Numerical simulation of a falling droplet surrounding by air under electric field using VOF method: A CFD study

This is a numerical study of a falling droplet surrounding by air under the electric field modeled with finite volume method by means of CFD. The VOF method has been employed to model the two-phase flow of the present study. Various capillary numbers are investigated to analyze the effects of electric field intensity on the falling droplet deformation. Also, the effects of electric potential on the heat transfer coefficient have been examined. The obtained results showed that by applying the electric field at a capillary number of 0.2 the droplet tends to retain its primitive shape as time goes by, with a subtle deformation to an oblate form. Intensifying the electric field to a capillary number of 0.8 droplet deformation is almost insignificant with time progressing; however, further enhancement in capillary number to 2 causes the droplet to deform as a prolate shape and higher values of this number intensify the prolate form deformation of the droplet and result in pinch-off phenomenon. Ultimately, it is showed that as the electric potential augments the heat transfer coefficient increases in which for electric potential values higher than 2400 V the heat transfer coefficient enhances significantly.     

电场作用下液滴分裂动力学行为的格子Boltzmann模拟

采用格子Boltzmann方法（LBM）伪势模型,耦合流场和电场控制方程,研究了电场作用下油水共存体系中水滴分裂的动力学行为及特性,借助形变率衡量液滴的形变大小,展现了液滴从形变至分裂的动态演变过程,分析了外加电场大小和液滴内外介电常数比对液滴分裂行为的影响。结果表明：外加电场能促使液滴发生振荡形变,且存在临界电毛细数和临界介电常数比决定液滴是否发生分裂：高于临界值,液滴形变率振荡幅度随时间不断增长,最终发生分裂;低于临界值,则液滴形变率振荡幅度不断衰减,并最终趋于一稳定值。在此基础上,综合考虑电场强度与介电常数比的影响,提出了基于现有电毛细数的修正电毛细数唯一地表征电场作用下液滴分裂与否。     

非均匀电场下乳化油中液滴变形动力学行为

外加电场下液滴的变形动力学行为是乳化液电脱水机理研究的重要内容。基于Cahn-Hilliard方程的相场方法,建立了液滴在非均匀电场下的仿真模型,研究了电场作用下乳化液中液滴在形变、移动和聚结过程中电荷密度和电场力的分布规律,以及流场和电场的耦合作用。仿真分析了液滴粒径、电场强度以及电场非均匀系数对液滴运动行为的影响。利用实验室小型脱水系统开展了乳化液脱水实验,并通过高速摄像机对乳化液中液滴的运动行为进行了观测与分析。研究结果表明,在非均匀电场中液滴表面的极化电荷分布不均,由液滴中部向两端逐渐增大,在靠近电场集中方向处的电荷密度和Maxwell应力值最大;在一定范围内增大电场强度、电场非均匀系数或液滴粒径,可使液滴形变量增大,液滴向电场集中区域的移动速度以及液滴间的聚结速度增加。     

Evaporation Kinetics of Single Droplets Containing Dissolved Bioaiass

Luikov approach was applied to predict drying time and temperature of a droplet containing liquid substrate of entobacterin in the falling drying rate period. Analytical expressions describing both average and local temperatures of the particle in the drying process were derived and solved. Constants necessary to solve the equations, describing certain material properties and material moisture bonding were found in simple experiments. An experimental relationship of Rebinder number and moisture content of the material enabled to calculate changes of average droplet temperature in the falling drying rate period. Analytical solutions of heat transfer equations for shrinkage core model both for a linear and exponential change of moisture content of the droplet in the drying process were delivered. Employing experimental heat transfer coefficient, drying time and droplct temperature field were determined. Comparison of experimental and predicted drying times as well as droplet temperatures shows small discrepancy. Results obtained can be used to predict quality of labile products in the course of drying.     

Evaporation Kinetics of Single Droplets Containing Dissolved Bioaiass

ABSTRACT

Luikov approach was applied to predict drying time and temperature of a droplet containing liquid substrate of entobacterin in the falling drying rate period. Analytical expressions describing both average and local temperatures of the particle in the drying process were derived and solved. Constants necessary to solve the equations, describing certain material properties and material moisture bonding were found in simple experiments. An experimental relationship of Rebinder number and moisture content of the material enabled to calculate changes of average droplet temperature in the falling drying rate period. Analytical solutions of heat transfer equations for shrinkage core model both for a linear and exponential change of moisture content of the droplet in the drying process were delivered. Employing experimental heat transfer coefficient, drying time and droplct temperature field were determined. Comparison of experimental and predicted drying times as well as droplet temperatures shows small discrepancy. Results obtained can be used to predict quality of labile products in the course of drying.     

Non-coalescence and chain formation of droplets under an alternating current electric field

The dynamic behaviors of two droplets and droplet cluster under an alternating current (AC) electric field are investigated. Two droplets generally undergo transformation from complete coalescence to partial coalescence and finally to non-coalescence as the electric capillary number Ca_p increases. The critical electric capillary number Ca_pc for complete coalescence in the AC electric field remains unchanged and is twice as large as that in the direct current (DC) electric field when the frequency f ≥ 250 Hz. Charge transfer and reversal of electric field result in the reversal of the direction of electric force, which is the fundamental mechanism of non-coalescence of two droplets and chain formation in droplet cluster. The number of rebounds dramatically increases as f increases, promoting the stability of droplet chain. The droplet chains in the high-frequency AC electric field are longer and more stable than those in the low-frequency AC electric field.     

Mass Transport from Single Droplets in Imposed Electric Fields

Abstract

The influence of electric charge phenomena on mass transfer in systems involving droplets in a continuous medium is of increasing importance. The enhanced transport behavior of droplets in imposed fields on mass transfer and the influence of naturally occurring charges on droplets, particularly in the atmosphere, are both subjects of current interest. The objective of this study is to elucidate the hydrodynamic and mass transfer effect of imposed fields on charged single droplets. Investigations of both static and pulsed electric fields are reported.

The experimental approach is based on the suspension of single droplets in a precisely machined expanding channel. A stationary, saturated water droplet is fluidized by the upflow of 2-ethylhexanol. This arrangement allows precise photographic monitoring of droplet size and shape as well as the hydrodynamics of both phases in the region of the interface.

Baseline continuous-phase mass transfer studies with internally circulating droplets corroborate earlier studies with the same system. The effect of the accumulation of unavoidable surfactant on droplet circulation and mass transport rate at long exposure times is reported. The imposition of a static electric field in the axial direction caused distortion of droplets into prolate spheroidal shape.

An electric field pulsed at a tuned frequency is observed to cause oscillation of droplets between prolate-and oblate-spheroidal shapes. In addition to frequency and field amplitude, the interfacial properties of the fluid system as well as viscosities and densities of the two phases influence the oscillation. The effect of the pulsation of the field on mass transfer to the continuous phase is reported. These data are compared with results for both nonoscillating mass transfer and theoretical models.     

微小通道内低Reynolds数液-液两相流动与换热特性实验研究

实验研究了圆形微小通道内液-液两相流的流动和换热特性。选用去离子水为分散相,高黏度二甲基硅油为连续相。通过处理高速摄像所拍摄的可视化图像,总结了液-液两相流流型和液滴的长度/形状特征。并在此基础上考察了低Reynolds数下液-液弹状流对微小通道的换热作用。结果表明,平均Nusselt数随着Reynolds数的增加而增加,且油水比越大传热系数增加幅度越明显。Nu随着含水率的增加而降低。虽然含水率增加会使两相平均热容量提高,但在低Reynolds数下,这种提高被其长液滴内较弱的循环强度所抵消。选用三种不同形式接头在相同混合速度和含水率的情况下生成不同长度的液滴,发现短液滴更有利于换热。相同工况下,液滴长度的优化可以使整体传热系数提高近26%。     

均匀电场中液滴变形特性的耗散粒子动力学模拟

基于耗散粒子动力学方法,建立了电场作用下近似的液滴粒子力学模型,对两相不相溶液体中液滴在电场作用下的变形特性进行了模拟。模拟结果与他人的实验结果比较表明,模拟结果对液滴形状随时间的演化预测基本符合实际,仅在液滴变形较大时有一定偏差。模拟结果还表明,当外加场强较小时,液滴变形度随时间呈现振荡状态,变形度不会随时间继续增大。增大外加场强,液滴变形幅度增大,振荡频率变慢。当外加场强增大到一定程度时,液滴变形度不再振荡,而是随时间急剧增大,以至液滴最终破碎。场强越大,液滴破碎所需的时间也越短。     

电场作用下基面液滴蒸发与内部流动数值模拟

为探究电场强化基面液滴蒸发的原理,本文采用有限元方法,对外加电场作用下的固体基面上液滴的蒸发过程进行了数值模拟,对比了不同电导率液滴的蒸发过程,分析了电场、液滴蒸发速率和内部流动的影响及其成因,以及液滴在电场作用下的内部流动与液滴传热传质的关系,结果表明,电场力的作用能够显著强化液滴内部的流动,对液滴的传热传质具有促进作用。此外,本文分析了温度对电场下基面液滴蒸发及内部流动的影响,发现温度对电场、液滴内部流动及蒸发的强化作用也有着较为明显的影响：对于电导率较低的纯水液滴,当电场强度低于和高于临界值6kV/cm时,温度对电场强化液滴内部流动和蒸发的影响有所不同;对于电导率较高的盐酸液滴,温度对电场强化液滴内部流动和蒸发的影响随电场强度升高均较大。本文为发展高效静电喷雾冷却技术提供了研究基础。     

HEAT TRANSFER IN A THIN LIQUID FILM IN THE PRESENCE OF AN ELECTRIC FIELD

Heat transfer enhancement in an evaporating thin liquid film utilizing a electric field under isothermal interfacial condition is presented. A new mathematical model subjected to van der Waals attractive forces, capillary pressure, and an electric field is developed to describe the heat transfer enhancement in the evaporating thin liquid film. The effect of the electrostatic field on the curvature of the thin film, evaporative flux, pressure gradient distribution, heat flux, and heat transfer coefficient in the thin film is presented. The results show that applying an electric field can enhance heat transfer in a thin liquid film significantly. In addition, utilizing electric fields on the evaporating film will be a way to expand the extended meniscus region to attain high heat transfer coefficients and high rates of heat flux.     

电场对竖直微槽润湿及毛细流动特性影响

竖直微槽群毛细结构广泛应用在重力热管、蒸发器等散热设备内,但受重力等因素影响易达到毛细极限。引入电场的主动强化方式来提高竖直微槽的毛细极限,并通过实验和建立数学模型研究电场对竖直微槽内液体润湿及毛细流动特性的影响。结果表明,电场可以提高竖直微槽内液体润湿高度,当电场为5.0 kV时与无电场时相比,润湿高度强化比可达到30.0%。同时,电场作用下流体在微槽道内的毛细润湿流动呈分段效应：润湿流动初期,润湿高度与时间的1/2次方呈线性关系,即h-t^1/2,润湿速率与润湿高度的倒数呈线性关系,即v-1/h;润湿流动中后期,润湿高度与时间的1/3次方呈线性关系,即h-t^1/3,润湿速率与润湿高度平方的倒数呈线性关系,即v-1/h²,且润湿速率随时间呈下降趋势。     

电场对竖直微槽润湿及毛细流动特性影响

竖直微槽群毛细结构广泛应用在重力热管、蒸发器等散热设备内,但受重力等因素影响易达到毛细极限。引入电场的主动强化方式来提高竖直微槽的毛细极限,并通过实验和建立数学模型研究电场对竖直微槽内液体润湿及毛细流动特性的影响。结果表明,电场可以提高竖直微槽内液体润湿高度,当电场为5.0 kV时与无电场时相比,润湿高度强化比可达到30.0%。同时,电场作用下流体在微槽道内的毛细润湿流动呈分段效应：润湿流动初期,润湿高度与时间的1/2次方呈线性关系,即h-t^1/2,润湿速率与润湿高度的倒数呈线性关系,即v-1/h;润湿流动中后期,润湿高度与时间的1/3次方呈线性关系,即h-t^1/3,润湿速率与润湿高度平方的倒数呈线性关系,即v-1/h²,且润湿速率随时间呈下降趋势。     

HEAT TRANSFER IN A THIN LIQUID FILM IN THE PRESENCE OF AN ELECTRIC FIELD

Heat transfer enhancement in an evaporating thin liquid film utilizing a electric field under isothermal interfacial condition is presented. A new mathematical model subjected to van der Waals attractive forces, capillary pressure, and an electric field is developed to describe the heat transfer enhancement in the evaporating thin liquid film. The effect of the electrostatic field on the curvature of the thin film, evaporative flux, pressure gradient distribution, heat flux, and heat transfer coefficient in the thin film is presented. The results show that applying an electric field can enhance heat transfer in a thin liquid film significantly. In addition, utilizing electric fields on the evaporating film will be a way to expand the extended meniscus region to attain high heat transfer coefficients and high rates of heat flux.     

A MODEL FOR MASS TRANSFER IN OSCILLATING-CIRCULATING LIQUID DROPS†

Velocity vector computations based upon flow-visualization techniques have enabled the development of a detailed model for flow patterns in a droplet-continuum system typical of liquid-liquid solvent extraction. Experiments show that the streamlines for flow in and around circulating droplets which are forced into regular oscillation by a pulsing electric field can be modeled as the vectorial sum of low-Reynolds-number internal circulation (Hadamard flow) and an oscillatory streaming caused by the prolate-to-oblate ellipsoidal shape changes of the droplet (Dirichlet flow). The convective-diffusion equations have been derived and numerically solved for mass transfer from both circulating droplets (Hadamard flow) and oscillating-circulating droplets (mixed Hadamard-Dirichlet flow). The resulting rate of mass transfer from an oscillating-circulating droplet is significantly greater than that from the equivalent circulating droplet. The rate of mass transfer is dependent upon oscillation frequency and amplitude, droplet Peclet number, the interphase distribution coefficient of the transferring species, and physical properties of each fluid phase.     

The Macroscopic Effects of Internal and External Electric Fields on Profile and Thermodynamics of a Dielectric Droplet

The effects of weak and strong axisymmetric electric fields on the profile and thermodynamic characteristics of a dielectric droplet in the vapor-gas environment have been considered. The procedure for numerical solution of the coupled nonlinear equations for the equilibrium droplet shape and the electric field potential has been illustrated in the case of an external uniform electric field and the case of a nonuniform internal field of the heterogeneous nucleus with an electric dipole moment. Analytical results of perturbation theory for small nonspherical deformations in the droplet shape and surface area have been shown to be really limited to small electric field effects. However, the analytical results for the chemical potential and free energy of droplet formation (which are of first importance for nucleation phenomena and liquid aerosol formation in a gaseous atmosphere) are valid even for rather strong fields due to mutual compensation between the nonspherical contribution to the surface area and the contribution due to droplet polarization.     

汽-液-液三相垂直管内充分发展流传热性能

研究了垂直管内连续相水和分散相戊烷泡滴之间的流动和传热性能 .在全面考虑了汽体的膨胀、水蒸气的蒸发、界面张力的作用、汽液两相的相互作用和滑移、泡滴的破碎等影响因素的基础上 ,建立了与实验结果吻合较好的一维流体力学模型和传热模型     

高压交流电场中单液滴变形度影响因素

采用不同的白油和水为实验介质对高压交流电场作用下单液滴的变形特性进行了研究。研究了电场强度、油品黏度、界面张力以及液滴直径等因素对液滴变形度的影响规律,并利用显微高速摄像系统结合图像处理技术对单液滴的变形规律进行了观察和分析。结果表明：液滴变形度主要受电场强度、液滴直径以及界面张力等的影响。与电场强度的N（1.7<N<2.4）次幂呈正比;与液滴直径近似呈线性关系;界面张力较低时,液滴更容易变形。油品黏度对液滴变形度没有明显影响。在变形度较小时,离心率和Weissenberg数具有较好的一致性,但We不适用于变形度较大的情况。     

MARANGONI AND ELECTRIC FIELD EFFECTS UPON MASS TRANSFER TO TRANSLATING DROPS

Interfacial stresses arising from the transfer of an interfacial tension-lowering solute (Marangoni effects) or the presence of an electric field may significantly alter the interfacial velocity of a moving droplet with consequent effects upon the rate of convective mass exchange between the drop and the external medium. The present theoretical study considers separately the Marangoni and electric field effects and delineates the conditions under which mass transfer enhancement should be observed. For Peclet numbers in the range of 10-100, enchancement is predicted for a Marangoni to Peclei number ratio of 100 or for a dimensionless electric velocity of 0.1, As an example, numerical results for a Peclet number of 50 indicate an increase of approximately 20% in the mass transfer coefficient for either a Marangoni number of 5000 or a dimensionless electric velocity of 0.5 for phases of comparable transport properties and solute solubilities.     

Deformation of an oil droplet on a solid substrate in simple shear flow

Displacement of immiscible fluids is important in sub-surface processes such as enhanced oil recovery, oil sand processing and detergency. In this study, simulation of an oil droplet deformation on a solid substrate in simple shear flow has been carried out using computational fluid dynamics tool (Fluent 6.3) and the shape of the oil droplet is compared with that of the experimental observation. The dynamic behavior of a two-dimensional oil droplet subject to shear flow in a closed channel is considered under the condition of negligible inertial and gravitational forces. The volume of fluid method is used in Fluent to determine the dynamics of free surface of the oil droplet during the fluid flow. The oil droplet deformation increases with the increase in capillary number, Reynolds number and size of the oil droplet. The deformation of an oil droplet attached to channel surface in simple shear flow is studied experimentally in laminar flow through visual observation using microscope (Ziess, SV11 APO) with high speed camera (PCO). Aniline and isoquinoline was used to form oil droplet and distilled water was used as shearing fluid. The deformation of aniline and isoquinoline droplets was recorded using a high speed camera connected to a PC. The recorded image was replayed and the deformation of aniline and isoquinoline droplets was analyzed using Axio Vision software and compared with the results obtained from CFD simulation. The deformation of different sizes of aniline and isoquinoline droplets at different flow rates of shearing fluid and with time are well predicted by the CFD simulation.