梯度润湿表面上液滴定向迁移及合并行为的格子Boltzmann模拟

采用改进的格子Boltzmann方法，对梯度润湿性表面上液滴的定向迁移及合并行为进行了数值模拟，该模型在精度和稳定性上都有很大改善，同时，研究了梯度润湿性表面上液滴定向迁移和合并的动力学特性，并对液滴尺寸及润湿梯度对液滴动力学特性的影响规律进行了分析。数值结果表明，液滴在梯度润湿性表面运动时会发生形变，且动态接触角逐渐减小。润湿梯度对液滴定向迁移行为有显著影响，润湿梯度越大，液滴左右侧接触线位移越大，润湿长度增加越快。但是液滴尺寸对接触线位移影响较小。润湿梯度对液桥宽度基本无影响，但对液滴初始合并时间有显著影响。     

Investigation the effects of shear rate on stationary droplets coalescence by lattice Boltzmann

Coalescence is the process by which two or more droplets merge to form a single droplet. It can take place in many processes, ranging from meteorology to astrophysics. When two stationary droplets are suspended in a bulk vapor, if the gap between the droplets has been smaller than a critical value, the two droplets will coalesce. In this paper, single component, two phase flow is modeled under shear flow using a free energy lattice Boltzmann approach and the coalescence of stationary droplets are investigated for different cases of radius and shear rate. The results show that there is a critical gap between droplets and for the values larger than that they will not coalesce. Also in the case of constant thermophysical properties, this critical gap is a function of droplet radius and shear rate.     

Lattice Boltzmann simulation of multiple droplets impingement and coalescence in an inkjet-printed line patterning process

Three-dimensional computations on the basis of the index-function lattice Boltzmann method are performed to simulate the process of multiple droplets impinging and coalescing into a line pattern on a solid substrate. The employed calculation model is validated by theoretical calculated values and experimental data from the literature. The influences of the equilibrium contact angle, droplet spacing and impinging velocity on the droplets impingement and coalescence behaviours are investigated. Numerical results demonstrate the width of the formed line depends significantly on the equilibrium contact angle and droplet spacing. The droplet spacing plays a significant role in controlling the coalescence moment of multiple droplets. The resolution of the printed pattern can be slightly increased with increase in impinging velocity.     

Collision between high and low viscosity droplets: Direct Numerical Simulations and experiments

Binary droplet collisions are of importance in a variety of practical applications comprising dispersed two-phase flows. In the present work we focus on the collision of miscible droplets, where one droplet is composed of a high viscous liquid and the other one is of lower viscosity. This kind of collisions take place in, for instance, spray drying processes when droplets with different solid content collide in recirculation zones. The aim of this paper is to investigate the details of the flow inside the colliding droplets. For this purpose, two prototype cases are considered, namely the collision of equal sized droplets and the collision between a small and highly viscous droplet and a bigger low viscous droplet. A new experimental method has been developed in order to visualize the penetration and mixing process of two colliding droplets, where a fluorescence marker is added to one liquid and the droplets are excited by a laser. The results show a delay in the coalescence which takes place during the initial stage of a collision of droplets with different viscosities. Direct Numerical Simulations based on the Volume-of-Fluid method are used to study these collisions and to allow for a more detailed inspection of the mixing process. The method is extended to consider a second liquid with a different viscosity. In order to reproduce the delay of coalescence, an algorithm for the temporal suppression of the coalescence is applied. A predictive simulation of the delay is not possible, because the extremely thin air gap separating the droplets cannot be resolved by the numerics. This approach is validated by comparison with experimental data. The results provide local field data of the flow inside the collision complex, showing in particular a pressure jump at the liquid–liquid interface although no surface tension is present. The detailed analysis of the terms in the momentum balance show that the pressure jump results from the viscosity jump at the liquid–liquid interface.     

DROPLET COLLISION AND COALESCENCE MODEL

A new droplet collision and coalescence model was presented,a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results,further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence,numerical simulations were carried out for model validation.Results show that the model presented is mesh-independent and less time consuming,it can not only maintains the system momentum conservation perfectly,but not susceptible to initial droplet size distribution as well.     

Large eddy simulation and experiment of shear breakup in liquid-liquid jet: Formation of ligaments and droplets

Understanding the shear breakup in jet flows and the formation of droplets from ligaments is important to determine the final droplet size distribution (DSD). The initial droplet size, which affects the final DSD, is considered to be generated by the shear breakup. Large eddy simulation (LES) was performed to investigate the shear breakup in liquid-liquid jet flows. The explicit Volume of Fluid (VOF) model with the geometric reconstruction scheme was used to capture the oil-water interface. The estimated oil distribution including wave peaks, ligaments, droplets and water streaks were compared to the experiments with a good agreement. The estimated DSD matched with the measurements favorably well. In the simulation, the formation of droplets with a smooth and curved surface from ligaments or sheet-like structures was obtained. Different mechanisms were observed along with the shear layer including the formation of droplets from ligament through the capillary forces, breakage of a droplet into smaller ones and attachment of a droplet to a ligament. The destructive shear forces and resisting surface tension forces were quantified on stretching and retracting ligaments. The influence of internal viscous force was found to be negligible due to low oil viscosity. The critical capillary number was found to be larger than 5.0 for ligaments breaking with the shear breakup. The capillary number was below unity for retracting ligaments. The coalescence of two equal-sized droplets was obtained in the shear breakup region. The shear stress magnitude at the contact region increased more than two folds. The total surface area decreased nearly 20% after the coalescence.     

Visualization of droplet merging in microchannels using micro-PIV

Flow visualization via micro-PIV has been conducted in order to investigate droplet-merging processes in microchannels. The dispersed-phase droplets seeded with 1-μm fluorescent particles are alternately generated in the cross-channel and merged downstream in a straight channel or in a divergent channel. Since droplet merging occurs within a millisecond, a high-speed camera capable of 6,000 fps is used to capture the images of the droplets and the tracer particles therein by observing through a 40× lens. These images reveal that droplets merge through a sequential process of attachment, drainage, interface coalescence, penetration or envelopment depending on the channel geometry. In the straight channel, where the droplets are confined by the channel walls, the rear droplet penetrates the front droplet at the instant of coalescence. However, when the droplets merge in the divergent channel, a strong vortex motion occurs while the rear droplet envelops the front one.     

气相中双液滴正碰过程数值模拟研究

液滴碰撞现象普遍存在于动力装置燃烧室喷嘴的下游区域,影响燃料的雾化性能。为了揭示相同直径的双液滴中心碰撞机理,求解了轴对称坐标系下的N-S方程,采用VOF(Volume of Fluid)方法捕捉液滴碰撞过程中气液自由表面的演化规律。利用Qian等提供的实验结果对计算模型进行数值校验,验证了模型的准确性。在此基础上,研究了环境压强对液滴碰撞反弹后不同结果(分离和融合)的影响,分析了环境压强和Weber数对液滴碰撞分离的影响。结果表明,液滴在碰撞反弹后的状态(分离或融合)是由液滴间气膜压强与环境气动阻力共同作用的结果,环境压强对液滴碰撞分离过程基本没有影响;Weber数越大,碰撞过程中变形的幅度越大。     

Coalescence of sessile droplets of varying viscosities for line printing

Coalescence of sessile droplets is studied experimentally with water–glycerin mixtures of different viscosities. Effects of viscosity on the dimensionless spreading length (Ψ) and the center-to-center distance (L) are investigated for two droplets; the first droplet (D_s) is stationary on a substrate and the second droplet (D₀) landing at a center-to-center distance L from the first droplet. For a low viscosity fluid, Ψ is maximum when L approaches zero (or λ → 1, where λ = 1 − L/D_s), which represents a head-on collision. For a high viscosity fluid, Ψ is minimum when λ → 0.6. The effect of λ on line printing for various viscosities is also examined by printing multiple droplets. We found that the larger the viscosity, the less the breakup between droplets; viscosities smaller than 60 wt% glycerin yielded line breakup. The overlap ratio of λ > 0.3 produced not a line, but a bigger droplet or puddle because of coalescence. Data obtained in this work can provide insights for the fabrication of conductive microtracks or microinterconnects in printed-electronics applications where a line breakup between droplets would lead to an electrical circuit short.     

Maximum spreading of electrically charged droplets impacting on dielectric substrates

In this work, the electric charging effect on the spreading of droplet impacting on dielectric substrates has been investigated. The charged water droplets were directed on the paraffin wax and the Teflon-coated plates. The impinging behavior was visualized and recorded using a CCD camera to identify the maximum extent of the flattened droplets. Droplet diameter and velocity approaching the wall were measured as well. The diameter of the electrically charged droplet at the maximum spread turned out to be larger compared to that of neutral droplet (at the maximum spread), and the difference becomes larger with increasing of the electric charge ratio (defined as the ratio of the actual electric charge to the Rayleigh limit). This phenomenon is considered to be due to reduction of effective interfacial tensions between the liquid and the gas and between the liquid and the solid by electric charging. Finally, an improved model was proposed to predict the maximum spreading ratio for electrically charged droplets by introducing correlations on the liquid–gas and the liquid–solid interfacial tensions.     

Effects of gas and droplet characteristics on drop-drop collision outcome regimes

Droplet-droplet collisions occur in many spray systems. The collision of two spherical droplets in a gas is considered in terms of the five primary phenomenological outcomes: slow coalescence (SC), bounce (B), fast coalescence (FC), reflexive separation (RS), and stretching separation (SS). The boundaries that separate these outcomes were investigated herein in terms of droplet viscosity and surface tension as well as gas pressure and density. Gas effects are not accounted for previous models, but can be important for hydrocarbon drops in pressurized sprays associated with many fuel systems. Based on a comprehensive review of available drop-drop collision data, phenomenological models were proposed herein for a wide variety of test conditions. For slow coalescence/bouncing (SC/B), increasing droplet viscosity and gas pressure were found to increase the probability of a bouncing outcome of the collision. For the B/FC boundary, increasing droplet viscosity and gas density were also found to increase bouncing probability. In both cases, the variations can be explained in terms of the stability of the gas layer that develops between the droplets. Additionally, the Brazier-Smith model for the FC/SS boundary was modified to increase robustness for a wide range of droplet viscosities. In general, the present models reasonably predicted collision outcomes for a large variety of gas pressures and densities as well as droplet viscosities and surface tensions. These are also the first models to include gas effects and the first models of the SC/B boundary. However, the droplet diameters of the data set were limited in range from 200 to 400 microns. Significantly larger droplet collisions may include effects on initial non-sphericity while significantly smaller drop collisions may include effects on non-continuum flow and gas viscosity.     

Droplet impact dynamics for two liquids impinging on anisotropic superhydrophobic surfaces

Droplet impingement experiments were performed on grooved hydrophobic surfaces with cavity fractions of 0, 80, and 93?% using droplets of water and a 50?%/50?% water/glycerol mixture. The influence of liquid viscosity, cavity fraction, and spreading direction, relative to the surface grooves, is explored qualitatively and quantitatively. The maximum droplet spread diameter, velocity of the rebounding jet, and the time delay between droplet impact and jet emission were characterized for Weber numbers, We, based on droplet impact speed and diameter, up to 500. The unequal shear stresses and contact angles influence the maximum spread diameters in the two primary spread directions. At We?>?100, the ratio of the spread diameter along the direction of the grooves to the spread diameter perpendicular to the grooves increases above unity with increasing We. The maximum droplet spread diameter is compared to recent predictive models, and the data reveal differing behavior for the two fluids considered. The results also reveal the existence of very high relative jet velocities in the range 5????We????15 for water droplets, while such jets were not observed for the more viscous mixture. Further, in the range 115????We????265, the water/glycerol jet formation dynamics are radically different from the water behavior. Most evident is the existence of two-pronged jets, which arise from the anisotropy of the surface and the unequal shear stresses and contact angles that prevail on the surfaces. It is these influences that give rise to differences in the maximum spread diameters in the two primary spread directions. Similar two-pronged jet emission was observed for water over the very narrow range of We from 91 to 96. The issuing jet velocities were also observed to increase with increasing cavity fraction for both fluids and over the entire range of We explored. Lastly, the elapsed time between droplet impact and jet emission decreased with increasing cavity fraction.     

A modified SPH method to model the coalescence of colliding non-Newtonian liquid droplets

This paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non-Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas-to-liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head-on binary collision of vdW liquid droplets. Both Newtonian and non-Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off-center binary collision of non-Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non-Newtonian liquid droplets without tensile instability.     

Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution

A theoretical model of a two-phase air/dispersed water spray flow in an icing wind tunnel is presented here. The mutual interactions taking place within the dispersed phase known as binary droplet collisions, as well as gravitational sedimentation are considered. Where large droplets and low air stream velocities are concerned, the effect of gravity on droplet dynamics is considerable. Gravity causes the vertical deflection of droplet trajectories and an increase in liquid water content (LWC) in the bottom half of the wind tunnel. Droplet collision tends to influence the size, trajectory and velocity of droplets thus affecting the characteristics of the flow and, thereby, the formation of ice on the object placed in the wind tunnel. The present model simulates droplet motion and droplet collision in an icing wind tunnel, where it may be observed that bouncing, stable coalescence, or coalescence followed by separation are the possible outcomes of collision. In the theoretical examination, firstly, the effect of gravity on the vertical deflection of droplet trajectories and on the vertical distribution of the LWC near the icing object are taken into account, while droplet collision is disregarded. Then both factors are considered and collision outcome is determined together with the size and velocity of post-collision droplets. The initial droplet size distribution (DSD), as it occurs at the nozzle outlet, is estimated by a curve in accordance with previous experimental results. The DSD is determined theoretically near the icing object, which makes it possible to calculate the median volume diameter and the LWC of the aerosol cloud. The simulation results with regard to the LWC are compared to the experimental results obtained in this research and a satisfactory qualitative coincidence is to be found between them.     

压电式微滴按需喷射的过程控制和规律

微滴喷射增材制造技术中沉积微滴的大小与均匀性是影响成型件质量的关键因素.本文设计了一种用于生成均匀微滴的压电驱动式微滴喷射装置,通过压电材料带动柔性膜片振动,将液体从喷嘴中喷出生成微滴,采用数值模拟和实验相结合的方法,研究了不同控制参数下膜片振幅及其对生成微滴尺寸和均匀性的影响.研究结果表明:膜片振幅大小受到驱动电压和压电频率的共同影响,压电频率是导致膜片中心点振幅实验测量值小于理论计算值的主要原因,膜片振动会导致喷嘴内部压力发生变化从而影响微滴生成尺寸.在相同驱动电压条件下,压电频率为10 Hz时存在压电膜片振幅最大值.随着膜片振幅的增大,喷孔处液体速度和液柱长度增大到临界值时可以生成微滴,当喷孔处的液柱长度超过临界值时,会形成卫星液滴. 当膜片振幅区间在30 $\mu$m$\sim $42 $\mu $m可以稳定生成微滴,生成最小微滴尺寸为339.8$\mu$m,直径最大变化率为0.29%,相邻两微滴间距最大变化率为2.67%,生成微滴的尺寸及均匀性较好.研究结果有助于提高压电式微滴喷射装置的液滴生成质量.      

Numerical simulation of droplet coalescence based on the SPH method

In this paper, the smoothed particle hydrodynamics (SPH) method is employed in modeling and numerical simulation of droplet coalescence. Considering the effect of tangential force on boundary material, besides normal force, tangential force is also introduced in the continuum surface force (CSF) model. The formation of droplet, the coalescence processes of two droplets and three droplets are simulated by the modified CSF model. The validity of the modified model is verified from the aspects of the morphological change of the droplet, the smoothness of free surface and the conservation of the centroid of the system. Compared with finite element method, the results of the modified CSF model show that tangential force plays a crucial role in the CSF model when dealing with model boundary with curves and sharp angles.     

The slow motion of two spherical particles along their line of centres

The motion of spherical, solid particles, liquid droplets or gas bubbles along their line of centres is considered. Conditions are limited to quasi-steady creeping flow and results are presented for drag coefficients and streamlines in these systems. Various interactions between two particles are reviewed and applications to gravity settling and droplet coalescence discussed.     

Experiments on the dynamics of droplet collisions in a vacuum

Highly controlled experiments of binary droplet collisions in a vacuum environment are performed in order to study the collision dynamics devoid of aerodynamic effects that could otherwise obstruct the experimental observations by causing distortion or even disintegration of the coalesced mass. Pre-collision droplets are generated from capillary stream break-up at wavelengths much larger than those generated with the typical Rayleigh droplet formation in order to reduce the interactions among the collision products. Experimental results show that the range of droplet Weber number necessary to describe the boundaries between permanent coalescence and coalescence followed by separation is several orders of magnitude higher than has been reported in experiments conducted at standard atmospheric pressures with lower viscosity liquids (i.e. hydrocarbon fuels and water). Additionally, the time periods of both the oblate and prolate portions of the coalesced droplet oscillation have been measured and it is reported for the first time that the time period for the prolate portion of the oscillation grows exponentially with the Weber number. Finally, new pictorial results are presented for droplet collisions between non-spherical droplets. Received: 30 June 1998/Accepted: 15 October 1999     

The use of single-point measurements to characterize dynamic behavior in sprays

In an effort to derive dynamic information from a single-particle counting device such as the phase-Doppler interferometer (PDI), a one-dimensional motion model and a sequential sorting algorithm have been developed to calculate the distance and velocity difference between consecutive droplets in sprays, as well as the number of droplets in close proximity (grouplets) and the frequency of grouplet formation. By focusing on sprays that are primarily uni-directional, this model can be used to highlight dynamic behavior and provide information that may indicate tendencies for clustering, collision, coalescence or evaporation among the droplets – information that is not available when considering the histograms of droplet size and velocity normally produced by PDIs. The motion model and sorting algorithm are validated for a mono-sized droplet stream generated by piezo-electric excitation, and are then applied to two other sprays to determine dynamic behavior. For a pressurized-liquid nozzle emitting water, the expected trends of droplet deceleration and spatial dispersion are found moving away from the exit of the nozzle, and significant in velocity differences between closely-spaced droplet pairs are observed. No dominant frequencies are present in the grouping of the droplets. For a droplet-laden air jet excited at a known frequency, similar results are calculated for droplet spacing, grouping and velocity differences, and the driving frequency is also obtained from analysis of the sequentially-sorted PDI data. Although the models developed assume an idealized PDI system, real operating characteristics of PDI systems place limits on the accuracy of these analyses. Received: 10 October 1998/Accepted: 5 October 1999