Vortex Flows in the Liquid Layer and Droplets on a Vibrating Flexible Plate

In certain conditions, in the layers and droplets of a liquid on a vibrating rectangular flexible plate, vortex flows are formed simultaneously with the excitation of capillary oscillations on the free surface of the liquid layers and droplets. Capillary oscillations in the form of two-dimensional standing waves form Faraday ripples on the free surface of the liquid layer. On the surface of the vibrating droplets, at the excitation of capillary oscillations a light spot reflected from a spotlight source moves along a trajectory in the form of a Lissajous figure observed with a microscope. When vortex flows visualized with graphite microparticles appear in the layer and droplets of a transparent liquid, the trajectory of the light spot on the layer and droplet surface is a two-dimensional trajectory in the form of an ellipse or a saddle. This indicates that the generation of the vortex flows in a liquid at vibrations is due to capillary oscillations in the orthogonally related directions. In the liquid layer and droplets on the surface of the flexible plate, the vibrations of which are generated by bending vibrations, the vortex flows appear due to the plate vibrations and the capillary oscillations of the surface of a layer or a droplet of the liquid. On the free surface of the liquid, the capillary waves, which are parametrically excited by the plate bending vibrations, are additionally modulated by the same bending vibrations in the transverse direction.     

喷印工艺控制参数对水性油墨墨滴形态的影响

目的为了提高水性油墨的喷墨印刷质量,通过控制喷印工艺参数以获得良好的墨滴形态。方法分析喷印工艺控制的关键参数以及墨滴形态的表征参数,通过单因素工艺参数对墨滴形态影响的实验,分析电压、点火频率和脉冲宽度对墨滴形态各评价指标的影响程度,并运用AHP法构建墨滴形态的质量分析模型;通过多因素工艺参数组合对墨滴形态影响的正交实验,分析各工艺参数与墨滴形态参数之间的关联性,并结合质量评价模型综合评判喷印工艺参数对墨滴形态的影响。结果喷印工艺参数电压、点火频率和脉冲宽度共同影响墨滴形态的质量,脉冲宽度对其影响最大,点火频率次之,电压的影响程度最小,其权重分别为0.462,0.272,0.266。结论水性油墨喷印工艺中,通过合理地控制喷印工艺的关键参数,可以有效地提高墨滴形态质量,从而获得良好的印刷品质量。     

Smoothed particle hydrodynamics-based numerical investigation on sessile, oscillating droplets

Forced oscillations in sessile droplets can be exploited in electrowetting mixing of fluid fractions. The necessary complex flows and large shape deformations require a numerical investigation of fluid dynamics in the transient regime. We provide a means to characterize oscillations qualitatively and quantitatively with the goal to examine and to classify flow patterns occurring inside. A superposition of different harmonic excitation patterns gives the possibility to control the convective flow. In this investigation, we apply a generic and accurate multi-phase smoothed particle hydrodynamics model to a two-dimensional three-phase flow and consider an oscillating droplet sitting on a substrate and immersed in a fluidic phase. These vibrations are investigated in two ways: the analysis of a step response due to an abrupt change of the contact angle is applied to identify the resonance frequencies. Secondly, the time evolution of the shape of the droplet in terms of harmonic functions is determined. Their amplitudes are examined in the time and frequency domain. This gives the possibility to relate resonance frequencies to mode shapes and to detect a coupling between them. Our approach is successfully applied to different numerical case studies.     

压电喷墨液滴撞击光滑壁面铺展行为的数值研究

目的 研究典型流体相关无量纲参数对墨滴在光滑承印物表面铺展行为的影响,确定各无量纲参数对铺展直径、铺展因子和稳定铺展时间的影响规律。方法 利用Ansys软件,建立墨滴撞击光滑壁面的数值计算模型,采用VOF模型追踪液滴形状,采用PISO算法计算压力速度耦合。引入韦伯数、雷诺数、奥内佐格数来分析墨滴撞击光滑承印物表面的铺展行为。结果 计算获得不同韦伯数、雷诺数、奥内佐格数下墨滴的最大铺展直径、最终平衡铺展直径、最大铺展因子和最终铺展时间。结论 韦伯数和雷诺数对墨滴最大铺展直径的影响较大,对最终平衡直径的影响较小。韦伯数或雷诺数越小,回缩阶段越短,越快达到平衡。韦伯数、雷诺数与最大铺展因子呈明显正相关。奥内佐格数对墨滴的最大铺展直径、最终平衡直径的影响都较小。奥内佐格数越小,回缩阶段越短,越快达到平衡,奥内佐格数与液滴最大铺展因子呈不明显的正相关性。     

Solidification contact angles of molten droplets deposited on solid surfaces

Droplet impact and equilibrium contact angle have been extensively studied. However, solidification contact angle, which is the final contact angle formed by molten droplets impacting on cold surfaces, has never been a study focus. The formation of this type of contact angle was investigated by experimentally studying the deposition of micro-size droplets (∼39 μm in diameter) of molten wax ink on cold solid surfaces. Scanning Electron Microscope (SEM) was used to visualize dots formed by droplets impacted under various impact conditions, and parameters varied included droplet initial temperature, substrate temperature, flight distance of droplet, and type of substrate surface. It was found that the solidification contact angle was not single-valued for given droplet and substrate materials and substrate temperature, but was strongly dependent on the impact history of droplet. The angle decreased with increasing substrate and droplet temperatures. Smaller angles were formed on the surface with high wettability, and this wetting effect increased with increasing substrate temperature. Applying oil lubricant to solid surfaces could change solidification contact angle by affecting the local fluid dynamics near the contact line of spreading droplets. Assuming final shape as hemispheres did not give correct data of contact angles, since the final shape of deposited droplets significantly differs from a hemispherical shape.     

Experimental and Theoretical Investigation on Rapid Evaporation of Ethanol Droplets and Kerosene Droplets During Depressurization

This paper reports an experimental and theoretical study of rapid evaporation of ethanol droplets and kerosene droplets during depressurization. For experimental method, an ethanol droplet or a kerosene droplet was suspended on a thermocouple, which was also used to measure the droplet center temperature transition. And the droplet shape variation was recorded by a high speed camera. A theoretical analysis was developed based on the heat balance to estimate the droplet center temperature transition, and the evaporation model proposed by Abramzon and Sirignano was used to describe the droplet vaporization. According to the experimental data and theoretical analysis, both of the environmental pressure and the initial droplet diameter have a prominent influence on the droplet temperature transition. Comparing the evaporation processes of ethanol droplets and kerosene droplets with water droplets, the ethanol droplets have the fastest evaporation rate, followed by water, and the evaporation rates of kerosene droplets are the slowest. Also it was found that a bubble can easily emerge within kerosene droplet, and its lifetime is more than 1 s.     

Delayed thermal explosion in flammable gas containing fuel droplets: Asymptotic analysis

The problem of thermal explosion in a flammable gas mixture with addition of volatile fuel droplets is studied based on the asymptotic method of integral manifolds. The model for the radiative heating of droplets takes into account the semitransparency of droplets. A simplified model for droplet heat-up is used. The results of the analysis are applied to the modelling of thermal explosion in diesel engines. Two distinct dynamical situations have been considered, depending on the initial droplet concentration. These are far zone (small initial liquid volume fraction and small droplet radii) and near zone (large initial liquid volume fraction and large droplet radii). The conditions of the first zone are typical for the areas in the combustion chamber which are far from the fuel injectors, while the conditions of the second zone are typical for the areas in the combustion chamber which are relatively close to the fuel injectors. It has been pointed out that small droplets heating and evaporation time in the far zone is smaller than the chemical ignition delay of the fuel vapor/air mixture. The total ignition delay decreases with increasing initial gas temperature. In the near zone for large droplets, the process starts with the initial gas cooling and slight heating of droplets. This is followed by a relatively slow heating of gas due to the chemical reaction, and further droplet heating. The total ignition delay in the near zone is larger than in the far zone. It is expected that before thermal explosion in the near zone takes place, the droplets break up and are removed from this zone. In optically thick gas effects of thermal radiation are negligible for small droplets but are noticeable for large droplets.     

Dynamics of ultra-thin two-layer films

The development of instabilities under the joint action of the Van der Waals forces and Marangoni stresses in a two-layer film on a heated or cooled substrate, is considered. The problem is solved by means of a linear stability theory and nonlinear simulations. Nontrivial change of the droplet shape in the presence of the Marangoni effect, which manifests itself as the deformation of a “plateau” into an “inkpot”, is observed. The appearance of the threshold oscillations predicted by the linear stability theory is confirmed by nonlinear simulations. In the case of a lateral heating, the film instability leads typically to formation of droplets which are driven by the thermocapillary flow and coalesce in an anisotropic way.     

Scaling Law for Electrospray Droplet Formation

There has been a lot of research on liquid atomization by means of electrospray, particularly because of its many practical applications. Nevertheless, full understanding and control of the electrospray mechanisms are still incomplete. An experimental setup was developed in order to investigate the frequency characteristics of droplet formation and ejection at the tip of Taylor's cone of aqueous electrosprays. Droplet formation and oscillations were monitored using a Kodak Ektapro high-speed camera. The frequency of droplet formation at the tip of the capillary needle was analyzed. Droplet frequency formation appears to exhibit three distinct regimes with an abrupt transition from one regime to another. Droplet formation was recorded at different needle-plate electrode distances. Based on the analysis of experimental data a scaling law for droplet formation was found.     

Granulation of ferrosilicon alloy by rotary multi-nozzles cup atomizer: Granulation behavior and model formation

Nowadays, ferroalloys are mainly produced by mold casting and crushing process in China which have obvious drawbacks like low efficiency and high energy consumption. In the present study, a novel process which was based on a rotary multi-nozzles cup atomizer (RMCA) was suggested on FeSi75 (alloy containing 75?wt.% Si). A circle of water curtain was set around the rotary multi-nozzles cup atomizer. According to the calculation results of atomization mechanism, the granulation process agreed with Rayleigh’s mechanism. During the breakup of the alloy ligament, the surface tension plays an important role on the formation of droplet, and the effect of centrifugal force on the diameter of the alloy droplets becomes obvious with the increasing of the rotating speed. In the current study, the models of the traveling trajectories and the heat transfer of the alloy droplet are established. It is found that the solidification time of droplet with different thickness of solidification layer increase with the increase the alloy droplets’ diameter. And the thickness of water curtain required for cooling the alloy increases with increasing the rotating speed.     

Mass spectrometry of acoustically levitated droplets

Containerless sample handling techniques such as acoustic levitation offer potential advantages for mass spectrometry, by eliminating surfaces where undesired adsorption/desorption processes can occur. In addition, they provide a unique opportunity to study fundamental aspects of the ionization process as well as phenomena occurring at the air-droplet interface. Realizing these advantages is contingent, however, upon being able to effectively interface levitated droplets with a mass spectrometer, a challenging task that is addressed in this report. We have employed a newly developed charge and matrix-assisted laser desorption/ionization (CALDI) technique to obtain mass spectra from a 5-microL acoustically levitated droplet containing peptides and an ionic matrix. A four-ring electrostatic lens is used in conjunction with a corona needle to produce bursts of corona ions and to direct those ions toward the droplet, resulting in droplet charging. Analyte ions are produced from the droplet by a 337-nm laser pulse and detected by an atmospheric sampling mass spectrometer. The ion generation and extraction cycle is repeated at 20 Hz, the maximum operating frequency of the laser employed. It is shown in delayed ion extraction experiments that both positive and negative ions are produced, behavior similar to that observed for atmospheric pressure matrix-assisted laser absorption/ionization. No ion signal is observed in the absence of droplet charging. It is likely, although not yet proven, that the role of the droplet charging is to increase the strength of the electric field at the surface of the droplet, reducing charge recombination after ion desorption.     

Self‐Propelling and Positioning of Droplets Using Continuous Topography Gradient Surface

A radial pattern with continuous topography gradient is presented, which induces a continuous inward wettability gradient and enables self‐propelling and accurate positioning of droplets to the pattern center. The effect of droplet size and wettability gradient of the pattern on the self‐mobility of droplets is investigated. The wettability gradient is found to increase towards the pattern center, enhancing the self‐motion of droplets at the inner area of the pattern. Moreover, larger droplets give rise to a larger solid‐liquid contact diameter, which helps to satisfy the self‐motion criteria that the advancing contact angle at front edge is smaller than the receding contact angle at rear edge. Consequently, a larger droplet size favors self‐motion initiated from the outer area of the pattern. The continuous topography gradient employed here allows the flexible dispensing of droplets at any place within a certain range, and avoids potential pinning defects to droplets at geometrical discontinuities. An average self‐motion velocity up to 4.0 cm/s for microliter‐sized droplets is achieved on the resultant patterned surface.     

Influences of support fibers on shapes of heptane/hexadecane droplets in reduced gravity

This paper describes analytical and experimental results related to the effects of support fibers on shapes of heptane/hexadecane mixture droplets (both burning and evaporating) in reduced gravity. The experimental results were obtained from large droplets (a few mm) investigated during the MSL-1 Flight of Spacelab. Theoretical (asymptotic) analyses are developed to predict droplet shapes. These analyses, which predict droplet shapes very well, illustrate important aspects of droplet shapes in a transparent fashion. The asymptotic theory shows that for small droplet-fiber contact angles, two spatial zones exist where droplet shapes behave differently. Away from a fiber, a droplet is essentially spherical. As the fiber is approached, however, deviations from spherical symmetry are significant. Previously developed analytical theory to predict macroscopic droplet shapes also compares well with experimental results. In addition, the experiments indicate that thin liquid films can form on support fibers. In the present experiments, these films apparently lead to transient formation of small droplets/bubbles on the support fibers at locations near the surface of a droplet.     

Understanding the formation of ultrafine maltodextrin particles under simultaneous convective drying and antisolvent vapour precipitation

Research on simultaneous antisolvent-vapour-induced precipitation and convective drying of a solute-containing droplet was extensively conducted since this technique was introduced. However, the internal droplet compositions, which were suggested to be related to the formation of particle morphologies, had not been explored. Herein, the ethanol-vapour-induced precipitation of multi-solvent droplets containing maltodextrin as the solute was used to analyse internal droplet compositions. The droplet mass and diameter profiles were obtained via an established single-droplet drying experiment, which mimicked the spray drying of droplets. Analysis revealed that the antisolvent concentration increased with time and was higher than solvent concentration towards the end of the process. It is interesting to find out that the final particle morphology was profoundly impacted by the ambient ethanol humidity and also how spontaneous the subsequent drying was during ethanol-vapour-induced precipitation of the solutes. The formation of the porous structure was favoured with the occurrence of spontaneous vaporization once the ethanol was present for precipitation. Therefore, low ethanol humidity (20% ERH in this study) was sufficient. In contrast, higher ethanol humidity (>70% ERH) was preferable to produce spherical particles. This study provides an insight into particle engineering to unveil the internal droplet conditions and physical phenomena during this unique process.     

Features of the Diffusiophoresis of Aerosol Droplets with Allowance for the Influence of the Evaporation (Sticking) Coefficient and Internal Flows

A new theory of diffusiophoresis of large volatile spherical aerosol droplets, which is a further development of the previous investigations, has been formed. Account has been taken of the influence of the evaporation coefficient of the droplet liquid, the surfacetension coefficient variable along the droplet surface, and internal flows in the droplet on the diffusiophoresis velocity. The formulas obtained enable one to directly find the velocity of motion of single large aerosol droplets in a binary gas mixture inhomogeneous in concentration.     

Evaporation and Settling Behavior of Metalworking Fluid Aerosols

Environmental and industrial hygiene issues have been receiving ever increasing attention. One important issue is metalworking fluid (MWF) mist formation since it can have a negative effect on workplace air quality. A model is presented to characterize the evaporation and settling behavior of a diluted water-soluble MWF mist under ambient conditions. The model is based on the Langmuir-Knudsen law and Stoke' law. The Langmuir-Knudsen law is employed to describe the evaporation process of each MWF droplet and allows for nonequilibrium effects associated with small droplet size. Stoke' law is applied to characterize the droplet settling mechanism at small Reynolds numbers. Experiments are performed to validate the model. Experiments show that the evaporation rate decreases to zero as the water in a droplet completely evaporates to produce a small nonvolatile oil drop. It is found that the evaporation and settling of a collection of MWF droplets can be predicted by the proposed model.     

ISS Droplet Combustion Experiments - Uncertainties in Droplet Sizes and Burning Rates

Methodologies are developed for evaluating uncertainties in droplet size measurements and burning rates for droplet combustion experiments that have been performed on the International Space Station. Different uncertainty sources are considered and propagated into the combined standard uncertainties via the Taylor series method. The local polynomial method is used to provide estimates of instantaneous burning rates. Results from analyses of non-sooting (methanol) or lightly sooting (heptane) droplets as well as moderately sooting (decane/propylbenzene) droplets are presented. Ninety-five percent expanded uncertainties in droplet diameters and burning rates are typically about 0.1 mm and 0.005 mm ²/s, respectively, for methanol and heptane droplets and 0.1 mm and 0.02 mm ²/s for decane/propylbenzene droplets, though uncertainties can be larger during ignition and extinction events.     

Droplet impingement dynamics in ink-jet deposition

Ink-jet deposition enables more efficient, economic, scalable manufacturing for a wide variety of materials than other additive techniques. The impact of droplets onto a substrate is critical for accuracy control and optimisation of the droplet deposition process. However, most previous research about droplet impact focused on the spreading radius of the droplet, which does not provide enough information for manufacturing purposes. This paper presents a new measure of droplet shape characterisation so that the droplet deposition process can be optimised to build desired geometries. A dimensional analysis is conducted to reduce the number of parameters of the impact conditions. Then the shape evolution of a wide range of impact conditions is simulated with a validated numerical model. The effects of the dimensionless numbers on the shape evolution are examined and analysed. Successive multiple droplets impact is also investigated.     

Surface Oscillations of an Electromagnetically Levitated Droplet

The natural oscillation frequency of freely suspended liquid droplets can be related to the surface tension of the material, and the decay of oscillations to the liquid viscosity. However, the fluid flow inside the droplet must be laminar to measure viscosity with existing correlations; otherwise the damping of the oscillations is dominated by turbulent dissipation. Because no experimental method has yet been developed to visualize flow in electromagnetically levitated oscillating metal droplets, mathematical modeling can assist in predicting whether or not turbulence occurs, and under what processing conditions. In this paper, three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k−ɛ turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem when the interior flow is turbulent. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to available experimental results.     

Melt Flow Instability and Turbulence in Electro-Magnetically Levitated Droplets

This article addresses fluid flow instabilities and flow transition to turbulent chaotic motions through numerical analysis and turbulence in electro-magnetically levitated droplets through direct numerical simulations. Numerical implementation and computed results are presented for flow instability and turbulence flows in magnetically levitated droplets under terrestrial and microgravity conditions. The linear melt flow stability is based on the solution of the Orr-Sommerfeld linearized equations with the base flows obtained numerically using high order numerical schemes. The resulting eigenvalue problems are solved using the linear transformation or Arnold's method. Melt flow instability in a free droplet is different from that bounded by solid walls and flow transits to an unstable motion at a smaller Reynolds number and at a higher wave number in a free droplet. Also, flow instability depends strongly on the base flow structure. Numerical experiments suggest that the transition to the unstable region becomes easier or occurs at a smaller Reynolds number when the flow structures change from two loops to four loops, both of which are found in typical levitation systems used for micro-gravity applications. Direct numerical simulations (DNS) are carried out for an electro-magnetically levitated droplet in a low to mild turbulence regime. The DNS results indicate that both turbulent kinetic energy and dissipations attain finite values along the free surface, which can be used to derive necessary boundary conditions for calculations employing engineering k--ε models.