DROPLET COALESCENCE AND BREAKAGE RATES IN LIQUID EXTRACTION COLUMNS

Abstract

A review is given of recent work on the measurement of droplet coalescence and breakage rates in a packed and a pulsed plate extraction column using a newly developed colorimetric technique. The results, which were interpreted in terms of second order coalescence and first order breakage rate constants, showed that the droplet interaction rates are considerably lower in the pulsed column. The rate constants can also be used to predict accurately the steady state droplet size distribution, and to study theoretically the effect of droplet coalescence and breakage on mass transfer rate. Deficiencies in the available mass transfer coefficient data for droplets, both individual and in “swarms”, are pointed out.     

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.     

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。     

Droplet Size Characteristics and Energy Input Requirements of Emulsions Formed Using High-Intensity-Pulsed Electric Fields

Abstract

Experimental methods have been developed to measure droplet size characteristics and energy inputs associated with the rupture of aqueous droplets by high-intensity-pulsed electric fields. The combination of in situ microscope optics and high-speed video cameras allows reliable observation of liquid droplets down to 0.5 m in size. Videotapes of electric-field-created emulsions reveal that average droplet sizes of less than 5 μm are easily obtained in such systems. Analysis of the energy inputs into the fluids indicates that the electric field method requires less than 1% of the energy required from mechanical agitation to create comparable droplet sizes.     

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 TRANSFER IN TURBULENT PULSATING FLOWS

The effect of flow oscillation to the mass transfer between turbulent fluid and solid wall was investigatedby measuring the mass transfer rate between fluid and pipe wall with imposed oscillating flow usingelectrochemical method.The velocity and concentration field in the viscous sublayer which controls the mass trans-fer in such a process was simulated by a simple wave model of single harmonics.Experimental results confirmthat the flow oscillation has no influene on time averaged mass transfer rate,but the phase difference betweenphase averaged velocity field and concentration field shifts with the frequency of imposed oscillating flow.Numeri-cal analysis reveals that the concentration boundarylayer which is responsible for the mass transfer is muchthinner than the viscous sublayer which greatly weakens the influence of imposed oscillating flow on mass transfer.     

The effect of electric field on mass transfer from drops dispersed in a viscous liquid

Mass transfer of benzoic acid from drops dispersed into a continuous phase of mineral oil with high viscosity has been investigated both with and without an imposed non-uniform d.c. electric field. Total mass transfer efficiency was significantly enhanced in the presence of the high voltage electric field. The results indicate that the application of the electric field to the drop formation process does not change the fundamental mass transfer mechanisms and the mass transfer during drop free fall can also be described by existing mass transfer models. The results also suggest that the high viscosity of the continuous phase inhibits the drops oscillation as well as circulation when the drop sizes become smaller under the applied high voltage electric field. Therefore the significant enhancement of mass transfer efficiency in the present work is mainly due to the increased specific interfacial area.     

无机盐浓度及种类对电脱水过程水滴极化的影响

为了深入探究无机盐对电脱水过程水滴极化的影响机理,分别改变无机盐浓度及种类,对高频高压脉冲电场作用下水滴的极化变形进行显微实验研究。结果表明,不同NaCl浓度条件下水滴的变形度随电场频率和占空比的增加呈先增大后降低,由于电导率增大、离子冲击效应等的影响,随着NaCl浓度的增大,水滴的变形度随之增大。高价无机盐离子所受的电场力是一价离子的数倍,有利于其冲击速度和冲击动量的提升,水滴变形度随离子价位升高而增大。另外,由于离子活泼程度以及水解等原因,在同一高压脉冲电场中,不同钠盐溶液水滴变形度顺序为：磷酸钠 >碳酸钠 >硫酸钠 >氯化钠 >硝酸钠。不同氯盐溶液水滴变形度顺序为：氯化镁 >氯化钙 >氯化钾 >氯化钠 >氯化铵。研究成果为高压高频脉冲静电破乳机理的深入探讨奠定了基础。     

A study of mass transfer from single large oscillating drops

A study was made of mass trasfer rates from single large oscillating drops of pure liquid-liquid systems, in the size range of 5 to 10 mm. A thrermostatically-controlled, 50 mm in diameter, 1000 mm long, rising drop column was used, in which mirrors in the jacket enabled front and side views of drops to be photographed simultaneously. The systems studied were (1) toluene and acetone (dispersed)-water (continuous), and (2) n-heptane and acetone (dispersed)-water (continuous). High concentrations of acetone (up to 3.75 kmol/m³) were used to examine the effect of different parameters on the mass transfer rate, frequency and amplitude of oscillation in countercurrent operation. Previous theories and empirical correlations [2–6, 12, 13, 15] for the prediction of overall mass transfer coefficients showed large deviations from measured values. These may have aarisen because the models do not represent droplet oscillation accurately, and/or apply only to oscillations of small droplets. Fair agreement was obtained for small oscillating droplets as low solute concentrations. The oscillations of a travelling drop were asymmetrical; the period of oscillation was uniform for mutually-saturated systems but changed when mass transfer was taking place. The periods were longer than those predicted by the Lamb [7] and Shroeder and Kintner [37] correlations. Terminal velocities predicted from literature correlations [32, 34] did not give reasonable agreement with experimental data when there was mass transfer of solute. The drag coefficient increased with increasing mass transfer rate from the drop. Correlation of the results and the dispersed phase mass trasfer coefficients by dimensional analysis resulted in the correlation

1 List of symbols at the end of the paper.

with a mean deviation of ±23%, by insertion of experimental oscillation frequency data. This will facilitate more accurate prediction of the dispersed phase mass transfer coefficients relating to equipment containing droplets in the oscillating regime, e.g. pulsed columns or agitated tanks.     

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.     

Simulation of interfacial mass transfer by droplet dynamics using the level set method

A unique approach to simulate mass transfer across the moving droplet where mass transport equations and governing equations of the levels set method are solved separately is proposed in this work. Mass transfer coefficients of the chemical species can be computed by equating the diffusive flux and the mass transfer flux at the interface, which are found to be of the same order of magnitude as of those obtained using an empirical correlation. Simulations underestimate mass transfer coefficients by roughly 25% across the range of low Reynolds number studied systematically. The level set method is used to track the motion of the interface to study droplet dynamics and mass transfer across a moving droplet because of the ease in defining the local curvature of the interface and in capturing any topological changes. We perform various numerical simulations by varying the physical properties of the system, in order to analyze the influence of dimensionless numbers such as the Reynolds number (Re), the Eotvos number (Eo) and the Morton number (M) on the shape of a buoyancy-driven droplet and compare them with the various shape regimes of drops and bubbles reported by Clift et al. [1978. Bubbles, Drops and Particles. Academic Press, New York]. It is shown that larger deformation occurs for buoyancy-driven droplets when interfacial forces are considerably greater than viscous forces (M?1 and Eo>10) and the droplets are almost undeformed when viscous forces dominate interfacial forces (M>10³ and Eo>10).     

Mass Transfer during Solute Extraction from a Droplet with Internal Circulation in the Presence of a Constant Uniform Electric Field

Mass transfer, under the influence of an constant uniform electric field in a ternary system, comprised of a transformed solute, a liquid dielectric continuous phase, and a stationary dielectric droplet, was considered in this study. The solubilities of the solute in the dispersed and continuous phases have the same order of magnitude, and the resistance to mass transfer in both phases is taken into account. The applied electric field causes Taylor circulation around the droplet, while the droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration boundary layer in the dispersed and continuous phases. The bulk of a droplet, beyond the diffusion boundary layer, is completely mixed and the concentration of solute is homogeneous and time‐dependent in the bulk. The system of transient coupled equations of convective diffusion for solute transport in the dispersed and continuous phases with time‐dependent boundary conditions is solved by combining a generalized similarity transformation method with Duhamel's theorem; the solution is obtained in the form of a Volterra integral equation of the second kind. Numerical calculations essentially show an enhancement of the rate of mass transfer for dispersed liquid‐liquid systems, under the influence of an electric field.     

Growth rate and oscillation frequency of electrified jet and droplet: Effects of charge and electric field

Electrified jets are applied industrially in agriculture, automobiles, targeted drug delivery systems, spacecraft propulsion units, liquid metal sprayers, ion sources, emulsifiers, dust scavenging systems, and ink-jet printers. Electrified columnar jets experience instability caused by electrohydrodynamic interactions of the charged liquid surfaces with electric fields. Electrostatic and surface tension forces competing along the liquid surface create surface pressure differences. The temporal rise and fall of the surface pressure induce oscillations of jets and droplet. A linear theory was derived to yield a dispersion equation determining the most dominant wavelength of oscillation for a given charge level and electric field; this enabled the estimation of the diameter of an atomized droplet. In addition, the frequency of oscillation was derived for a cylindrical jet and spherical droplet. Parametric studies were performed for various charging levels and electric field strengths.

© 2018 American Association for Aerosol Research     

电场对液滴界面张力及动力学特征影响的研究进展

电场是改变液滴界面张力的重要因素,施加不同类型的电场对驱动微流体运动、变形、分裂及合并等行为起着至关重要的作用,该技术广泛用于微液滴操控、电子显示和原油脱水等领域,并具有潜在的应用前景。文中综述了电场作用下微液滴气-液、气-固与液-液交界面张力的变化,分析了与界面张力对微液滴运动学行为影响相关的实验现象及模拟成果;指出电场作用下气-液交界面处表面张力的变化趋势,因实验及模拟方法不同目前仍存在较大争议;探讨了直流电和交流电对电润湿过程液滴铺展的不同影响和液滴形态振荡特征;分析了直流电、交流电及电脉冲对电破乳过程中液滴运动行为的重要作用。总结了电场对液滴界面张力影响研究中存在的问题,并提出了值得进一步深入研究的可能方向。     

液滴流微反应器的基础研究及其应用

综述了近些年来快速发展的液滴微流控技术, 回顾了微流控系统中液滴的基本行为, 如液滴的生成、运动、聚并和分裂等研究进展, 重点探讨微液滴作为反应器其内部的流动、传质和反应过程, 以及液滴流微反应器已有的和潜在的重要应用价值。通过精确调控液滴在微尺度上的行为(产生、聚并与分裂、内部的混合与反应等), 使单个液滴成为新型受限空间内的微型间歇反应器, 而微通道内的液滴流进而形成了若干间歇反应器构成的连续流反应器新型式。除了微流控技术普遍具有的微小尺寸效应带来传质传热强化、易于放大等优势外, 液滴流微反应器还具有诸如避免试剂交叉污染、液滴内部可控混合、易于独立调控、便于高通量筛选或者制备等独特特点, 使得其在功能材料制备、化学合成以及生物化工方面有着广泛的应用。     

Physical and reactive extraction of salicylic acid—II. Investigations on fixed,freely suspended and pulsed droplets

By the use of the modified liquid scintillation technique, new information of high accuracy and high time resolution was gained on physical and reactive extraction on droplets. The influence of the size and hydrodynamics of droplets on the physical and reactive extraction of salicyclic acid is investigated on fixed, freely suspended single droplets in a steady as well as in a pulsated flow. At pH 0.8, the physical extraction parameters are determined. With increasing pH, the enhancement factor increases at first due to the spontaneous dissociation of acid, at higher pHs due to gradual elimination of the mass transfer resistance in the continuous phase. At pH 12, this resistance is completely eliminated. This allows us to determine the fractional mass transfer coefficients in the droplet phase k_d and in the continuous phase k_c. The influence of the concentration of a secondary amine, LA-2—which forms a complex with the acid—on the fractional mass transfer coefficient k_d is investigated also.     

Transient convective mass transfer for a fluid sphere dissolution in an alternating electric field

In this study, we considered mass transfer in a binary system comprising a stationary fluid dielectric sphere embedded into an immiscible dielectric liquid under the influence of an alternating electric field. Fluid sphere is assumed to be solvent-saturated so that an internal resistance to mass transfer can be neglected. Mass flux is directed from a fluid sphere to a host medium, and the applied electric field causes a creeping flow around the sphere. Droplet deformation under the influence of the electric field is neglected. The problem is solved in the approximations of a thin concentration boundary layer and finite dilution of a solute in the solvent. The thermodynamic parameters of a system are assumed constant. The nonlinear partial parabolic differential equation of convective diffusion is solved by means of a generalized similarity transformation, and the solution is obtained in a closed analytical form for all frequencies of the applied electric field. The rates of mass transfer are calculated for both directions of fluid motion—from the poles to equator and from the equator to the poles. Numerical calculations show essential (by a factor of 2/3) enhancement of the rate of mass transfer in water droplet-benzonitrile and droplet of carbontetrachloride-glycerol systems under the influence of electric field for a stagnant droplet. The asymptotics of the obtained solutions are discussed.     

Visualization of Flow Fields and Interfacial Phenomena in Liquid-Liquid Solvent Extraction

Abstract

Use of a video camera apparatus with a helium-neon laser light source has enabled the detection of flow fields in and around a circulating aqueous droplet which is suspended in a flowing stream of 2-ethyl-l-hexanol. Droplet Reynolds numbers were in the range of 7 to 22. The behavior of the streamlines for flow both inside and outside the droplet was shown to be similar to that predicted for circulating droplets at low Reynolds numbers. Formation of stagnant caps of surfactant at the rear of the droplets was found to suppress the flow patterns inside the droplet and decrease the associated internal fluid velocities.     

Vergleich des Stofftransports von hängenden und akustisch levitierten Wassertropfen in CO2

High‐pressure acoustic levitation devices allows a contact‐free investigation of liquids. Here, acoustically levitated water droplets and pendant water droplets were examined in regards to the mass transfer coefficient in a static CO₂‐atmosphere under elevated pressures. Based on the droplet geometry and the decrease of the droplet volume over time, it was possible to calculate the mass transfer coefficient of water into CO₂ at any given time. Additionally, open questions regarding possible differences between pendant and acoustically levitated water droplets were discussed.