Transient rise velocity and mass transfer of a single drop with interfacial instabilities—Numerical investigations

Full 3D-simulations of transient interfacial mass transfer accompanied by Marangoni convection at a single spherical droplet in a quiescent liquid were performed in a moving reference coordinate system. The flow and concentration field are solved simultaneously, coupled via the additional Marangoni stress generated by concentration gradients at the interface. Fluid dynamics and mass transfer are investigated in the Marangoni convection dominated toluene/acetone/water system. The numerical results are qualitatively and quantitatively compared with own experimental results. The simulation results reveal that mass transfer is always enhanced—compared to calculations where no Marangoni convection appears—independently from the initial solute concentration. The enhancement factor of mass transfer ranges between 2 and 3.     

Investigation of the mass transfer across the interface of two concurrent laminal flowing liquids in a horizontal cylindrical channel—I Experimental results

The concentrations of the solute (pyridine) were measured by means of modified liquid scintillation techniques to within 0.66,μm of the interface as well as in the bulk of the organic (toluene) phase during the solute transfer from the toluene to the water phase at different temperatures, flow rates and solute concentrations. These measurements allow the comparison of the mass transfer resistance of the diffusive transfers with the interfacial resistance. In extremely pure systems the interfacial resistance is negligible in comparison with the resistances of the diffusive transfers. In the presence of surface active agents the interfacial resistance strongly increases and exceeds those of the diffusive transfers. The solute transfer from the water to the toluene phase because of the Marangoni instabilities could only be considered qualitatively.The concentrations of the solute (pyridine) to within 0.66 μm of the interface and in the bulk of the organic phase (toluene) during the solute transfer from the organic to water phase in a horizontal cylindrical flow channel with concurrent flow of the phases at different temperatures, flow rates and solute concentrations were measured by means of a modified liquid scintillation technique. These measurements allow the comparison of the mass transfer resistances of the diffusive transfers to and from the interface with the interfacial resistance. In extremely pure systems, the solute concentration at the interface quickly drops to very low values with increasing distance from the channel entrance, which indicates that the mass transfer resistance of the interface is negligible in comparison with the resistances of the diffusive transfers in the laminar flow region. In the presence of surface active agents (LPC) the solute concentration to within 0.66 μm of the interface dramatically increases and exceeds the solute concentration in the bulk of the toluene phase. This indicates a strong increase of the mass transfer interfacial resistance. The high solute concentration at the interface, exceeding its bulk concentration, is caused by the enrichment of the solute in the interface, which was measured by the interfacial tension depression in the presence of the solute. Because the solute transfer from the water to the toluene phase causes interfacial (Marangoni) instabilities, which increase the geometrical interfacial area due to uncontrolled eruptions and formations of microemulsions, the solute concentration could not be measured to within 0.66 μm of the interface in the toluene phase during the water to toluene solute transfer. Only qualitative statements could be made with regard to the area of the interface. Further measurements are necessary in order to determine quantitative relationships with regard to the mass transfer interfacial resistance as a function of different process parameters     

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.     

Effect of mass transfer on drop size in a Karr column

This paper presents experimental data on drop size distribution and Sauter mean drop diameter in a 7.6 cm diameter reciprocating plate extraction column with and without mass transfer, using the liquid system toluene—acetone—water.The measured drop size distribution curves show that most of the break-up of the dispersed drops was achieved by the first few plates. The agitation rate was found to be the predominant factor in determining the mean drop diameter and the total interfacial mass transfer area.During mass transfer both the drop size distribution and the mean drop diameter were found to depend on the mass transfer direction.The measurements of the mean drop diameter in the absence of mass transfer were compared with published data and new correlations presented.     

Flow characteristics of large oscillating drops in liquid-liquid systems

A study was made of the flow characteristics of large oscillating drops of pure liquid-liquid systems, using a thermostatically-controlled, rising drop column, 50 mm in diameter and 1000 mm in length. Mirrors in the jacket enabled front and side views of drops to be photographed simultaneously. Single drops in the size range 5–10 mm were investigated with both mutually-saturated phases and when the solute was being transferred from the dispersed phase. The systems studied were (1) toluene and acetone (dispersed)-water (continuous), and (2) n-heptane and acetone (dispersed)-water (continuous). Acetone concentrations were varied up to 3.75 kmol/m³. The oscillations of a travelling drop were asymmetrical; therefore, the amplitude cannot be expressed accurately in terms of only two axes. The area change of the drop compared to that of a sphere of equal volume ‘ε’, was shown to represent the amplitude accurately. The periods of droplet oscillation were uniform for the mutually saturated systems of constant physical and flow properties but changed when mass transfer was taking place. The interfacial tension exerted a marked effect on the amplitude, which also depended upon the oscillation frequency. The amplitude changed with droplet size in a similar manner to the terminal velocity, i.e. it increased with increasing size until it reached a maximum, subsequently decreasing less rapidly. The drag coefficient increased with increasing rate of mass transfer from the drop. Correlation of the results and the area eccentricity ‘ε’ by dimensional analysis embracing all possible parameters and physical properties affecting drop oscillation, resulted in the correlation ε = 0.22 Sr^0.42 We^?0.53 M^0.13 with a mean deviation of ± 14%. This will facilitate more accurate prediction of the interfacial area for mass transfer calculations, relating to equipment containing droplets in the oscillating regime.     

Experimental investigation of Marangoni effect in 1-hexanol/water system

In this work, the interfacial phenomena of a single hanging drop have been observed and captured by a Schlieren optical system. The extraction fractions at different hanging times were determined. For the system without surfactant, the Marangoni effect induced by interphase mass transfer of a solute displays regular convection patterns. The addition of surfactants changed the mode of interfacial instability significantly but in different ways: SDS enhanced the mass transfer and Triton X-100 reduced the extraction fraction.     

Simulation of Marangoni convection effects on the hydrodynamics of liquid–liquid extraction drops

Concentration induced Marangoni convection (MC) effect has many applications in the chemical engineering processes. In this study, the MC effects have been investigated in the toluene/acetone/water (T/A/W) liquid–liquid extraction system, focusing on the mass transfer and hydrodynamics. For the first time, the VOF-CSS model has been used, and the mass transfer equation has been coupled with the hydrodynamic equations of the VOF model, using the surface tension force model of the CSS. A single mass transfer equation has been solved for the two phases, modifying the unsteady, convective, and diffusive terms based on the equilibrium distribution coefficient. The MC effect has been implemented in the CSS surface tension model with a concentration-dependent surface tension coefficient. Simulations have been carried out in 1, 1.5, and 2?mm drops in the wide range of concentration (0.9–30?g/L). Good agreements have been achieved for the concentration and reduced velocity values compared with the existing experimental data. Simulation results showed that the reduced velocity values remain almost constant for every drop diameter, in the initial concentration range from 3.7 to 30?g/L. The reacceleration time for the three drop sizes with the different initial concentrations has been obtained from the simulation results and compared. The MC effects on the axial velocity profiles and drag coefficients were also reported providing comprehensive information about the MC effects on the hydrodynamics.     

Terminal and transient drop rise velocity of single toluene droplets in water

The knowledge of the drop rise velocity in dispersed systems is of fundamental importance. Especially, the residence time is needed for calculation of mass transfer rates in extraction columns. This work deals with fluid dynamic measurements of toluene droplets rising in water ranging from 1.0 to 7.0 mm, with the premise of high purity of the used chemicals. The toluene/water‐system is widely used as a test system with high interfacial tension. A semiempirical correlation for pure systems to predict the terminal velocity of single rising/falling droplets based on experimental data is presented. Results show that a distinction between maximum and characteristic mean values of the drop rise velocity is necessary, especially in the diameter range 2.4–3.0 mm where unexpected velocity fluctuations occur. Two distinct terminal rise velocities were observed for 3 mm droplets. Furthermore, comparisons of the Weber‐Reynolds‐correlation and the drag coefficient with correlations from literature show good agreement. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Experimental investigation and numerical simulation of Marangoni effect induced by mass transfer during drop formation

Marangoni effect induced by interphase mass transfer plays an important role in liquid–liquid extraction and reaction processes. The interaction of Marangoni effect and interphase mass transfer during drop formation at different injection rates and different initial solute concentrations was investigated by experimental and numerical simulation. The extraction fraction was measured and the corresponding correlation was proposed. The level‐set method coupled with mass‐transfer equation is for the first time used to simulate the mass‐transfer induced Marangoni effect during drop formation. The simulated drop volume, shape, and extraction fraction are in good accordance with experimental data. Through the numerical simulation, it is found that the mass transfer in the first mass‐transfer period is the most efficient during drop formation when Marangoni convection occurs. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4424–4439, 2013     

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.     

Surface-tension-induced interfacial convection and its effect on rates of mass transfer

Surface-tension-induced interfacial convection (Marangoni phenomena) can appear as a result of mass and heat transfer, compression and dilatation of surface films or their non-Newtonian behaviour and owing to presence in the interface of electrostatic charges. In process engineering problems the mass transfer effect is usually predominant and, depending on the geometry of the system, leads to surface renewal or changes in interfacial area. The surface renewal phenomena can appear as instabilities or disturbances and their effect on mass transfer is presented for transfer to and from drops as well as across flat interfaces in stirred and laminar flow contactors. Mass transfer coefficients and drag coefficients of drops are compared under conditions of undisturbed (diffusional) transfer, cellular convection and interfacial turbulence for stable and unstable direction of transfer. The importance of gravitational instability is indicated.     

Numerical simulation of the Marangoni effect on transient mass transfer from single moving deformable drops

A level set approach was adopted in numerical simulation of interphase mass transfer from a deformable drop moving in a continuous immiscible liquid, and the simulation results on Marangoni effect were presented with respect to three experimental runs in the methyl isobutyl ketone–acetic acid–water system. Experiments showed that when the solute concentration was sufficiently high, the Marangoni effect would occur with the interphase mass transfer enhanced. Numerical results indicated that the mass‐transfer coefficient with Marangoni effect was larger than that without Marangoni effect and stronger Marangoni effect made the drop deform more easily. The predictions were qualitatively in accord with the experimental data. Numerical simulation revealed well the transient flow structure of Marangoni effect. © 2011 American Institute of Chemical Engineers AIChE J, 2011     

竖直流动皂膜中解吸导致的Marangoni对流观察

In gas-liquid mass transfer processes,Marangoni convection may occur due to the surface tension gradient produced by mass transfer near the interface.With a falling soap film tunnel and the Schlieren optical method,the Marangoni convection patterns along the film surface were observed directly in the desorption process of acetone from the falling soap film.The Schlieren images showed the regular roll convection in the thin falling soap film during the acetone desorption.The hydraulic characteristics were determined experimentally by measuring the variation of acetone concentration in the film and the surface tension of the soap liquid.The results show that the acetone concentration gradient vertical to the falling direction is very small because the thickness of the soap film is in the order of 10^-6 m.The variation of acetone concentration along the falling film is large,so there is a significant surface tension gradient,resulting in the Marangoni roll convection.The experimental results and a qualitative analysis may be helpful to understand the mechanism of Marangoni convection near the interface in the mass transfer.     

伴有Marangoni效应的传质动力学

结合Marangoni对流的流体动力学条件，通过建立的半经验模型研究了伴有Marangoni效应的传质动力学，阐述了Marangoni效应增强传质的机理，得到了传质Sherwood数与Marangoni数之间的连续指数关联，从而得以解释不同实验过程中得到的不同Sherwood数与Marangoni数之间的关系.研究表明，由Marangoni效应而增强的传质系数与界面Marangoni湍动的表现形式有关.     

Effect of system properties on the performance of Liquid—Liquid extraction columns—II: Oldshue—Rushton column

Mean drop size, fractional hold-up of dispersed phase and axial mixing characteristics have been determined in a 72 mm diameter mechanically agitated extraction column of Oldshue—Rushton type, using the two liquid—liquid mass transfer systems, toluene—acetone—water and MIBK-acetic acid—water. As for normal conditions of packed column operation described in Part I, solute presence and the direction of mass transfer has a significant effect on mean drop size, fractional hold-up and to a lesser extent, axial mixing in the dispersed phase. Probably the most dramatic effect however is the manner in which solute transfer affects dispersed phase behaviour. Highly coalescing conditions with transfer from the dispersed to the continuous phase can make the column practically unoperable. As for the packed column, axial mixing in the continuous phase is unaffected except in so far as solute presence and direction of mass transfer affect the hold-up of dispersed phase.     

Visualization of Mass Transfer during Droplet Formation

The impact of mass transfer in liquid‐liquid extraction during droplet formation in a quiescent continuous phase was investigated. The impact of droplet size, concentration, and formation rate on a hanging droplet was analyzed via laser induced fluorescence (LIF) using rhodamine 6G as tracer in the system of toluene and acetone in water. The droplet formation rate has a major impact on mass transfer and the mixing pattern inside the droplet. Very fast mass transfer induced by Marangoni convection was visualized at a high local resolution independently of concentration and formation rate.     

单滴内的传质Ⅰ

本文应用Colburn-Welsh方法研究了正丁醇和异丁醇向下降的环流水滴的传质速率。实验结果经校正端效应后,曾与Kronig-Brink理论值以及Johnson和Heertjes等的数据作了比较。 实验结果表明,Kronig-Brink模型仅可适用于Re<50或60的情况,而在Re>80完全不能适用。实验结果和Johnson的单滴数据甚为符合,但较Heertjes的喷洒塔数据为高。异丁醇-水系的数据一般较正丁醇-水系的略高,但从光纹技术观察,两个系统都无可察见的介面骚动现象。     

Local analysis of Marangoni effects during and after droplet formation

The influence on the mass transfer in liquid-liquid extraction was investigated during droplet formation in a quiescent aqueous continuous phase for the two transition components, acetone and acetonitrile, in toluene. Both transition components have similar characteristics. However, an approximately eight times slower mass transfer of a droplet hanging on a capillary in relation to a rising droplet could be observed. The droplet formation time and the initial solute concentration are decisive for the mass transfer behaviour. A lower volumetric flow leads to slower droplet formation and a higher specific mass transfer area enhancing mass transfer, which is visualized via laser induced fluorescence (LIF). Additionally, as expected, higher initial solute concentrations promote Marangoni turbulences and thus mass transfer, which is measured via confocal Raman spectroscopy inside a fixed hanging droplet.     

界面湍动对气液传质的影响

气液传质过程中经常伴有界面湍动。界面湍动由传质的不均匀性引起,反过来又极大地促进传质。介绍了界面湍动的产生机理和形成条件,对4种不同Ra和Ma准数的情况分别进行了分析。讨论了界面湍动强度对气液传质系数的影响关系。传质系数与Man成正比,其中n随着Marangoni对流胞类型的不同而在1/3和1之间变化。在气液系统中,液相与气相阻力比越大,由界面湍动引起的传质的增强效应越显著。     

Simulation of interfacial Marangoni convection in gas-liquid mass transfer by lattice Boltzmann method

Interfacial Marangoni convection has significant effect on gas-liquid and/or liquid-liquid mass transfer processes. In this paper, an approach based on lattice Boltzmann method is established and two perturbation models, fixed perturbation model and self-renewable interface model, are proposed for the simulation of interfacial Marangoni convection in gas-liquid mass transfer process. The simulation results show that the concentration contours are well consistent with the typical roll cell convection patterns obtained experimentally in previous studies.