Computer simulations of the growth of breath figures

We describe computer simulations of the growth of breath figures, the patterns formed when droplets condense on a cold surface. The focus is on the coalescence of droplets, which is an important growth mechanism, and the conditions for self-similar patterns, which are experimentally observed. It is assumed that individual droplets grow according to a power law; droplets that touch coalesce instantly and are replaced by a new droplet at the center of gravity of the coalescing pair. The average droplet radius, distribution of droplet sizes, surface coverage, and radial distribution function are determined as a function of the time for a variety of initial coverages and polydispersities. These quantities are compared to those determined by experiment, and our simple model is found to be in good accord with the observed behavior. It is observed that the process of coalescence induces spatial correlation between droplets.This paper is dedicated to Howard Reiss on his 66th birthday.     

Numerical simulation on partial coalescence of a droplet with different impact velocities

Partial coalescence is a complicated flow phenomenon. In the present study, the coalescence process is simulated with the volume of fluid(VOF) method. The numerical results reveal that a downward high-velocity region plays a significant role in partial coalescence. The high-velocity region pulls the droplet downward continuously which is an important factor for the droplet turning into a prolate shape and the final pinch-off. The shift from partial coalescence to full coalescence is explained based on the droplet shape before the pinch-off. With the droplet impact velocity increasing, the droplet shape will get close to a sphere before the pinch-off. When the shape gets close enough to a sphere, the partial coalescence shifts to full coalescence. The effect of film thickness on the coalescence process is also investigated. With large film thickness,partial coalescence happens, while with small film thickness, full coalescence happens. In addition, the results indicate that the critical droplet impact velocity increases with the increase of surface tension coefficient but decreases with the increase of viscosity and initial droplet diameter. And there is a maximum critical Weber number with the increase of surface tension coefficient and initial droplet diameter.     

等直径微液滴碰撞过程的改进光滑粒子动力学模拟

运用一种改进光滑粒子动力学(SPH)方法模拟了相溶和不相溶两种情况下的等直径微液滴碰撞动力学过程. 为提高传统SPH方法的数值精度和稳定性, 采用一种不涉及核导数计算的核梯度改进形式; 为处理液滴界面张力采用修正的van der Waals表面张力模型. 通过模拟牛顿液滴碰撞聚并变形过程并与相关文献或试验结果进行对比, 验证了改进SPH 方法模拟微液滴碰撞过程的可靠性. 随后, 研究了基于van der Waals模型相溶聚合物微液滴碰撞聚并变形过程及不相溶微液滴碰撞后的反弹、分离过程, 讨论了碰撞过程中碰撞速度、碰撞角度、密度比等参数对碰撞变形过程的影响, 分析了流体桥、旋转角度等因素的变化情况. 关键词： 光滑粒子动力学 微液滴 聚合物液滴 碰撞     

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence.     

微尺度下锥形微操作探针表面液滴形成的研究（英）

基于液滴的转移方法可实现微操作任务中微对象的拾取,锥形操作探针则常作为一种毛细力微操作执行工具。主要研究在空气冷凝模式下锥形探针端面的液滴形成。建立了微液滴形成的数学模型,主要包括初始液滴的形成、液滴的合并和液滴的移动,研究了影响操作液滴的关键参数,分析表明:过冷度决定最小液滴半径。对单液滴的生长机制进行理论分析,并通过数值求解的方法模拟了锥形操作探针端面的液滴形成。搭建实验测试平台,实验研究了微尺度下锥形微操作探针端面的液滴形成。实验结果表明:在空气冷凝模式下,操作探针端面能够形成微液滴。经过初始液滴的形成,液滴的合并和移动等过程最终可形成稳定的微液滴,且不同锥顶角下液滴的形成呈现多样化。     

滴状冷凝过程液滴自由表面温度场分析

对于滴状冷凝过程及其传热强化机理, 一般通过分析冷凝壁面上液滴分布和运动规律进行研究, 并且将单个液滴视为稳定的个体, 很少涉及液滴内部运动特征. 本文通过红外热像仪观测了纯蒸气滴状冷凝过程中, 液滴运动时自由表面温度场的演化过程. 发现在疏水壁面上, 液滴由于合并或脱落而发生移动过程中, 其自由表面温度先降低, 而后升高并高于移动前温度. 通过分析疏水表面上液滴移动过程的物理模型, 认为液滴移动时表面液膜发生履带式滚动现象, 或者发生液滴内部与自由表面附近的液体间形成对流和掺混现象. 对液滴运动时表面温度演变规律的分析表明: 触发液滴表面发生持续冷凝可能需要克服一个临界过冷度, 当气液间温差超过该临界值时才诱发冷凝; 液滴合并或脱落等整体运动过程, 导致了液滴内部的运动特征, 并促进了较大尺寸液滴表面发生直接冷凝, 这为强化冷凝传热的研究提供新的思路.     

非对称布置液滴在波纹状基底上的聚并过程

基于润滑理论建立在波纹基底上两个含表面活性剂液滴聚并的演化模型，模拟液滴位于波纹基底波峰和波谷处的聚并过程，分析液滴初始间距和基底高度对聚并的影响，并与对称布置液滴进行比较.结果表明：液滴高度随时间呈现五个阶段变化；活性剂浓度在短时间内完成三个阶段变化；初始间距的增大将延长液滴及活性剂聚并时间；增大基底高度将缩短液滴及活性剂聚并时间；非对称液滴相较于对称液滴聚并时间短，聚并速度快.     

Some general features of limited coalescence in solid-stabilized emulsions

We produce direct and inverse emulsions stabilized by solid mineral particles. If the total amount of particles is initially insufficient to fully cover the oil-water interfaces, the emulsion droplets coalesce such that the total interfacial area between oil and water is progressively reduced. Since it is likely that the particles are irreversibly adsorbed, the degree of surface coverage by them increases until coalescence is halted. We follow the rate of droplet coalescence from the initial fragmented state to the saturated situation. Unlike surfactant-stabilized emulsions, the coalescence frequency depends on time and particle concentration. Both the transient and final droplet size distributions are relatively narrow and we obtain a linear relation between the inverse average droplet diameter and the total amount of solid particles, with a slope that depends on the mixing intensity. The phenomenology is independent of the mixing type and of the droplet volume fraction allowing the fabrication of both direct and inverse emulsion with average droplet sizes ranging from micron to millimetre.Received: 4 April 2003, Published online: 8 July 2003PACS: 82.70.-y Disperse systems; complex fluids - 82.70.Kj Emulsions and suspensions - 68.15.+e Liquid thin films     

Hydrodynamic binary coalescence of droplets under air flow in a hydrophobic microchannel

Based on the volume of fluid(VOF) method, we conduct a numerical simulation to study the hydrodynamic binary coalescence of droplets under air flow in a hydrophobic rectangular microchannel. Two distinct regimes, coalescence followed by sliding motion and that followed by detaching motion, are identified and discussed. Additionally, the detailed hydrodynamic information behind the binary coalescence is provided, based on which a dynamic mechanical analysis is conducted to reveal the hydrodynamic mechanisms underlying these two regimes. The simulation results indicate that the sliding motion of droplets is driven by the drag force and restrained by the adhesion force induced by the interfacial tension along the main flow direction. The detachment(i.e., upward motion) of the droplet is driven by the lift force associated with an aerodynamic lifting pressure difference imposed on the coalescent droplet, and also restrained by the adhesion force perpendicular to the main flow direction. Especially, the lift force is mainly induced by an aerodynamic lifting pressure difference imposed on the coalescent droplet. Two typical regimes can be quantitatively recognized by a regime diagram depending on Re and We. The higher Re and We respectively lead to relatively larger lift forces and smaller adhesion forces acting on the droplet, both of which are helpful to detachment of the coalesced droplet.     

Numerical assessment of ultrasound supported coalescence of water droplets in crude oil

In this study, a numerical assessment of the coalescence of binary water droplets in water-in-oil emulsion was conducted. The investigation addressed the effect of various parameters on the acoustic pressure and coalescence time of water droplets in oil phase. These include transducer material, initial droplet diameter (0.05–0.2 in), interfacial tension (0.012–0.082 N/m), dynamic viscosity (10.6–530 mPas), temperature (20–100 °C), US (ultra sound) frequency (26.04–43.53 kHz) and transducer power (2.5–40 W). The materials assessed are lead zirconate titanate (PZT), lithium niobate (LiNbO₃), zinc oxide (ZnO), aluminum nitride (AlN), polyvinylidene fluoride (PVDF), and barium titanate (BaTiO₃). The numerical simulation of the binary droplet coalescence showed good agreement with experimental data in the literature. The US implementation at a fixed frequency produced enhanced coalescence (t = 5.9–8.5 ms) as compared to gravitational settling (t = 9.8 ms). At different ultrasound (US) frequencies and transducer materials, variation in the acoustic pressure distribution was observed. Possible attenuation of the US waves, and the subsequent inhibitive coalescence effect under various US frequencies and viscosities, were discussed. Moreover, the results showed that the coalescence time reduced across the range of interfacial tensions which was considered. This reduction can be attributed to the fact that lower interfacial tension produces emulsions which are relatively more stable. Hence, at lower interface tension between the water and crude oil, there was more resistance to the coalescence of the water droplets due to their improved emulsion stability. The increment of the Weber number at higher droplet sizes leads to a delay in the recovery of the droplet to spherical forms after their starting deformation. These findings provide significant insights that could aid further developments in demulsification of crude oil emulsions under varying US and emulsion properties.     

On the role of capillary waves in the mechanism of coalescence of a droplet cluster

Packets of capillary waves on the surface of a horizontal water layer generated at coalescence with a layer of microdroplets (with a characteristic diameter of 50–100 μm) of the dissipative structure “droplet cluster” have been detected by high-speed video recording and the schlieren method. The shortest experimentally observed waves have a length of about 130 μm and their phase velocity exceeds 1.8 m/s. It has been found that the coalescence of a single drop initiates a self-sustained wave process, which induces the coalescence of hundreds of droplets in a time shorter than 1 ms, which form a cluster.     

Stability of cellulose lyotropic liquid crystal emulsions

We studied a new kind of W/O emulsions based on a lyotropic liquid crystal as the aqueous droplet phase. The cholesteric phase, a solution hydroxypropyl cellulose in water was dispersed in the continuous oil matrix, paraffin oil or heptane. We made a specific choice of surfactant in order to impose director anchoring conditions at the oil-water interface and orient the liquid crystal inside the droplet. The strong anchoring conditions resulted in a topological defect inside the droplets of size above the critical value R^*. The defect elastic energy creates a barrier against droplet coalescence, the effect of topological size selection. We have studied the orientation of the director inside the droplets and their size distribution.     

High dielectric anisotropy compound doped transmission gratings of HPDLC

Effects of high dielectric anisotropy compound (MLC) and oligomer molecular weight on the grating formation and electro-optical properties of transmission holographic polymer dispersed liquid crystal (HPDLC) have been studied. Addition of MLC reduced the response time and switching voltage with the increased formulation viscosity which introduced a sequence of phenomenon, i.e. slow diffusion, polymerization, phase separation, grating formation, and droplet coalescence giving small droplet size and enhanced diffraction efficiency of the film. Apparently, increase in oligomer molecular weight gave effects similar to those of increasing MLC content since both variables control droplet coalescence through different mechanisms.     

Decompressing emulsion droplets favors coalescence

The destabilization process of an emulsion under flow is investigated in a microfluidic device. The experimental approach enables us to generate a periodic train of droplet pairs, and thus to isolate and analyze the basic step of the destabilization, namely, the coalescence of two droplets which collide. We demonstrate a counterintuitive phenomenon: coalescence occurs during the separation phase and not during the impact. Separation induces the formation of two facing nipples in the contact area that hastens the connection of the interfaces prior to fusion. Moreover, droplet pairs initially stabilized by surfactants can be destabilized by forcing the separation. Finally, we note that the fusion mechanism is responsible for a cascade of coalescence events in a compact system of droplets where the separation is driven by surface tension.     

A comparative study of the self-propelled jumping capabilities of coalesced droplets on RTV surfaces and superhydrophobic surfaces

Understanding the mechanism of coalescence-induced self-propelled jumping behavior provides distinct insights in designing and optimizing functional coatings with self-cleaning and anti-icing properties.However,to date self-propelled jumping phenomenon has only been observed and studied on superhydrophobic surfaces,other than those hydrophobic surfaces with weaker but fairish water-repellency,for instance,vulcanized silicon rubber(RTV) coatings.In this work,from the perspective of thermodynamic-based energy balance aspect,the reason that self-propelled jumping phenomenon does not happen on RTV coatings is studied.The apparent contact angles of droplets on RTV coatings can be less than the theoretical critical values therefore cannot promise energy surplus for the coalesced droplets onside.Besides,on RTV and superhydrophobic surfaces,the droplet-size dependent variation characteristics of the energy leftover from the coalescence process are opposite.For the droplets coalescing on RTV coatings,the magnitudes of energy dissipations are more sensitive to the increase in droplet size,compared to that of released surface energy.While for superhydrophobic coatings,the energy generated during the coalescence process can be more sensitive than the dissipations to the change in droplet size.     

Binary collision of a burning droplet and a non-burning droplet of xylene: Outcome regimes and flame dynamics

The binary collisions of a burning droplet and a non-burning droplet of xylene are experimentally investigated. The experimental parameters span an extensive range of Weber number and impact parameter, covering the collision outcome regimes of coalescence, reflexive separation, and stretching separation. A high-speed camera captures the temporal details of the collision process, involving flame spread, visible radiation, and flame distributions around droplets. For reflexive separation and stretching separation, the flame from the droplet spreads to the ligament, surrounding it during the interaction process, and then spreads around separated droplets and satellite droplets. Highly-interactive flames are formed in-between the droplets, with very sooty flames generated for most collisions. For the coalescence case, a swirling flame forms around the rotating coalesced droplet. For similar Weber numbers, visible flame radiation is compared for different collision regimes. The visible flame radiation changes more significantly for the reflexive and stretching separation cases than it does for the coalescence case. The change of the averaged visible flame radiation for reflexive separation and stretching separation is more than two times higher than that for coalescence. The map of three different collision regimes is plotted in the Weber number versus impact parameter domain and compared with available theoretical model predictions. Although the different outcomes of collision with the presence of flame can be well predicted by the model, using fluid properties determined by the averaged properties of the two droplets, the dynamics of the detailed processes involved in the collisions are very interesting and have strong implications on overall combustion behavior that go well beyond the mapped regimes.     

Visualization of aggregation process of dispersed water droplets and the effect of aggregation on secondary atomization of emulsified fuel droplets

The effect of aggregation of dispersed water droplets on secondary atomization of emulsified fuel droplets in a heating process was investigated. Secondary atomization was observed using a single droplet experiment in which a water-in-oil (W/O) emulsified fuel droplet prepared using colored water was heated by a halogen heater. The initial diameter of dispersed water droplets before heating was controlled, and the change in the diameter of dispersed water droplets was measured by image analysis. As a result, the aggregation process of dispersed water droplets in the heating process was successfully visualized. The dispersed water droplet diameter increased with an increase in W/O emulsified fuel droplet temperature. The occurrence probability of micro-explosion increased with an increase in the dispersed water droplet diameter in emulsified fuel droplets. It is suggested that the occurrence probability of micro-explosion can be increased by accelerating the aggregation and coalescence of dispersed water droplets below 430 K, which is the average temperature of the starting point of puffing.     

On the coalescence of sessile drops with miscible liquids

Sessile drops sitting on highly wettable solid substrates fuse in qualitatively different ways after contact, depending on the surface tension gradients between the mixing droplets. In early time evolution the drop coalescence can be fast or delayed (intermittent). In long time evolution a secondary drop formation can occur. We study numerically droplet dynamics during coalescence in two and three spatial dimensions, within a phase field approach. We discuss criteria to distinguish different coalescence regimes. A comparison with recent experiments will be done.     

Difference in the dynamic scaling behavior of droplet size distribution for coalescence under pulsed and continuous vapor delivery

Dynamic scaling behavior of the droplet size distribution in the coalescence regime for growth by pulsed laser deposition is studied experimentally and by computer simulation, and the same is compared with that for continuous vapor deposition. The scaling exponent for pulsed deposition is found to be (1.2 +/- 0.1), which is significantly lower as compared to that for continuous deposition (1.6 +/- 0.1). Simulations reveal that this dramatic difference can be traced to the large fraction of multiple droplet coalescence under pulsed vapor delivery. A possible role of the differing diffusion fields in the two cases is also suggested.     

Ultrasound emulsification: effect of ultrasonic and physicochemical properties on dispersed phase volume and droplet size

Ultrasonic emulsification of oil and water was carried out and the effect of irradiation time, irradiation power and physicochemical properties of oil on the dispersed phase volume and dispersed phase droplet size has been studied. The increase in the irradiation time increases the dispersed phase volume while decreases the dispersed phase droplets size. With an increase in the ultrasonic irradiation power, there is an increase in the fraction of volume of the dispersed phase while the droplet size of the dispersed phase decreases. The fractional volume of the dispersed phase increases for the case of groundnut oil-water system while it is low for paraffin (heavy) oil-water system. The droplet size of soyabean oil dispersed in water is found to be small while that of paraffin (heavy) oil is found to be large. These variations could be explained on the basis of varying physicochemical properties of the system, i.e., viscosity of oil and the interfacial tension. During the ultrasonic emulsification, coalescence phenomenon which is only marginal, has been observed, which can be attributed to the collision of small droplets when the droplet concentration increases beyond a certain number and the acoustic streaming strength increases.