A state-of-the-art review on single drop study in liquid-liquid extraction:Exper

Jiyizhe Zhang,Yundong Wang, *,Geoffrey W.Stevens,Weiyang Fei

1 The State Key Laboratory of Chemical Engineering,Department of Chemical Engineering,Tsinghua University,Beijing 100084,China

2 Department of Chemical Engineering,The University of Melbourne,Parkville,Victoria 3010,Australia

Keywords:Solvent extraction Mass transfer Single drop Drop breakage and coalescence CFD simulation Population balance model

ABSTRACT The experimental and numerical investigations of single drop in liquid/liquid extraction system have been reviewed with particular focus on experimental techniques and computational fluid dynamic simulation approaches.Comprehensive surveys of available experimental techniques and numerical approaches for single drop rising and falling were given.Subsequently,single drop mass transfer was also reviewed both experimentally and numerically.Additionally,single drop breakage and coalescence process and the influencing factors were summarized and compared,so as to establish sub-models for population balance model.Future directions on single drop mass transfer,drop breakage and coalescence were suggested.It is believed that the single drop is a powerful tool to assist extraction process design from lab-scale to pilot-scale.

1.Introduction

Liquid-liquid extraction processes are well suited to industries which need to separate heat-sensitive,relatively nonvolatile or high value liquid feeds[1].They are widely used in hydrometallurgical,petrochemical,pharmaceutical,environmental and nuclear fuel reprocessing industries.Liquid-liquid extraction is based on the partial miscibility of liquids and used to separate a dissolved component from its solvent by mass transfer to a second solvent.Typical industrial application includes recovery of metals such as copper,cobalt,nickel and rare earth elements from acidic leach liquors,extraction of aliphatic aromatic and naphthenic chemicals,refining of uranium,plutonium and other radioactive isotopes from spent fuel elements,extraction of antibiotics and separation from fermentation broth,recovery of vegetable oil from natural substrates,etc.

Extractors are usually classified according to the ways of interdispersing the phases and producing the countercurrent flow pattern,namely,mixer-settler,column and centrifugal contactors[2].Mixer-settlers are widely used when a process requires longer residence times and when the solutions are easily separated by gravity.But they also require a large facility area and high capital cost.Therefore,mixer-settlers are commonly applied in nuclear industry,hydrometallurgy,as well as rare earth separation[3,4].Extraction columns have many types,including a rotating disc contactor column(RDC),pulsed column,packed column,and sieve tray column[5].Centrifugal extractors employ a spinning rotor that intensively mixes the two phases and separates the two phases inside the rotor,resulting in efficient and fast phase separation[6].It is obvious that centrifugal extractors can treat systems with low density difference and systems with short contact time.They are inevitably high capital,operation and maintenance cost.

Despite years of study,the design of extraction equipment still relies on pilot-scale experiments to realize a full-scale design for a new process.The pilot-scale experiments usually cause most of the costs and time,which is difficult for the chemical companies to catch up with the rapid changing market.On the basis of these experiments,models are derived for the scale-up design,like stage-wise models,dispersion or back-mixing model.These models are mainly based on experiences and far from optimum due to oversimplified assumptions.Moreover,the extraction process is very complicated because a range of interactions between droplets and the continuous phase and the internals of the column influence the overall conditions.Interactions like drop rising or falling,breakage and coalescence,as well as mass transfer[7]coupled with different time and length scales make the scale-up design difficult.Although rapid progress has been made,various simulation methods provide insights into the transport phenomena and are a useful design tool,it is still difficult to perform exact simulation of the extraction process and describe the above interactions(Fig.1).

Fig.1.Complex interactions within extraction column.

Therefore,a more scientific way to reduce the effort of pilot-scale experiments and avoid previous experience and oversimplified model is being sought.Single drop experiments consume less chemicals to obtain design parameters which seems to be a good choice.In this case,hydrodynamic and mass transfer behavior,like drop terminal velocity,coalescence probability,mass transfer coefficient could be determined in a lab-scale unit.Several advantages are summarized below(Fig.2):

▪Reduce the complexity of the drop swarm to single drops,which makes it easier for study;

▪Diminish the number of influencing factors of the extraction process and identify separately;

▪Small amount of liquid is used to save cost with considerable effort;

▪Easy to control and analyze.

There is an obvious gap between single drop study and the whole extraction process design,therefore,accurate and reliable models are required to predict droplet behaviors with various time and length scales.A promising approach to explain the complex droplet interactions is the population balance model(PBM).Within the model,characteristic features of droplet,such as terminal velocities,breakage and coalescence behavior and mass transfer mechanisms are described as sub-models or parameters,which could be measured from single drop experiment.By establishing more accurate sub-models and connecting them together,it is possible to predict the drop size distribution(DSD)as fundamentals for the scale-up process.In this way,PBM builds a bridge between single drop study and scale-up design and offers a more rational and efficient way for industrial application.Simulation in conjunction with simple experiments is likely to provide basic information in the sub-models,such as single drop behavior which are not accessible by observation.Furthermore,computational fluid dynamic(CFD)simulation coupled with PBM are able to predict the DSD and the fluid flow structure simultaneously,which is needed for the scaleup design.

The present paper attempts to review the research available from a fundamental single drop perspective for deep understanding of the liquid-liquid extraction process.Firstly,basic hydrodynamic behavior of rising and falling drops is introduced,where the terminal velocity is mainly discussed.Next,single drop mass transfer is reviewed,which is of major importance and can be influenced dramatically by various factors.Then,interactions between drops as coalescence and breakage are considered.These two situations are studied because they are closely related to drop size distribution(DSD),and eventually influence the mass transfer rate and the operational conditions.Both experimental techniques and simulation methods are summarized in the above three sections.Finally,several prospects of the single drop studies are suggested.

2.Single Drop Rising and Falling

Fig.2.Single drop study to breakdown the complexity.

Fig.3.Drop behavior as a function of drop diameter.(Adapted from[8].)

Although single drop rising and falling in an ambient quiescent liquid rarely occur in extraction column for several reasons such as different flow patterns,swarm effect,mass transfer or column internals,it is one of the most fundamental cases for further studying and modeling of two-phase flow in an extraction unit.

For single drop rising without heat and mass transfer,drops with different diameters have different corresponding terminal velocities.Fig.3 shows the relationship between the drop terminal velocity and its diameters when rising or falling in a continuous phase[8].Four sections are involved,namely,rigid,circulating,oscillating and deformed drops.When the diameter is very small,drops can be modeled as rigid particles(A)with immobile interface.As shear force at the interface increases with the drop diameters and the internal circulation is induced,terminal velocities increase for circulating drops(B),therefore,a mobile interface has to be taken into account.As the drop diameter increased further,the drop cannot maintain its spherical shape and starts to become oblate ellipsoidal and oscillate periodically(C).In the last stage,drops are deformed and are likely to wobble through the continuous phase(D).

Single drop rising or falling is governed by physical properties of dispersed and continuous phases,as well as properties of the interface.With the help of single drop experiment and simulation,the above influencing factors can be identified and even quantified by correlations and models.The most prominent case is to determine the terminal velocity as a function of drop diameter,which can be derived from the Navier-Stokes equations.However,the analytical solution for the equations have been only derived for creeping flow by Hadamard[9]and Rybczynski[10].For higher Reynolds number,terminal velocity can be calculated in three ways[11]:

▪Indirectcalculationbyso-called standard dragcurve.Thedragcoefficient was plotted as a function of Reynolds number.To predict terminal velocity,an iteration procedure was needed since Reynolds number contains terminalvelocityaswellas dropdiameter.Manycorrelations wereavailable in literatures such as Hamielec[12],and Feng and Michaelides[13].However,these correlations are restricted to certain range of Reynolds number.Some of the correlations are summarized in Table 1.

▪Use of generalized graphical correlation of Reynolds number versus Eotvös number.Proposed by Clift et al.[18],the diagram was given in double logarithmic scale covering spherical,ellipsoidal,wobbling and some other regimes.But it should not be applied to systems with extreme continuous and dispersed phase density or viscosity ratios.

▪Explicit correlation of terminal velocity against drop diameter.These correlations were semi-empirical in most cases.For example,correlation by Grace et al.[19]permitted to predict terminal velocity in contaminated systems by using a correction function.Another widely used model proposed by Henschke[20]needs to be fitted by experimental data.

Table 1 Drag coefficient correlations in literature

2.1.Experimental studies

As summarized in Table 2,different models and correlations for single drop rising/falling were tested or extended and the application scopes were determined.Different test systems were used and were kept extremely pure with special caution.Experimental setups were considerably simple and mostly in extraction columns filled with continuous phase liquid.Then the dispersed phase was injected from the bottom or released from the top of the column.Earlier studies[21-25]measured terminal velocity of a variety of liquid drops immersed in water,covering a wide range of physical properties.Drop size was measured by drawing a specific volume with a capillary tube or burette,or by counting the number of drops produced by a given volume of dispersed liquid.These methods required careful operations and were sometimes tedious.The terminal velocities were measured by timing method,i.e.measuring the time when droplets pass through a certain distance.The passage of the drops should ensure the terminal velocities are reached and also avoid the end effects.Transient velocities were difficult to obtain with this method.

Generalized curve obtained by Hu and Kinter[21]could be used directly to predict terminal velocity,drag coefficient and Reynolds and Weber numbers for any given drop size.Klee and Treybal[22]proposed two correlations for terminal velocity and studied the eccentricity of drops.Since oscillation of drops was very complex,this area has been paid much attention by many researchers.Oscillation frequencies and amplitudes of nineteen pure systems were measured by Schroeder and Kintner[23].Empirical equation of terminal velocity for circulating and oscillating drops was derived by Thorsen et al.[24]from seven high interfacial tension systems.Additionally,oscillation frequency and terminal velocity of oscillation drops were proposed by Edge and Grant[25].A transition from non-oscillating to oscillating drop was found at a break when plotting a modified Weber number against a modified Ohnesorge number.

Recently,with the help of photographic technique,the configuration and trajectory of single drop rising/falling can be recorded by camera.Drop with certain diameter can be obtained by either precision dosing pump,or via image processing.The latter is done through commercial software to know the pixel length and then convert them into actual length.A high speed camera was set perpendicularly to the column to record the entire or part of the path.After image processing,the velocities could be calculated by vertical position of the mass center of the drop for each frame.In this way,both transient velocities and terminal velocities can be measured accurately and reduce the operational errors.

Wegener et al.[27]presented single drop experiment to study toluene droplets rising in water ranging from 1.0 to 7.0 mm.A semiempirical correlation to predict the single drop rising/falling terminal velocity based on experimental data was presented.Interestingly,for 3 mm droplets,a bifurcation velocity was observed,which two distinct terminal rise velocities were observed,as shown in Fig.4.Different interfacial tension standard systems were investigated by Baümler et al.[28].Comparisons between different systems were presented and terminal rise velocity,aspect ratio,and the onset of shape oscillation were determined.However,they found that investigated correlations lost accuracy with the decrease of interfacial tension.

Although the test systems were retained extremely clean,contaminations or surfactants inevitably existed in real situation.These factors would block the mobility of the drop surface and thus slowed down the velocity[29-32].

2.2.Simulation studies

To reduce time and effort to precisely control the purity and to have an in-depth insight into the transport phenomena,computational fluid dynamic(CFD)simulation provides an efficient way.The simulation of single drops in a continuous liquid phase reveals a more detailed look on time and length scales where experiments are not accessible,and can be served as a validation of the experimental data.Unlike solid particles,droplets move with topological changes,along with mass transfer and surfactant which largely influence the structure of the interface.Thus,one of the main issues in simulation is to describe the interface changes exactly with low numerical cost.Generally,methods to deal with interface change are summarized in Fig.5.Moving mesh method and fixed mesh method are widely used in most cases.Diffuse interface method and Lattice Boltzmann method also provide a feasible way.There are several Options for fixed mesh Methods,e.g.front-capturing method,front-tracking method and hybrid the previous methods.Interfacial forces are also crucial when describing the interface.In this case,continuous surface stress(CSS)model,continuum surface force(CSF)model and ghost fluid method(GFM)are most widely-used.

Several representative studies were listed in Table 3.For moving mesh method,as the name suggested,a moving mesh is used to trackthe interface.As the topology of the interface changes,the nodes are moving in accordance with the change,allowing direct implementation of boundary conditions at the interface.This results in a very exact and sharp representation of the interface,but is limited to moderately deformed interface without significant topological changes,i.e.droplet coalescence or breakup.Baümler et al.[28]investigated three standard test systems suggested by EFCE[33]with no mass transfer experimentally and numerically.The simulation was performed by the academic code NAVIER with mesh moving method to feature the interface.The numerical results were in excellent agreement with experiment results in all three test systems.

Table 2 Single drop free rising/falling experimental studies

Fig.4.Experimental result of toluene-water system[27].((a)terminal velocity as a function of drop diameter and(b)drop rise bifurcation velocity.)(Reprinted from AIChE Journal,56,M.Wegener,M.Kraume,A.R.Paschedag,1-9,Copyright(2019),with permission from John Wiley and Sons.)

Fixed mesh method uses a fixed mesh with different approaches to locate the interface between the phases,including front-capturing method,front-tracking method and hybrid capturing and tracking method.These methods are able to describe large deformation of the interface.But the main difficulty arises in maintaining a sharp interface between phases.

Front-capturing method represents the interface by using special markers or indicator functions in an implicit way,which can be categorized in point-based or marker-based,surface capturing and volume capturing method.Marker-based method is one of the oldest methods where massless marker particles are used to identify each fluid and thus the motion of the interface.Although it is easy to be implemented,it fails to describe large deformation due to the necessity of redistributing the markers.Another well-known method is volume capturing method,e.g.volume of fluid(VOF)[34]method.The basic idea is to use a volume fraction function to describe the phases and the interface.The method is capable of handling problems with significant interface topology deformation and does not suffer from mass losses;however,these usually come at a high computational cost.Surface-capturing method offers another more accurate option,like the level-set[35]method.In this method,the topology changes of the interface are fully described by the zero-level set function.The method is more accurate and is easy to be implemented in three-dimensional calculation.However,the main drawback is the possible loss of mass for significant deformed topology.Several representative works are briefly reviewed here.Bertakis et al.[36]utilized level-set function for capturing the interface movement to simulate n-butanol droplets freely sediment in water.The finite-element and extended finite-element methods were implemented and evaluated.Compared to the traditional method,the extended method provided more accurate results and a wide spectrum of droplet diameters that also covers the oscillating region.In the study of Engberg and Kenig[37],level-set code was developed for simulate single drop rising in three standard test systems.Interfacial force is described by both continuum surface force(CSF)model and the ghost fluid method(GFM)to prevent volume(or mass)loss during the reinitialization of the level set function.Simulation results were in accordance with experimental results and the onset of oscillations was correctly predicted.Huang and Wang[38]applied VOF method in conjunction with the CSF model to investigate the effects of physical properties on the drop rising behaviors.The simulation results showed a good agreement with experiments.

Fig.5.Different simulation methods for single drop study.

Table 3 Single drop free rising/falling simulation studies

Front-tracking method,on the other hand,tracks the interface explicitly as the interface moves.This approach is extremely accurate and robust yet rather complex to implement.Dijkhuizen et al.[39]studied the air bubble or toluene drop rising in water by 3D front-tracking model.Drag coefficients and lift forces were computed with a high accuracy.Recent years,hybrid capturing and tracking method[40]is proposed to combine the advantages and eliminate the weakness of the previous two methods.Normally,a stationary grid is used for fluid flow and the interface is tracked by a separate grid,but is rather complex.

Other methods like diffuse interface method do not require any explicit interface treatments.The interface changes naturally based on the thermodynamics of the model.The method provides a feasible way to run simulations of large-scale three-dimensional system and with significant topological deformation of the interface,but may not be accurate enough since the width of the interface is enlarged to allow easier computations.Another method known as the LBM was used in Komrakova et al.[41]to study the motion of n-butanol drop in water.Space and time are discrete in LBM method and identical particles of equal mass populate at each lattice.LBM is able to capture the drop shape especially in the oscillating regime was demonstrated.The results were compared to experimental and numerical ones and to semi-empirical correlations.

3.Single Drop Mass Transfer

Single drop with mass transfer is a relatively complex situation compared to drop rising or falling in a quiescent liquid.A third or more component[45]is added and could be transfer from one phase to another across the interface by different solubilities.As the most crucial part influencing the whole extraction performance,mass transfer should be analyzed and understood in detail before analyzing contactor behavior.

3.1.Experimental studies

To study mass transfer performance for single drop in a lab-scale test cell,two types of cells are mainly used.One is the traditional drop rising column with a funnel on the top to collect the dispersed phase,which is easy to operate.However,the total length of the column should be high enough to have the long residence time.Another type of cell is like a conical Venturi tube as Fig.6 shows,in which the drop firstly rises for a distance and then suspends for a while when the continuous phase begins to flow in an opposite direction.In both cases,the direction of mass transfer occurs from either continuous to disperse phase(c→d)or disperse to continuous(d→c).

Mass transfer resistance lies in three cases:inside the droplet only(internal problem),outside the droplet only(external problem),or in both phases(conjugate problem)[11].During the mass transfer process,various phenomena are involved,namely,the shift of moving trajectory,interfacial instability and turbulence,or the contamination may affect the mass transfer rate.Several representative studies were listed in Table 4.Perspectives of these studies related to mass transfer can be categorized as[46]:hydrodynamic change,interfacial instability,contamination and some other factors.

3.1.1.Hydrodynamic factors

Considering a single drop moving in a quiescent liquid,it experiences three stages during its life:drop formation,rising or falling as well as coalescence at the end of bulk interface.The fulfillment of mass transfer in the above stages is different.

▪Drop formation

As the initial stage,drop formation plays an important role as to determine the primitive drop size,initial velocity and mass transfer condition for the following process[63].Some[64-67]even showed that around 3%-50% of the mass transfer was completed in formation stage,which should not be neglected.Especially during the drop formation stage,the concentration gradient is relatively high which can cause Marangoni effect(discussed later).In this case,influencing factors involving drop diameter,initial solute concentration and mass transfer directions were discussed by Wegener et al.[56]to account for the impact of the Marangoni effect on mass transfer during formation.A correlation by taking initial solute concentration into account was proposed to predict extraction efficiency with reasonable accuracy.However,difficulties arise due to short time and length scales between drop formation and finalized at the Teflon tip and the role of coalescence at the tip remains unclear.

▪Drop rising or falling

Most of the single drop mass transfer studies are concerned with drop freely rising or falling.As mentioned in Section 2.1,single drop experiences internal circulation,oscillation or deformation,which thus eventually affects mass transfer.Models of mass transfer coefficient or Sherwood number were obtained for each occasion with different application scopes,as summarized in Table 5.

The first reported study of this type was that of Sherwood et al.[47],who investigated acetic acid transfer from drop of benzene and methyl isobutyl ketone to water.The results indicated that the interior of the drop was not stagnant but rather agitated.Extraction coefficients were calculated by comparison in spray and packed columns.However,West et al.[48]found that the results were different as much as fivefold from Sherwood's,which was likely caused by the difference in purity of the benzene used in experiment.More recently,Huang et al.[61]presented mass transfer study along single drop rising in a system with high density difference,and a specific cleaning procedure was performed before each experiment run.Different influencing factors were involved.To predict mass transfer coefficient,a mass transfer enhancement factor was introduced to modify the model,which showed a good accordance with experimental results.

Fig.6.Schematic of single drop mass transfer cell.(a)Single drop rising column and(b)conical Venturi tube for single drop mass transfer.

For larger drops,mass transfer is superposed by oscillation and shape deformation.Yamaguchi et al.[26]measured mass transfer rate on single drop rising or falling with oscillation.Frequency and amplitude of oscillation were investigated by a high-speed camera.An empirical equation was proposed for predicting mass transfer coefficient as well as for the critical drop diameter of oscillation onset.Hassan et al.[52]improved the models for larger droplets with size range from 5 to 10 mm.Mass transfer coefficient of dispersed phase was obtainedby dimensional analysis.For deformed drops,strong interfacial instabilities coupled with mass transfer make it difficult to exactly describe the correlations.With a slight parameter modification to the Handlos and Baron model,the mean droplet concentration of the transferred component was successfully modeled as a function of Fourier number[51].In comparison with droplets with only slight deformations,the fluid dynamic behavior of oscillating or deformed droplets is substantially different and less predictable,which is due to the unsteady drop shape change.

Table 4 Single drop mass transfer experimental study

Table 5 Mass transfer correlations for different drop behavior

▪Drop coalescence at the bulk interface

Generally,drop formation and terminal coalescence are eliminated by mass transfer experiments with drop free rising or falling.An inverted funnel located at the top of the column is always with narrow channel and proper extraction rate of dispersed phase to avoid additional mass transfer.Li et al.[71,72]designed a novel totally-closed extraction column to minimize the terminal effect of drop coalescence on the accuracy of mass transfer measurements.Two liquid-liquid systems were tested and focused on the effect of the coalescing interface area on the mass transfer measurements.It showed that failing to minimize the terminal effects would lead to poor repeatability of experimental data.Thus,it is necessary to design the experiments with high rates of drop phase injection as well as withdrawal for the mass transfer study.

3.1.2.Interfacial instability

Mass transfer of a solute between two liquid phases is mainly influenced by the complicated fluid dynamic behavior caused by movable interface.In this case,local interfacial tension and additional tangential shear forces may occur due to solute transfer,which will trigger interfacial instabilities like the Marangoni effect as a result.Marangoni convection occurs when there is an interfacial tension gradient,which accounts for the phenomena so-called“tears of wine”.As shown in many studies[67,73],Marangoni convection can improve internal mixing within droplets and lead to significant mass transfer enhancement.Due to the complexity of these interfacial instabilities with mass transfer,single drop as the basic mass transfer unit is of great interest(Fig.7).

Henschke and Pfennig[20]proposed an instability constant CIPto describe nonstationary mass transfer in test system.The parameter characterizes the instability at the interface specific to the system.Wegner et al.[55],investigated simultaneous Marangoni convection in toluene-acetone-water system.Key parameters such as initial solute concentration and drop diameter were discussed.It was found that mass transfer increased for higher initial concentrations as well as smaller drop diameter.Later in the same test system,Wegner and Paschedag[59]studied the effect of soluble anionic surfactants on hydrodynamic and mass transfer behaviors of single droplet with Marangoni instabilities.It was found that mass transfer was still greatly improved by Marangoni convection though high surfactant concentration was believed to slow down interfacial movement.In a recent study in the system of n-propyl acetate/acetic acid/water by Zheng et al.[60],for a single rising droplet with given diameter,there was a competing mechanism between reduction of velocity and mass transfer enhancement due to the Marangoni effect.To date,the Marangoni effect is not fully elucidated.Additional flow patterns generated by the Marangoni effect resulted in complex interactions between flow and concentration field.Therefore,on the one hand,further work should be done in the clean single drop systems;on the other hand,contaminations like surfactants interact with the Marangoni effect should be paid more attention.

3.1.3.Contamination

Fig.7.Schematic of flow patterns in rising drops.[11].(a)Without Marangoni convection and(b)with Marangoni convection.(Reprinted from International Journal of Heat and Mass Transfer,71,M.Wegener,N.Paul,M.Kraume,475-495,Copyright(2019),with permission from Elsevier.)

In general,contamination of the interface by surfactants will reduce the mass transfer rate.One reason is that the adsorbed surfactant may form an interfacial barrier layer on the interface which hinders the transfer of solute.It is so-called the physicochemical effect[54,74-77].From a hydrodynamic perspective,another reason is that the adsorbed surfactants may reduce the internal circulation of droplet and thus decrease the terminal velocity or damping the oscillation and inhibit the interfacial turbulence[78-80].Therefore,some studies showed pronounced reduction in mass transfer caused by surfactant contamination.For instance,by adding surfactants,Skelland and Caenepeel[81]found mass transfer reduction to 10% of that in pure system,while Steiner et al.[51]found mass transfer slowed down 30 and 70 times due to contamination.Taking contamination caused by surfactant into account,a new model was proposed by Slater[50]to determine mass transfer coefficients for a wide range of drop diameters.Although the influences caused by contaminations have been studied intensively,it is still difficult to describe the degree of contamination to quantify its influence on overall mass transfer.

3.1.4.Other factors

Despite the above factors,others like physical properties of the system(e.g.viscosity,temperature,pH)and outside intensification(e.g.column internals,ultrasonic waves)also play an important role to mass transfer.Recent years,considering there will be a change in extraction column feeding to renewable biological origin with high viscosity and low vapor pressure in the future,Donni Adinata[8]investigated single drop behavior in high viscosity system.By increasing viscosity either in the continuous phase(water)or in the dispersed phase(toluene),the mass transfer rate was strongly affected by the viscosity change of continuous phase.Influence of temperature was studied by Saien and Daliri[82]in toluene/acetic acid/water system within a range of 15-40°C.Results showed that mass transfer rate was significantly enhanced by average 93.6%by elevating thermostat temperature.In addition,the influence of aqueous phase pH was also investigated by the same group[83].It was found that mass transfer was inhibited with increasing pH from 5 to 8,which may be attributed to the adsorption of the hydroxyl ions in the interface due to NaOH addition to increase pH.The reduction in mass transfer was more obvious for small drop size.

Internals are widely used as a simple method to intensify mass transfer.Concerning this factor,Azizi et al.[57]compared random and structured packings in spray and packed columns.Results demonstrated that the structured ones have a positive effect on mass transfer and improve mass transfer coefficient.Different sets of structure packing and their location heights in columns were studied in detail in their later study[62].However,Slater et al.[50]found in their studies that Raschig ring packings slowed down the drop velocity and consequently reduced the mass transfer coefficient.For ultrasonic wave intensification of liquid-liquid extraction,Saien and Daneshamoz[84]investigated the effect of ultrasonic waves on single drop mass transfer,where mass transfer could be improved by this method.

In real industrial process,liquid-liquid extraction is performed under the various influencing factors and operating conditions.It is necessary to explore the influences of these factors on mass transfer primarily in a single drop way.

3.2.Simulation studies

Strong coupling between momentum and mass transfer makes it difficult to simulate mass transfer behavior.Despite solving the continuity equation and Navier-Stokes equations,the mass balance equations must be coupled and solved at the same time[85-89].Due to mass transfer,the concentration exhibits a step change at the interface,since the interface is deforming,resulting a challenging task.Simulation method should ensure an accurate estimate of the interfacial movement as well as concentration change.An ideal case is to assume the droplets as rigid sphere with constant shape during mass transfer process[85,86,90-93](Fig.8).

Another difficulty concerns the Marangoni effect.Generally,Marangoni effects are highly non-linear and evolve during the mass transfer[63,94,95].Additional flow patterns are generated and result in complicated interactions between flow and concentration field.In this context,a link describing the influence of the solute concentration on the interfacial tension is necessary.In general,Marangoni effects are strongest in the drop formation stage due to high interfacial gradient.Later,when mass transfer begins,the Marangoni effect decreases and results in a reacceleration of droplet[94].

Despite the above difficulties,mass transfer simulation has been successful using various interface description methods,e.g.VOF[96]and level-set method[88,89,94,95,97,98]as described in Section 2.2.Part of or the whole lifetime of a droplet motion can be investigated,including drop formation[63,98],internal circulation[92],oscillating[94,95]and deformed[97,99]and then validated with the experimental results.

Several representative studies are listed in Table 6.Wegener[90]performed a detailed numerical parameter study of the physical properties on the temporal evolution of the Marangoni convection in freely single rising drops.Full three-dimensional simulations were achieved but restricted to a spherical drop.Furthermore,in the study of Engberg et al.[94],deformable and oscillating droplets with simultaneous interfacial phenomena were simulated rather than spherical particles.CFD code based on the level set method was implemented and showed good accordance with experimental measurements.To investigate the Marangoni effect in detail,Mao et al.[91]solved the coupled fluid flow and solute mass transfer equations in an axisymmetric boundaryfitted coordinate system at the same time.It was found that the Marangoni convection does not necessarily result in mass transfer enhancement but above a certain critical value.Proposed by Wegener[90]the Marangoni stress was implemented via the shear stress balance at the interface.Above all,simulation provides a powerful tool to quantitative and qualitative single drop mass transfer behavior.It is more accurate to track the position of the interface by various methods mentioned before and then solve the convection-diffusion equations in order to study mass transfer across the interface.Furthermore,it is necessary to develop fully three-dimensional simulations for Marangoni effects in order to investigate the effects on momentum and mass transfer.

4.Single Drop Breakage and Coalescence

Drop-size distribution(DSD)is a main influencing factor for liquidliquid extraction,which will determine the overall process efficiency and operating conditions.From a microscopic perspective,DSD is influenced by various parameters concerning drop swarm and interactions,like drop breakage and coalescence,which have not been fully understood yet.From a macroscopic aspect,in general,a constant DSD is expected when scaling up an extraction process.Most of the previous models rely on geometric similarity or constant power input,thus to overcome these problems.Investigators turn to the mechanism models.Population balance model(PBM)is one of the powerful tools to realize it.By using fundamental breakage and coalescence sub-models,which could be obtained from single drop experiment and solved numerically,PBM can provide DSD of the system.In this way,PBM connects both microscopic of single drop to the macroscopic behavior of drop swarms,which seems to be a“bottom-up”approach[101],as is shown in Fig.9.Factors influencing DSD are decoupled to sub-models,which could be studied by small scale single drop experiment individually.The sub-models then are integrated together to predict droplet swarm behaviors and are verified by lab-scale experiment.

4.1.Population balance model(PBM)

Population balance model(PBM)is a powerful modeling approach to predict time dependent DSD by considering negative(death)and positive(birth)source terms for drop breakage and coalescence,respectively.First proposed by Hulburt and Katz[103],the number density transport equation,often referred to as the population balance equation[104,105],can be written as:

Fig.8.Streamlines from simulation by level-set method[94].(a)Without Marangoni convection and(b)with Marangoni convection.(Reprinted from Chemical Engineering Science,117,R.F.Engberg,M.Wegener,E.Y.Kenig,114-124,Copyright(2019),with permission from Elsevier.)

where Sband Screpresent source terms for number density generated by coalescence and breakage,respectively.Sphis the source term caused by phase change.Furthermore,in the absence of phase change like evaporation or dissolution and considering the flow as uniform,the equation can be simplified to:

To close the problem,one of the key challenges associated with the formulation of predictive PBM is to develop reliable drop breakage and coalescence functions as source terms Sband Scin the model.

Table 6 Single drop mass transfer simulation study

In this case,details of droplet coalescence and breakage should be carefully studied.Over the past decades,a variety of models have been proposed for the breakage frequency Ω(Vi)and daughter size distribution β(Vi,V)function in the breakage model,coalescence frequency λ(Vi-V,V)and efficiency h(Vi-V,V)in the coalescence one.For liquid-liquid extraction,Valentas et al.[106]presented the first PBM applied to model drop breakage in 1966.Once the population balance equation has been set up and each source term has been determined separately,the equations can be solved by various methods,for example,method of moments,method of characteristics,Monte Carlo simulation,finite difference method and differential maximum entropy method.Detailed reviews on different solution approaches referred to[5,107-109].In terms of liquid-liquid system,population balance equations were solved for mixer-settler[110,111],rotating disc column[112-115],Kühni column[116,117],pulsed column[118]and so on.

4.2.Experimental studies

To study breakage and coalescence in lab-scale,experimental setup is more complex than single drop rising or mass transfer test cell.As seen in Fig.10,for drop breakage,in general,external energy was needed,such as stirring,pulsation,and rotation[119,120].For drop coalescence,it is considered more complicated than drop breakage since several steps such as collision,contact and deformation,film drainage and coalescence are involved.Experimental setups for coalescence can be distinguished into static drop contacts or dynamic drop collisions.In the static drop contact case,drops are produced and fixed on nozzles or lying on the top or next to each other where film drainage and liquid bridge can be observed in detail[121].However,during extraction process,drop coalescence is a dynamic behavior influenced by droplet movement.Thus,coalescence under dynamic conditions is of special interest.In general,one drop is free moving while the other one is fixed[122].In order to maintain the repeatability of the experiment,great effort should be done to precisely control the flow rate or keep extreme cleanness without any contamination.Several typical studies are summarized in Table 7.

Generally,parameters of sub-models concerning breakage and coalescence are determined by statistical measurements.In such experiments,a large number of droplets are recorded by a high-speed camera due to high spatial and temporal resolution,aiming to determine the breakage time,breakage probability,number of daughter drop fragments for breakage and coalescence time,and coalescence probability for coalescence.Based on this,parameters of submodels are fitted and then applied to PBM equations.Reviews of numerous breakage and coalescence sub-models are available in[7,104,105].In the following section,only pure system is involved.For system in the presence of contaminants,breakage and coalescence models can be found in[123].Several representative studies are listed in Table 7.

Fig.9.From single drop study to DSD prediction.(Adapted from[102].)

4.2.1.Breakage

Drop breakage can be induced by various factors,namely,the collision of drops with internals of turbulent eddies and shear forces within the continuous phase.Therefore,the process of breakage is dependent on the size of the drop,the physico-chemical properties of the liquids(i.e.density,viscosity,interfacial tension)as well as the local energy dissipation.In most cases,breakage mechanism can be expressed as a force balance between external stress from the continuous phase which intends to destroy the droplet,and the surface and viscous stress of the droplet to restore the change[104].When the disruptive stress becomes dominating,the droplet starts to stretch and deform,leading to formation of a neck that subsequently contracts,and finally forms two or more fragments.For single drop breakage study,some[124,125]suggest to determine the single drop breakage event as“entire breakup cascade”which is more meaningful,rather than only consider the“initial breakup”.But in most of the studies,a binary breakage event is usually assumed,which is a rough assessment of the physical truth(Fig.11).

Galinat et al.[126]performed single drop breakage experiment in turbulent pipe flow in a vertical column.Breakage probability,mean number of fragments and daughter drop distribution were obtained for identifying different breakage mechanisms.After the statistical analysis of single drop breakage,the sub-model was implemented in a simple global PBM to predict the DSD.A similar study[127]was carried out in another n-heptane-water-glycerin solution system.

Fig.10.Lab-scale test cells for single drop study.((a),(b)Test cell for breakage;(c),(d)test cell for coalescence.)

Table 7 Single drop breakage and coalescence experimental study

Breakage mostly occurs in a system with a stirrer for mixing.In this case,Maaß et al.investigated and modeled the breakage phenomena in a stirred tank.Improved models as daughter drop size distribution[128]and breakage time[129]were proposed,by taking the property influence of viscosity or interfacial tension into account,which result in better predictions.In the study of Solsvik and Jakobsen[130],single drop experiments were carried out in four oil-in-water systems.It was noticeable that the multiple breakage events were more frequently observed than binary breakage and breakage time was defined as finishing“entire breakup cascade”.Single drop breakage was also investigated in a rotor-stator mixer[131],the result revealed when,where and how the droplets break inside the mixer.It was suggested that turbulent vortices whose size was close to the mother droplet controlled the breakage process.More work should be done to understand how the different scales of turbulence influence the process better.

For extraction columns with mechanical agitators,study of single drop breakage has been shown in Karr columns[132],Kühni columns[119,133-135],pulsed disc and doughnut column,rotating disc contactor(RDC)columns[136]and so on.It was noteworthy to mention that in the study of Korb[119],a reactive extraction system ZnSO4/D2EHPA was selected for single drop breakage in a lab scale Kühni column.Several existing correlations and kernels for drop breakage probability and daughter DSD were validated.A new unified breakage correlation was proposed and would be further proved.

A relatively small test cell for single drop breakage was also designed for study[127,137].The cell consists of a rectangular channel with a fixed single blade representative for a section of a Rushton turbine.Breakage events occurred in the vicinity of the stirrer blade were recorded by high-speed imaging.In this case[137],the influence of droplet substance and diameter was determined.

4.2.2.Coalescence

Fig.11.Definition of single drop breakage event.

Coalescence is rather more complicated than breakage.On the one hand,the coalescence process can be divided into several stages and numerous influencing factors are involved.Additionally,as coalescence is inherently determined by interfacial properties,small amount of impurities as well as mass transfer can change the process dramatically.In general,coalescence process involves approach of drops,contact and deformation,film drainage and coalescence or repulsion[101].When the two interfaces of drops come near each other,a thin film of surrounding continuous phase has to drain between the interfaces.When a certain critical distance between the interfaces is reached,coalescence happens[102].However,the collision of drops may not result in coalescence necessarily,but may also end in repulsion.Plenty of factors affect this process due to coalescence being an interfacial phenomenon.Physico-chemical properties of the continuous and dispersed system(i.e.viscosity,density,ionic strength),especially the interface(i.e.mass transfer,surface active components)between them,as well as the environmental conditions(i.e.temperature,pressure,geometry,electrostatic field,microwaves,ultrasound)may have an impact on coalescence,as shown in Fig.12.As a consequence,it is a challenging task to perform the experiment precisely and repeatedly.

Influence of ions on single droplet coalescence was studied in[138-140].Dynamic coalescence process was analyzed systematically by Villwock et al.[140]with the standard test system of toluene/water.Influencing factors like salt concentration and drop size ratio on coalescence probability were investigated.The results showed that coalescence inhibition occurred due to high concentration of ions while no clear impact of drop size ratio was observed.Later,influence of ions on film drainage and coalescence time was analyzed by the same group[138].Ion concentration,ion species and equivalent drop size were varied in single drop coalescence experimental study.An increased equivalent drop diameter leads to higher coalescence probability in spite of an increase in the coalescence time.As a result,an empirical correlation was proposed to account for the influence of equivalent droplet diameter and ion concentration on the coalescence time.Kopriwa and Pfennig[139]provided an option to perform single drop coalescence in a sedimentation cell.In this way,the coalescence behavior of a system could be characterized by fitting a system-specific parameter to the sedimentation and the coalescence curves as well as the settling time of the system.Thus,the coalescence time of two drops could be calculated.

Influence of drop size and superimposed mass transfer on coalescence was evaluated in toluene/acetone/water test system by Kamp and Kraume[122].Results showed that the drop size ratio seems to be interfered by the different relative velocities of the drops.Significant influence of superimposed mass transfer on coalescence was observed,in which mass transfer from disperse to continuous phase led to coalescence while the opposite transfer directions retarded the coalescence almost completely.

4.3.Simulation studies

Numerical study can also be divided into two types.Similar to single drop rising,simulation can be done to investigate the detailed knowledge of breakage or coalescence by varying operating conditions.Apart from this,simulation can serve as an aid to single drop experiments to determine some important parameters such as turbulent kinetic energy and shear stresses,which are difficult to obtain from experiments.

Fig.12.Influencing factors on coalescence probability.(Adapted from[101].)

4.3.1.Fundamental simulation of breakage and coalescence regime

Usually,drop breakage and coalescence occur in an extreme short period of time,which presents challenges in determining the start and over time by means of experimental methods.However,computational fluid dynamics(CFD)can provide local spatial and time resolved information about the breakage and coalescence.It also shows reproducible results which make up the shortcomings of experimental studies.In some occasions,dynamic mesh in the vicinity of the interfaces should be refined[142]to fully describe the interface behavior.

Eiswirth et al.[143]considered a binary coalescence situation consisting of two rising toluene droplets with different diameters that coalesce in surrounding water.With the help of COMSOL software and level-set capturing method,it was found that the liquid bridge growing between the two drops during coalescence was of the inertial regime and the bridge radius grew in proportion to the square root of time.The simulation results were in good agreement with the experimental data.Gebauer et al.[142]performed CFD simulations with VOF method to study single drop coalescence interactions to further reveal the hydrodynamics and film drainage.The simulations were performed for the interaction of two differently sized droplets at industrial relevant impact velocities.An algorithm based on experimental studies was implemented to account for the contact time and the dimple formation.Also,by utilizing VOF method,a multi-scale simulation method was used to investigate the coalescence behavior of droplets undergoing a symmetric binary collision[144].A subgrid-scale model was involved to describe thin-film drainage due to the computational difficulty of capturing all length scales involved with a single discretization mesh.Combined by large eddy simulations(LES),VOF method was also implemented in simulating droplet breakage in order to reveal the mechanism of breakage in turbulent flows[145].Simulation results showed that the size of the turbulent vortices contributed to the breakage and more energy is needed to be transferred from the vortices at the final stage for breakage occur.

4.3.2.CFD aided single drop investigation

Despite of fundamental simulation for breakage and coalescence process,CFD can also provide more information of local turbulent kinetic energy,shear stress or other fluid parameters,which can serve as supplement to the previous single drop experimental study.

As in the study of droplet breakage in stirred tank by Maaß et al.[137],CFD was used to give the opportunity to control the local dissipation rate of turbulent kinetic energy in the breakage cell.Regions with highest energy dissipation rates and the velocity field were found to be the drop breakage location.Based on drop diameter and physical properties of the test systems,different breakage mechanisms can be derived.Drop breakage in a square-sectioned pulsed disc and doughnut column was investigated by Liu et al.[120].Three breakup patterns were observed and shear stress was the dominant factor in common.However,shear stress is hard to determined by experimental study,so that it is calculated based on the simulation.After that,breakage submodels were correlated with the shear stress and finally applied in a simplified PBM to predict DSD.Single droplet breakup in a rotorstator mixer was investigated by Ashar et al.[131].Turbulent inertial stress induced droplet breakup at different operating conditions was studied.CFD simulations were applied to predict the flow field and turbulent kinetic energy dissipation rate to explain the tendency of droplet breakup at different locations in the rotor-stator.

5.Outlook

Single droplet in liquid-liquid extraction system has been investigated in detail over the last decades.For about 50 years,efforts have been made to describe the behavior of single droplet and interfaces.Based on this fundamental knowledge,attempts have been tried to utilize basic sub-models to predict the behavior of extraction columns.For recent 10 years,with the development of computer science,simulations were set up with improving accuracy[7].Research method,experimental as well as simulation techniques are becoming more and more mature and systematical.On the basis of previous studies,several possible directions in the future are suggested.

5.1.Fundamental study for novel extraction system

In most of the tradition extraction techniques,volatile organic compounds(VOCs)including halogenated hydrocarbons,aliphatic and aromatic hydrocarbons,some esters,alcohols,ethers,aldehydes and ketones are the most commonly used organic solvents[146].However,as increasing attention is paid on environmental protection and sustainable development,application of these toxic and highly flammable organic solvents is restricted.In these cases,it is necessary to develop novel sustainable solvents which accord with“green chemistry”concept.Meanwhile,another alternative is to intensify the present extraction process as to promote extraction efficiency as well as reduce the organic solvent use.Previous studies of single drop is mainly in a common organic-water system,and fundamental analysis of a novel system are not much.

5.1.1.Reactive ionic liquid system

Room temperature ionic liquids are new emerging solvents which are salts with melting temperatures below 100°C and are composed of large amount of ions.They are generally called“designer solvents”because various cation/anion combinations enable them with tunable properties[147,148].As a salt,they have negligible volatility and high thermal stability and are non-flammable and usually of high viscosity[149],which seems to be a potential alternative.For extraction application,ion exchange process by ionic liquids allows extraction of specific anions,cations and even neutral compounds.Despite these advantages,ionic liquids now are relative novel solvents resulting in comparably high costs.Therefore,single drop experiments provide a convenient approach for ionic liquids with limited amount and low cost for design and scale-up.

Buchbender et al.[150]performed single drop sedimentation experiment with heptane(c)-toluene-[3-mebupy][DCA](d)to acquire parameters so as to fit sedimentation models.Involving drop breakage and influence of internals,models were simulated by“ReDrop”to obtain hydrodynamic parameters such as hold-up and Sauter mean diameter,which are in a good agreement with the experimental data.In the work of Badieh[151]ionic liquid 1-hexyl-3-methylimidazolium hexafluorophosphate(HMIMPF6)was chosen as a disperse phase to extract acetone from water.Although a relatively high viscosity with HMIMPF6,the single-drop experiments showed that the mass transfer was not as slow as expected.The Henschke model was applied to this novel system with good accuracy.

5.1.2.Aqueous two-phase system

The extraction of value-added compounds from natural sources exhibit great potential in the future,especially in biotechnology as separation of antibodies,proteins,antibiotics and natural plant ingredients[152].As these components are mostly heat-sensitive and easily deactivated by organic solvents,the aqueous two-phase system(ATPS)can be an alternative.The aqueous two-phase systems can be formed by two incompatible polymers or a polymer and a salt,detailed types of system can refer to[153].Generally,the aqueous two phase system is of high viscosity,low difference in density and low interfacial tension,which may result in low mass transfer rate[154].Several extraction trials have been performed in mixer-settler,spray column,perforated rotating disc contactor,pulsed cap column and so on[155].But it is still far from practical use due to lack of feasible predictive performance models and guidelines for design and scale-up.Thus,detailed investigations should be made from single drop study.

Sawant et al.[156]intended to isolate and purify BSA(Bovine Serum Albumin)by using two-phase aqueous system polyethylene glycol(PEG)and dextran in a spray column.Single drop experiment was used to measure overall mass transfer coefficient.Bhawsar et al.[157]investigated the extraction of α-amyloglucosidase in a sieve plate column.The aqueous two-phase system was formed by sodium sulfate-polyethylene glycol(PEG)-water and the solute was dissolved in PEG-rich phase.Hydrodynamic parameter like terminal velocity and mass transfer coefficient was determined by single drop experiment.Correlations were proposed for true mass transfer coefficients.Srinivas et al.[158]dealt with the extraction of horseradish peroxidase using a PEG/salt ATPS in a simple spray column.It was shown that mass transfer rate increased in the presence of NaCl,but the detailed mechanism required further study.Concerning drop formation,an attempt was made by Barhate et al.[159]to develop a model for drop formation in ATPSs.By using polyethylene glycol(PEG)/salt systems of different phase compositions at various flow rates,models were developed and compared with experimental results.In consideration of high viscosity with ATPS,Quaresima et al.[160]used PEG/salt system with protein albumin as mass transfer component from continuous phase to PEG-rich droplet phase.Single drop experiment results served as the basis of the models introduced to“ReDrop”.It was concluded that mass transfer was strongly influenced by the viscosity of both phases as well as the molecular size of the transferred component.

5.1.3.Nanofluid intensification of extraction

Nanofluids have attracted great attention as effective working fluids in heat and mass transfer enhancement.It is found that the addition of a small amount of nanoparticles exert considerable impact on the hydrodynamic and mass transfer performance of solvent extraction processes[161,162].Although it has a prosperous future in process intensification,limited attempts are made in liquid-liquid extraction.In terms of single drop studies,some of the fundamental works are summarized in Table 8.

In terms of hydrodynamic behavior,a reduction in terminal velocity with addition of nanoparticles was observed in most cases.Influencing factors as types of nanoparticle[163,164],size distribution[168],addition amount[163-169]and their addition in continuous or disperse phase[166]were systematically investigated.For mass transfer investigation,it is interesting to find that mass transfer rate increased as more nanoparticles were added.However,after reaching an optimum point,a decreasing variation was observed[163].It might be attributed to Brownian motion of nanoparticles and subsequent micro-convection or aggregation and clustering of nanoparticles[169](Fig.13).

Other factors as temperature[165]and in the presence of magnetic field[167]were taken into consideration.For the purpose of industrial use,a great deal of work remains to be done concerning simulation or downstream separation process for recycling the nanoparticles as well as solvent.

5.2.Detailed analysis of single drop interfacial behaviors

As mentioned above,interfacial behaviors like the Marangoni effect or contaminations make it much more complicated for liquid-liquid extraction system.Drop swarms with many interactions may not be the suitable test system,in this case,single drop system tends to be a more appropriate one to break down the complexity.For the Marangoni effect,as it is reviewed in preceding Section 3.1,it is a three-dimensional behavior coupling with mass transfer.On the one hand,in experimental studies,effort should be made in building up mechanism models to predict the onset and end point of the Marangoni effect and determining quantitative and qualitative influences made by it.Additionally,single droplet with variable interfacial tension and Marangoni effect should be further simulated in a 3D way to visualize the process[11].

Contamination is one of the crucial factors influencing the extraction equipment performance and their actual industrial utilization.It is because contaminations may slow down the terminal velocity,moderate mass transfer rate and hinder droplets from coalescence.Further work should be done in terms of quantifying these factors and predicting the extraction performance with higher accuracy.

5.3.Coupled CFD-PBM simulation

Starting from single drop extraction concept and combining with population balance models,a bottom-up method can provide a guideline for industry,as it eliminates pilot plant trials and saves both money and effort.Up to now,several studies have realized this approach.Kamp and Kraume[102]designed a scale-up study considering the influence of collision velocity and drop size on coalescence probability.Parameters of coalescence efficiency can be obtained from single drop experiments.Based on the derived parameters,it is possible to utilize PBM equations to predict the DSD in dispersions.In this case,a sound scale-up is possible by population balance equation simulations.A simulation tool called“ReDrop”was designed by Pfennig et al.[170]for the design of extraction columns based on single-drop experiments.Input data containing the properties of the system,operating conditions,and the geometry of the internal were loaded into the program together with the system-specific parameters of the models from single drop experiments.Simulation was carried out by the Monte-Carlo method until steady-state conditions were reached.Extraction performances,fluid dynamic behavior,and flooding limits could be predicted.To solve the population balance equations,an algorithm was developed and implemented via a computer program called liquid-liquid extraction column module(LLECMOD)for hydrodynamics simulation of liquid-liquid extraction columns by Bart et al.[171,172].Sub-models in the population balance equations were determined by single drop experiments.The simulation process showed a flexible way that allows the user to define the breakage and coalescence frequencies,droplet terminal velocity,and the other internal geometrical details of the column.More recently,Attarakih et al.[173,174]presented a new population balance based module so called“PPBLab”for modeling the hydrodynamics and mass transfer processes.Different types of extraction columns like Kühni column[173]as well as pulsed packed bed column[174]were simulated and tested.In the future,it is a tendency to link PBM with CFD for high precision engineering and a direct modeling of industrial scale extraction equipment design[175].With this coupled method,detailed information about the flow fields,turbulent energy dissipation and their influences on drop breakage,coalescenceand mass transfer could be determined.Attempts have been made in CFD-PBE simulations[111,118,176],and models utilized in PBM are either embedded in commercial software or from literature.Considering the differences in test systems,models based on single drop experiment will provide more solid and reasonable predictions for extraction performance.

Table 8 Single drop with addition of nanoparticles experimental studies

Fig.13.Addition of nanoparticles.

6.Conclusions

To simplify the complexity of the liquid-liquid extraction separation process,single drop is considered to be an investigation object in order to reduce time and efforts.Single drop rising and falling are the most basic phenomena influenced by physical properties of the binary system.The terminal velocities of single drop with various diameters are obtained experimentally and numerically.Then the correlations and models are compared to the derived results.As the most crucial part of liquid-liquid extraction,mass transfer studies in single drops are interesting.In general,the influence of mass transfer direction,solute concentration and system properties is investigated.In addition,the induced Marangoni convection will cause a significant effect on mass transfer,which could not be neglected.

For drop-drop interactions,breakage and coalescence are considered as two fundamental factors for they will affect mass transfer area consequently.These two processes are more complicated due to high time and spatial resolution.In this case,a high speed camera is commonly used to visualize the interactions.Simulation is also used as an assistant tool to reveal the whole process.

In conclusion,single drop investigations have become a trend to study the complex process of liquid-liquid extraction.Future studies could be carried out such as,the mass transfer with Marangoni convection,ion influence on breakage and coalescence,and quantifying the contaminant effect.More novel systems should be investigated to broaden the study on standard system.Based on the single drop experimental and numerical study,the scale-up design of extraction unit will be more efficient and accurate in the future.

Nomenclature

ATPS Aqueous two-phase system

BnCoefficients in series expansion

BSA Bovine Serum Albumin

CDDrag coefficient

CSF Continuum surface force

DLMolecular diffusivity of solute in dispersed phase,cm2·s-1

DSD Drop size distribution

d Diameter of droplet,m

GFM Ghost fluid method

h Collision frequency,m3·s-1

kdObserved dispersed phase mass transfer coefficient

LES Large eddy simulation

NPe′Modified Peclet group

n Droplet number density

PEG Polyethylene glycol

Re Reynolds number

SbSource terms caused by droplet breakage

ScSource terms caused by droplet coalescence

SphSource terms caused by phase change

t Time,s

ViDroplet volume,m3

VOF Volume of fraction

β Daughter droplet size distribution

λ Coalescence efficiency,s-1

μ∗Viscosity ratio

Ω Breakage frequency,s-1