainment. Furthermore, through the comparative study of the side view of the spray and the liquid film caused by spray impingement, it is shown that non-uniform spray structure is likely the cause of liquid film wavy motions. These observations suggest that wave entrainment should be considered by numerical models and experimental designs to accurately predict spray impingement phenomenon.     

液滴冲击液膜过程实验研究

实验显示了液滴撞击物体表面液膜后产生水花、发生飞溅,特别是产生“钟形”水花等的流动现象.根据实验结果,探讨了液滴冲击速度、液体黏性、表面张力、液滴直径和液膜厚度等对液滴冲击后产生的流动现象,以及液膜形状演化的影响,分析了观测到的鲜有文献报道的液滴撞击液膜后产生“钟形”水花的现象. 关键词： 液滴 液膜 冲击 流动显示     

Numerical Simulation of Vapor Bubble Growth and Heat Transfer in a Thin Liquid Film

A mathematical model is developed to investigate the dynamics of vapor bubble growth in a thin fiquid film, movement of the interface between two fluids and the surface heat transfer characteristics. The model takes into account the effects of phase change between the vapor and liquid, gravity, surface tension and viscosity. The details of the multiphase flow and heat transfer are discussed for two cases： （1） when a water micro-droplet impacts a thin liquid film with a vapor bubble growing and （2） when the vapor bubble grows and merges with the vapor layer above the liquid film without the droplet impacting. The development trend of the interface between the vapor and liquid is coincident qualitatively with the available literature, mostly at the first stage. We also provide an important method to better understand the mechanism of nucleate spray cooling.     

Combining Brillouin spectroscopy and laser-SAW technique for elastic property characterization of thick DLC films

Surface Brillouin spectroscopy (SBS) has been widely used for elastic property characterization of thin films. For films thicker than 500 nm, however, the wavelength of surface acoustic wave in the frequency range available for SBS is smaller than film thickness, and the SBS measures only the Rayleigh wave of the film. The laser-SAW technique, on the other hand, measures only the low-frequency portion of the surface acoustic wave dispersion and can estimate only one elastic modulus of the film (typically Young's modulus). In this work, we have combined the two methods to determine both Young's modulus and Poisson's ratio of a diamond-like carbon (DLC) film. It was found that reasonable estimates can be obtained for the longitudinal wave velocity, shear wave velocity, and Young's modulus of the film. The Poisson's ratio, however, still has a relatively large measurement error.     

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.     

Wave phase conjugation of the stokes component of Brillouin scattering of ultrasound

Wave phase conjugation of a low-frequency ultrasonic wave due to Brillouin scattering of high-frequency parametrically phase conjugate waves in liquid was theoretically and experimentally studied. It was shown that the envelope of the low-frequency conjugate wave is proportional to the product of envelopes of high-frequency waves. The conjugation efficiency corresponds to the angular diagram of the resonant interaction of ultrasonic beams. Compensation for the phase shift of the plane low-frequency wave due to its wave phase conjugation was demonstrated.     

Vibration characteristics of aluminum surface subjected to ultrasonic waves and their effect on wetting behavior of solder droplets

The vibration characteristics of an aluminum surface subjected to ultrasonic waves were investigated with a combination of numerical simulation and experimental testing. The wetting behavior of solder droplets on the vibrating aluminum surface was also examined. The results show that the vibration pattern of the aluminum surface is inhomogeneous. The amplitude of the aluminum surface exceeds the excitation amplitude in some zones, while the amplitude decreases nearly to zero in other zones. The distribution of the zero-amplitude zones is much less dependent on the strength of the vibration than on the location of the vibration source. The surface of the liquid solder vibrates at an ultrasonic frequency that is higher than the vibration source, and the amplitude of the liquid solder is almost twice that of the aluminum surface. The vibration of the surface of the base metal (liquid solder) correlates with the oxide film removal effect. Significant removal of the oxide film can be achieved within 2 s when the amplitude of the aluminum surface is higher than 5.4 μm or when the amplitude of the liquid solder surface is higher than 10.2 μm.     

单液滴正碰球面动态行为特性实验研究

在考虑空气阻力影响,确定液滴撞击球面速度的基础上,对较高韦伯数液滴撞击干燥球面动态行为过程进行了实验研究,分析了球面曲率与韦伯数对液滴撞击行为和铺展因子的影响,并与前人撞击平面结果进行了对比.实验表明,靠近撞击球面时,液滴降落速度出现明显波动;球面曲率对液滴撞击后行为影响明显,曲率较大时,液滴撞击后铺展液膜会超出球面直径并滑落,曲率较小时,液滴撞击后在球面上呈现明显的铺展、回缩、震荡、着附动态变化行为,此时最大铺展因子受曲率影响小,随曲率减小,逐渐趋向于撞击平面时的最大铺展因子;韦伯数对液膜铺展速率影响较小,但对液膜回缩时间影响明显,最大铺展因子随韦伯数增加逐渐增大,获得的关联式呈指数变化.     

微纳间隙受限液体的界面黏着机理研究

利用球-盘接触黏着试验仪对微量受限液体的界面黏着行为的研究发现：临界体积范围内（皮升到纳升）的受限液滴达到临界厚度后将出现自动铺展和瞬时收缩行为（分别对应球-盘趋进和分离过程）,并同时提供一定幅值的法向黏着力及伴随出现力的突变;该界面黏着力与液滴体积、球的直径等相关,并很好地揭示了昆虫或树蛙爪垫与光滑表面间的湿黏着行为.在进一步试验的基础上,利用球—面接触模型的毛细黏着力公式对所观察到的试验现象进行了机理揭示,认为临界体积受限液滴出现的自动铺展和瞬时收缩行为与接触副的刚度相关,最大法向黏着力随液体体积的减小而减小,与接触副之间受限液体的中心区厚度有关.结合生物黏着爪垫进行了受限液体界面黏着控制机理的分析,可以指导仿生黏着爪垫的设计与控制. 关键词： 生物黏着爪垫 毛细黏着力 受限液体     

About the effect of microtexture on liquid film formation on a vertical surface

Formation of a liquid film on the surface of a cylinder with microtexture was studied visually. The effect of microtexture on evolution of waves on the surface of viscous liquid falling over the outer surface of a vertical cylinder under the action of gravity depending on Reynolds number is shown. The phenomenon of microwave formation on the film surface was determined; the size of these waves is comparable with the microtexture pitch.     

A Predictive Model for the Initial Droplet Size and Velocity Distributions in Sprays and Comparison with Experiments

The distribution of sizes and velocities of droplets initially formed in sprays is an important piece of information needed in the spray modelling, because it defines the initial condition of the spray droplets in the predictive calculations of the downstream two‐phase flow fields. A predictive model for the initial droplet size and velocity distributions in sprays is formulated in this study. The present model incorporates both the deterministic and the stochastic aspect of spray formation process. The deterministic aspect takes into account of the unstable wave motion before the liquid bulk breakup through the linear and nonlinear instability analysis, which provides information for the liquid bulk breakup length, the mass‐mean diameter and a prior distribution for the droplet sizes corresponding to the unstable wave growth of various wavelengths. The stochastic aspect deals with the final stage of droplet formation after the liquid bulk breakup by statistical means through the maximum entropy principle based on Bayesian entropy. The two sub‐models are coupled together by the various source terms signifying the liquid‐gas interaction, the mass mean diameter and the prior distribution based on the instability analysis. The initial droplet size and velocity distributions are measured experimentally by phase‐Doppler interferometry for sprays generated by a planar research nozzle and a practical gas turbine airblast nozzle. For the two nozzles, the liquid bulk sheet is formed before its breakup in a coflowing air stream. It is found that the model predictions are in satisfactory agreement with the experimental data for all the cases measured. Hence the present model may be applied to a variety of practical sprays to specify the initial conditions for the spray droplets formed in practical spray systems.     

Ultrasonic Interferometer on Shear Waves in Liquids

Russian Physics Journal - The developed ultrasonic interferometer on low-frequency shear waves in liquids is described. The problem of the piezo-quartz crystal – liquid interlayer –...     

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.