Measurement and Correlation of the Mass-Transfer ... - ACS Publications

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Measurement and Correlation of the Mass-Transfer Coefficient for the Methyl Isobutyl Ketone−Water−Phenol System Yongli Sun,†,‡ Qiudi Zhao,† Luhong Zhang,*,† and Bin Jiang†,‡ †

School of Chemical Engineering and Technology and ‡National Engineering Research Center for Distillation Technology, Tianjin University, Tianjin 300072, P. R. China S Supporting Information *

ABSTRACT: To determine the mass-transfer behavior in the extraction of phenol from water with methyl isobutyl ketone, single-droplet experiments were performed to measure mass-transfer coefficients under various conditions. For this purpose, the droplet diameter, the initial concentration of phenol in the aqueous phase, the temperature, and the pH of the aqueous phase were investigated. For the aim of modeling, the molecular diffusivity was multiplied by an empirical factor (R). Then, the molecular diffusivity (Dd) was replaced by the enhanced molecular diffusivity (RDd) in the Kronig−Brink equation. Finally, the modified correlation of the mass-transfer coefficient model was found to fit well all of the experimental data under all experimental conditions.

1. INTRODUCTION Phenolic effluents represent one of the most common pollutants from various types of industries and process operations, including chemical (polymeric resin, bisphenol A, alkyl phenols, caprolactams, adipic acid, etc.), petrochemical (oil refining), metallurgical (smelting, iron, steel, and coke), pharmaceutical, textile, plastic, explosive, coffee, ceramic, paint and varnish, pesticide production, and electrolytic strip tincoating plants.1 Phenol is a toxic organic compound listed as a priority pollutant by the U.S. Environmental Protection Agency (EPA).2 It affects the liver, kidneys, lungs, and vascular system. The ingestion of 1 g of phenol is deadly for humans. Therefore, finding a technique to remove phenol from wastewater is particularly crucial. Techniques for the treatment of phenolic effluents can be divided into destruction and recovery methods. Destruction methods include biological oxidation,3 incineration, ozonization in the presence of UV radiation, oxidation with wet air, and electrochemical oxidation. Among recovery methods are solvent extraction, distillation, membrane separation,4 and adsorption.5 Liquid−liquid extraction is economically feasible compared to other techniques, especially when the phenolic effluent is highly concentrated. The design of a sieve-plate extraction tower is mainly based on an analysis of the mass-transfer process in extraction and the established corresponding mathematical model. Therefore, studies on laboratory-scale apparatuses are unavoidable. Extraction methods mainly include physical extraction and complexation extraction. Benzene, tricresyl phosphate, and butyl acetate have been used as solvents for extraction, but at present, the most common physical solvent is methyl isobutyl ketone (MIBK). MIBK is favored because it has the highest equilibrium distribution coefficient6 for phenol among known physical solvents and it can be recovered from the raffinate by distillation. © 2014 American Chemical Society

At present, most studies of the MIBK−phenol−water system focus on liquid−liquid equilibrium data.7 The mass-transfer processes of this system have not yet been investigated. In this work, single-droplet experiments were used to investigate the mass-transfer processes of the MIBK−phenol− water system. The control step of the mass-transfer process was analyzed. Then, the extraction process conditions such as temperature, aqueous-phase pH, and initial aqueous-phase concentration of phenol were studied. The experiments measured the mass-transfer coefficients and correlated the experimental mass-transfer coefficients with the modified Kronig−Brink model. Then, a mass-transfer model of MIBK−phenol−water system was established for a sieve-plate extraction column.

2. EXPERIMENTAL SECTION 2.1. Materials and Physical Properties. The MIBK− phenol−water chemical system was chosen for study. One of the important properties of this system is its relatively low interfacial tension (8 mN·m−1). The purities of the methyl isobutyl ketone and phenol used in this work exceeded 99.9%, and high-purity water was used throughout. The densities of the phases were measured using a self-adjustable temperature density meter (Mettler Toledo DE40) with an accuracy of ±10−4 g/cm3. Viscosities were measured using a rotational viscometer (Brookfield DV-II+) with an uncertainty of ±1 × 10−2 mPa·s. The physical properties of the aqueous phase are listed in Table 1, and the properties of the organic phase are listed in Table 2. The influence of pH variations on the density and viscosity of the aqueous phase was found to be negligible. 2.2. Setup. A jacketed Pyrex column (30-mm diameter and 1000-mm height) was used as the contactor (Figure 1). The Received: Revised: Accepted: Published: 3654

October 31, 2013 February 12, 2014 February 12, 2014 February 12, 2014 dx.doi.org/10.1021/ie4036862 | Ind. Eng. Chem. Res. 2014, 53, 3654−3661

Industrial & Engineering Chemistry Research

Article

Table 1. Densities and Viscosities of the Aqueous Phase for Different Solute Concentrations at Different Temperatures CC6H5OH (mg·L−1) 1000 2000 4000 6000 8000 1000 2000 4000 6000 8000 1000 2000 4000 6000 8000 1000 2000 4000 6000 8000 1000 2000 4000 6000 8000

aqueous-phase density (kg·m−3) Temperature 997.5 998.9 999.2 999.3 999.4 Temperature 994.7 995.7 996.0 996.8 997.0 Temperature 991.2 991.5 992.1 993.8 993.9 Temperature 985.7 986.0 988.3 990.0 990.1 Temperature 978.3 979.2 982.8 983.4 984.7

aqueous-phase viscosity (mPa·s)

= 15 °C 1.01 1.03 1.06 1.09 1.13 = 25 °C 1.00 1.02 1.05 1.07 1.10 = 35 °C 0.97 0.98 1.00 1.02 1.04 = 45 °C 0.88 0.89 0.92 0.95 0.99 = 55 °C 0.79 0.85 0.86 0.87 0.91

Table 2. Density and Viscosity of the Organic Phase at Different Temperatures temperature (°C)

organic-phase density (kg·m−3)

organic-phase viscosity (mPa·s)

15 25 35 45 55

805.6 796.3 787.0 777.8 768.4

0.66 0.57 0.50 0.44 0.39

inner diameter was large enough to avoid any influence of the wall on the fluid motion for all droplet diameters in this study. A variety of stainless steel nozzles were used to generate droplets of different sizes at different heights in this column. The aqueous phase was held in a syringe conducted by a precision syringe pump (Harvard Pump 11 Plus, Harvard Apparatus, Holliston, MA) and flowed through a Teflon tube to the stainless nozzle. The column containing the organic phase and conducting tubes were thermostatted to reach the desired temperature by a calibrated thermostat (DC-0506, China) with an uncertainty of ±0.05 °C. The pH of the aqueous phase was adjusted to 5.0, 6.0, 7.0, 8.0, and 9.0 using saturated NaOH solution and dilute H2SO4 solution. The measurement of pH values was performed with a pH meter (PHS-25, China) with an uncertainty of ±0.01. The conical-shaped bottom of the column was used to sample the dispersed drop phase so as to reach the minimum drop coalescence interface to minimize additional mass transfer at the coalescence interface. Thus, the terminal effect of mass transfer at the drop-phase collector was brought under better

control. Three samples were collected for each condition and kept in closed sample tubes. Then, the samples were analyzed by high-performance liquid chromatography (HPLC). 2.3. Procedure and Analysis. Before each run, the organic and aqueous phases were mutually saturated to avoid additional mass transfer. The column was first filled with organic phase as the continuous phase. Then, the syringe and the connection tube to the nozzle tip were filled with aqueous phase to produce drops. After release, each drop fell through the continuous phase to the bottom of the column. The syringe pump was initially calibrated with respect to the specified volume scale on the calibrated syringe. From the flow rate and the time of generation of 40 drops measured with a stopwatch (±0.01 s), the drop volume was easily calculated. Then, the drop diameter was calculated using the drop volume. The contact time of the drops from the initial point to the collection point was measured several times with a stopwatch, and its average was considered. The terminal velocity of the droplets was obtained with respect to the average time. Droplets were spaced typically more than 60 mm apart, a 3655

dx.doi.org/10.1021/ie4036862 | Ind. Eng. Chem. Res. 2014, 53, 3654−3661


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3. RESULTS AND DISCUSSION 3.1. Hydrodynamic Investigations. The size of the droplets used in this work ranged from 2.496 to 3.282 mm. The range of the Reynolds numbers10 (Re = ρcutd/μc) was between 304 and 840. The values of the dimensionless group Eö11 (Eö = gΔρde2/γ) were in the range of 1.34−3.76. The range of drop Weber numbers12 (We = dut2ρc/γ) was 2.31 < We < 9.73 . From these data, one can conclude that the flow pattern of the drops used in this work was between transition flow and turbulence flow. Furthermore, most of the experimental droplets were in the oscillating regime (see Figure 2). The oscillations should play

Figure 1. Experimental setup: 1, precision pump; 2, thermometer; 3, sedimenting drop; 4, extraction column; 5, distance marking; 6, Teflon needle valve; 7, thermostat.

distance for which Skelland and Vasti8 showed that interactions are negligible. In the experiments, four different heights of 400, 550, 750, and 950 mm were used to change the contact time between the drops and the continuous phase. The concentration of phenols in the aqueous phase was measured by HPLC (Agilent Technologies, Palo Alto, CA) using a 4.6 × 150 mm × 5 μm Mp-C18 capillary column. All equipment and glassware were cleaned with distilled water, absolute ethyl alcohol, and absolute ether and finally blown dry with air prior to experiments. 2.4. Overall Dispersed-Phase Mass-Transfer Coefficient. The overall process of mass transfer can be divided into three stages: (a) drop formation and subsequent accelerating motion after release from the nozzle, (b) steady buoyancydriven motion of drops at a constant terminal velocity, and (c) coalescence of drops at the drop collector.9 It is generally believed that the interference of terminal coalescence and drop formation can be eliminated by repeating mass-transfer experiments with drops freely falling for different distances. R is the mass-transfer rate as per unit time through unit cross-sectional area of the component quantity. The masstransfer driving force is the component concentration difference. Therefore, the mass-transfer rate expressed in terms of the dispersed-phase concentration is given by R=

Vd dCd(t ) A dt

= Kod[Cd(t ) − Cd*]

Figure 2. Experimental droplet diameter compared with the critical diameter.

an additional effect on the mass-transfer rate. The critical diameter (dcr) that determines when drop oscillations begin can be predicted by the Klee and Treybal correlation13 dcr = 0.33ρc−0.14 Δρ−0.43 μc 0.3 γ 0.24

Drop oscillations are expected when the drop size is larger than the critical diameter. When the drops tend to oscillate, they undergo symmetric periodic changes from an oblate ellipsoid to a prolate ellipsoid and back.14 The alternating creation and destruction of interfacial area occurs with oscillatory movements, producing interfacial turbulence. In this work, large drops tended to fall in an erratic helical path. Such wobbling drops had a damped oscillation because of their sliding sidewise movement, which also damped the internal circulation within the drops. 3.2. Effect of Drop Diameter on Mass Transfer. As Figure 3 shows for experiments carried out at T = 15 °C, the mass-transfer coefficient increased with the drop size. The droplet diameter changed from 2.511 to 3.167 mm, and the Kod values were within the range 33.98−91.85 μm/s. When the droplet diameter increased for large-size nozzles, the Reynolds number increased to the range of 342−518, and the Weber number ranged from 2.86 to 5.02. Very small drops at low Reynolds number were rigid spheres with no circulation. In this region, mass transfer depends on molecular diffusion, which is very slow. As the drop diameter increased, the droplets started to deform to symmetry-axis oblate ellipsoids, and the droplets tended to exhibit internal rolling cells. As the drop diameter increased further, the Reynolds numbers increased, and the

(1)

Then, the time-average overall mass-transfer coefficient can be determined experimentally using the equation d ln[Cd(t ) − Cd*] =

AKod 6Kod dt = dt Vd d

(3)

(2)

where Cd(t) and C*d are the initial and equilibrium solute concentrations, respectively, in the dispersed phase. Because the concentration in the continuous phase is zero, Cd* is zero for this case. The mass-transfer coefficient was obtained from the slope of a plot of −ln[Cd(t)] versus t using eq 2. The squares of linearly dependent coefficients (R2) were all above 0.95. 3656



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Figure 3. Variation of overall mass-transfer coefficient with drop size at different initial solute concentrations.

Figure 5. Variation of overall mass-transfer coefficient with initial solute concentration for different nozzles.

ranged from 30.53 to 95.33 μm/s as the initial concentration changed. This was primarily due to a concentration gradient, which caused interfacial turbulence. One possible cause of the instability is the Marangoni effect. When droplets of one phase are dispersed in a continuous ambient phase, a solute is transferred from the droplets into the continuous phase of lower viscosity. If the interfacial tension is sensitive enough to the solute concentration, which varies over the droplet surface, the Marangoni effect will appear.16 From Figure 6, one can see

internal circulation patterns became more complex, with the formation of ring vortices behind each drop that move along with it. Normal droplet oscillation occurred that did not cause the breakup of droplets. The movements of the droplets changed from approximately linear motion to tortuous zigzag trajectories, which reduced the mass-transfer resistance within the droplets. On the other hand, the larger the droplets, the greater the mass-transfer area, which is beneficial to mass transfer. The surface-stretch model postulates that all elements on the surface remain on the surface during an oscillation cycle; surface extension occurs due to stretching and thinning of the surface as the area increases.15 3.3. Effect of Initial Aqueous-Phase Concentration of Phenol on Mass Transfer. The influence of the initial solute concentration on the drop diameter is shown in Figure 4. The higher the initial solute concentration, the larger the drop diameter. The drops ranged from 2.496 to 3.282 mm with different initial concentrations in the aqueous phase. As Figure 5 shows, the mass-transfer coefficient increased with the initial solute concentration. The obtained mass-transfer coefficients

Figure 6. Variation of interfacial tension with the solute concentration in the aqueous phase.

that the interfacial tension changed with the solute concentration in the MIBK−phenol−water system and the transfer direction was from the droplet to the continuous phase of lower viscosity. Therefore, the Marangoni effect likely occurs in this system. Another possible source of interfacial turbulence is the Rayleigh instability caused by density differences arising from concentration differences. The emergence of the Rayleigh− Marangoni phenomenon in a mass-transfer process promotes liquid surface renewal and strengthens the infiltration of the solute into the continuous phase. The higher the initial solute concentration, the stronger the Marangoni instabilities.17 Thus, high initial concentrations provide enhanced mass-transfer rates.

Figure 4. Variation of drop size with initial solute concentration for different nozzles. 3657



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of the solvent.18 In addition, the solubility of phenol in water increased with increasing temperature, which decreased the mass-transfer resistance in the dispersed phase. As a result, the transfer coefficient increased. The drop size decreased with temperature, which is unfavorable to mass transfer according to section 3.2. On the whole, the mass-transfer coefficient increased with temperature. 3.5. Effect of Aqueous-Phase pH Value on Mass Transfer. Figure 9 shows that the drop diameter decreased

In addition, the drops increased as the initial solute concentration increased, which also benefitted mass-transfer enhancement. For interpretations that the mass-transfer coefficient increases with droplet diameter, see section 3.2. 3.4. Effect of Temperature on Mass Transfer. The ranges of droplets sizes generated by various solute concentrations are depicted in Figure 7. The size of the droplets decreased with increasing temperature.

Figure 7. Variation of drop size with temperature at different initial solute concentrations.

Figure 9. Variation of drop size with aqueous-phase pH for different nozzles.

As Figure 8 shows, the mass-transfer coefficient increased with temperature. As reported in Table 2, the viscosity of the

with increasing pH of the aqueous phase, which can be explained by the decrease in the interfacial tension with increasing pH.19 The drop size ranged from 3.140 to 2.774 mm. The Reynolds number increased from 463 to 607 as the pH decreased from 9.00 to 5.00. Figure 10 shows that the overall mass-transfer coefficient decreased as pH increased. Because of the moderate acidity of phenol, phenol in the aqueous phase tends to dissociate as pH increases. Phenol is mainly in the form of ions at high pH values, which makes extraction of phenol difficult. Moreover, negative hydroxide ions are adsorbed specifically and spontaneously at the aqueous droplet surface.20 The ions

Figure 8. Variation of overall mass-transfer coefficient with temperature at different initial solute concentrations.

continuous phase decreased with temperature, which resulted in an increase in Reynolds number from 454 to 840. The range of Reynolds numbers was above 500 when the temperature was above 25 °C under the experimental conditions. Most of the droplets were in the turbulence zone. The droplets tended to have higher internal circulation or turbulence as their temperature increased, which is beneficial to mass transfer. The most relevant parameter for this enhancement is the molecular diffusivity, which depends directly on the absolute temperature of the liquid medium and inversely on the viscosity

Figure 10. Variation of overall mass-transfer coefficient with aqueousphase pH for different nozzles. 3658



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charge and stabilize the dispersed droplets.21 This makes a wider charge layer around the droplets and reduces the droplets’ circulation. Finally, all of these factors result in a reduced mass-transfer coefficient. 3.6. Modeling the Mass-Transfer Coefficient. 3.6.1. Estimation of Liquid Diffusivities. Attempts have been made to predict liquid diffusivities, and many correlations have been proposed. In this article, the Wilke−Chang equation22 was used to calculate the liquid diffusivities of phenol in water. Thus 0 DAB

(φ MB)1/2 T = 7.4 × 10−12 B μB VA 0.6

coefficient values were used to calculate each relevant enhancement factor. The values of R were found to be in the range from 4.77 to 41.00. Steiner et al.28 also proposed a correlation to evaluate R values on the basis of data from nine sources ⎛ μ ⎞0.89 c ⎟⎟ Scd 0.23 R = 1 + 0.177Re 0.43⎜⎜ μ + μ ⎝ c d⎠

(for R < 10) (8)

⎛ 2μc ⎞ ⎟⎟ R = 5.56 × 10−5⎜⎜Re ⎝ μc + μd ⎠

1.42

(4)

The diffusion coefficient (D0AB) is a function of the molar volume of phenol in water based on data from the literature23 (see Table 3). The molar volumes (VA) used throughout this work are values at the normal boiling point estimated for complex molecules by the atomic contributions of Le Bas.24

(for R > 10)

R = 1 + 0.218Re

volume (cm3·mol−1)

component

volume (cm3·mol−1)

C (atom) H (atom)

14.8 3.7

O (atom) benzene ring

7.4 −15

(9)

Using the dimensionless variables and the exponents, these correlations were also used for modeling R values in this article

Table 3. Additive Volume Increments of Le Bas for the Calculation of Molar Volumes at Normal Boiling Points component

̈ Scd 0.67Eο0.12

⎛ μ ⎞0.89 c ⎜⎜ ⎟⎟ Scd 0.23 ⎝ μc + μd ⎠

0.43

(for R < 10) (10)

1.42 ⎛ 2μc ⎞ ⎟⎟ Scd 0.67Eο0.12 ̈ R = −26.02 + 7.846 × 10−5⎜⎜Re ⎝ μc + μd ⎠

(for R > 10)

3.6.2. Mass-Transfer Coefficient Correlations. Overall masstransfer coefficients can be determined by the additivity of individual resistances. Thus 1 1 m = + Kod kd kc (5)

(11)

Figure 11 is a parity plot of simulated values of Kod calculated by the modified Kronig−Brink equation with the experimental

where kc and kd are the local mass-transfer coefficients in the continuous and dispersed phases, respectively. The distribution coefficient of phenol between MIBK and the aqueous phase is 100.6 Thus, phenol tends to stay in the organic phase, and the mass-transfer resistance exists completely in the aqueous phase, that is, Kod ≈ kd. Various theoretical models have been proposed for estimating dispersed-phase mass-transfer coefficients. Kronig and Brink25 developed a model for mass transfer in circulating drops for the case of zero external resistance and drop Reynolds number values less than unity, assuming that the internal circulation pattern conformed to that suggested by Hadamard26 and Rybczynski.27 The result for the mass-transfer coefficient is kd = −

d ⎡⎢ 3 ln 6t ⎢⎣ 8

∞

⎛ 64λnDd t ⎞⎤ ⎟⎥ d 2 ⎠⎥⎦

∑ Bn2 exp⎜⎝− n=1

Figure 11. Comparison between experimental and calculated overall mass-transfer coefficients.

(6)

Using only first term of the summation in this equation results in the approximation 17.9Dd kd = (7) d

values under all experimental conditions. The maximum relative deviation of these values is ±30% (except for one data point with more deviation). The average relative deviation in the values of Kod predicted using eqs 10 and 11 in conjunction with eq 7 is 14.8%.

From section 3.1, one can see that most of the experimental drops were in the oscillating region. The Kronig−Brink model does not considerate these effects. The Hadamard streamlines cannot describe the chaotic convection patterns in the droplets. In this work, to describe the mass-transfer process of all kinds of drops, the molecular diffusivity was multiplied by an empirical factor (R). Then, the molecular diffusivity (Dd) in the Kronig−Brink equation was replaced by the enhanced molecular diffusivity (RDd). The experimental mass-transfer

4. CONCLUSIONS A study on the mass-transfer coefficients of falling droplets has been carried out for the MIBK−phenol−water system. From the hydrodynamic investigation, most of the drops were in the oscillation regime because of the low viscosity of the continuous phase under the experimental conditions. The 3659



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Greek Symbols

internal circulation was instead by chaotic convection, which led to enhanced radial mixing and thus higher mass-transfer rates. Because an increase in the Reynolds number leads to stronger internal circulation, the overall mass-transfer coefficient increased with increasing drop diameter. The higher the initial solute concentration, the stronger the interfacial instabilities, and the larger the value of Kod. When the temperature was increased, the molecular diffusivity increased significantly. Thus, the overall mass-transfer coefficient of the drops increased greatly with temperature from 15 to 55 °C. Kod decreased when the aqueous-phase pH increased, mainly because of the adsorption of hydroxyl ions onto the interface and the dissociation of phenol. An enhancement factor R was introduced to modify the Kronig−Brink equation. The experimental data was modeled by the modified model, which used an effective diffusivity in place of the molecular diffusivity. This model was able to account for the effects of the droplet diameter, the initial solute concentration, the temperature, and the aqueous-phase pH. The average relative deviation between the predicted and experimental values was 14.8%. Thus, the modified model can be used for the design of liquid−liquid extraction columns.

■

γ = interfacial tension (mN·m−1) μ = viscosity (mPa·s) ρ = density (kg·m−3) ψB = association parameter equal to 2.6 for water and 1.0 for unassociated liquids Subscripts

A = solute B = solvent c = continuous phase d = dispersed phase Superscript

■

REFERENCES

(1) Rosatto, S. R.; Freire, R. S.; Druan, N.; Kobuta, L. T. Amperometric Biosensors for Phenolic Compounds Determination in the Environmental Interess Samples. Quim. Nova 2001, 24 (1), 77. (2) Toxic Substances Control Act; U.S. Government Printing Office: Washington, D.C., 1976. (3) Guieysse, B.; Norvill, Z. N. Sequential Chemical−Biological Processes for the Treatment of Industrial Wastewaters: Review of Recent Progresses and Critical Assessment. J. Hazard. Mater. 2014, 267, 142. (4) Garavand, F.; Madadlou, A. Recovery of Phenolic Compounds from Effluents by a Microemulsion Liquid Membrane (Mlm) Extractor. Colloids Surfaces A 2014, 443, 303. (5) Pal, S.; Mukherjee, S.; Ghosh, S. Application of HYDRUS 1D Model for Assessment of Phenol−Soil Adsorption Dynamics. Environ. Sci. Pollut. Res. 2014, 1. (6) Yang, C. F.; Qian, Y.; Zhang, L. J.; Feng, J. Z. Solvent Extraction Process Development and On-Site Trial-Plant for Phenol Removal from Industrial Coal-Gasification Wastewater. Chem. Eng. J. 2006, 117 (2), 179. (7) Yang, C.; Qian, Y.; Jiang, Y.; Zhang, L. Liquid−Liquid Equilibria for the Quaternary System Methyl Isobutyl Ketone−Water−Phenol− Hydroquinone. Fluid Phase Equilib. 2007, 258 (1), 73. (8) Skelland, A.; Vasti, N. C. Effects of Interaction between Circulating or Oscillating Droplets on Drop Formation, Free Fall, and Mass Transfer. Can. J. Chem. Eng. 1985, 63 (3), 390. (9) Li, T. W.; Mao, Z. S.; Chen, J. Y.; Fei, W. Y. Terminal Effect of Drop Coalescence on Single Drop Mass Transfer Measurements and Its Minimization. Chin. J. Chem. Eng. 2004, 9 (2), 204. (10) Temos, J.; Pratt, H.; Stevens, G. Mass Transfer to FreelyMoving Drops. Chem. Eng. Sci. 1996, 51 (1), 27. (11) Grace, J.; Wairegi, T.; Nguyen, T. Shapes and Velocities of Single Drops and Bubbles Moving Freely through Immiscible Liquids. Trans. Inst. Chem. Eng. 1976, 54 (3), 167. (12) Hu, S.; Kinter, R. The Fall of Single Liquid Drops through Water. AlChE J. 1955, 1 (1), 42. (13) Klee, A. J.; Treybal, R. E. Rate of Rise or Fall of Liquid Drops. AlChE J. 1956, 2 (4), 444. (14) Laddha, G.; Degaleesan, T. Transport Phenomena in Liquid Extraction; McGraw-Hill: New York: 1978. (15) Angelo, J. B.; Lightfoot, E. N.; Howard, D. W. Generalization of the Penetration Theory for Surface Stretch: Application to Forming and Oscillating Drops. AlChE J. 1966, 12 (4), 751. (16) Sternling, C.; Scriven, L. Interfacial Turbulence: Hydrodynamic Instability and the Marangoni Effect. AlChE J. 1959, 5 (4), 514. (17) Wegener, M.; Paschedag, A. R. Mass Transfer Enhancement at Deformable Droplets Due to Marangoni Convection. Int. J. Multiphase Flow 2011, 37 (1), 76. (18) Saien, J.; Daliri, S. Performance Improving with Temperature in Liquid−Liquid Extraction Using Cumene−Isobutyric Acid−Water Chemical System. J. Ind. Eng. Chem. 2014, 20 (1), 238.

ASSOCIATED CONTENT

S Supporting Information *

Process of calculating drop diameter and Kod (Figure S1). Experimental data on single-drop mass transfer in the dispersed phase at 15 °C with an initial solute concentration of 8000 mg/ L (Table S1). Comparison between predicted and experimental results in our work (Table S2). This material is available free of charge via the Internet at http://pubs.acs.org.

■

* = equilibrium

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel./Fax: +86 22 27400199. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS We are grateful for the financial support from the National Natural Science Foundation of China (No. 21336007). SYMBOLS USED A = drop surface area (m2) C = solute concentration (mg·L−1) d = drop diameter (mm) DAB0 = diffusion coefficient of A in B at infinite dilution (m2· s−1) Eö = Eötvös dimensionless number Kod = overall mass-transfer coefficient (μm·s−1) m = solute distribution coefficient MB = molecular weight of the solvent (g·mol−1) R2 = squares of linearly dependent coefficient Re = drop Reynolds number Sc = Schmidt number based on the dispersed phase t = contact time (s) T = temperature (°C) ut = terminal velocity of the drops (m·s−1) VA = molecular volume of the solute (cm3·mol−1) Vd = drop volume (m3) We = drop Weber number (dut2ρc/γ) 3660



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(19) Saien, J.; Daliri, S. Mass Transfer Coefficient in Liquid−Liquid Extraction and the Influence of Aqueous Phase pH. Ind. Eng. Chem. Res. 2008, 47 (1), 171. (20) Marinova, K.; Alargova, R.; Denkov, N.; Velev, O.; Petsev, D.; Ivanov, I.; Borwankar, R. Charging of Oil−Water Interfaces Due to Spontaneous Adsorption of Hydroxyl Ions. Langmuir 1996, 12 (8), 2045. (21) Gäbler, A.; Wegener, M.; Paschedag, A.; Kraume, M. The Effect of Ph on Experimental and Simulation Results of Transient Drop Size Distributions in Stirred Liquid−Liquid Dispersions. Chem. Eng. Sci. 2006, 61 (9), 3018. (22) Wilke, C.; Chang, P. Correlation of Diffusion Coefficients in Dilute Solutions. AlChE J. 1955, 1 (2), 264. (23) Wilke, C. Estimation of Liquid Diffusion Coefficients. Chem. Eng. Prog. 1949, 45 (3), 218. (24) Le Bas, G. The Molecular Volumes of Liquid Chemical Compounds; Longmans: London, 1915. (25) Kronig, R.; Brink, J. C. On the Theory of Extraction from Falling Drops. Appl. Sci. Res. 1950, A2, 142. (26) Hadamard, J. Mouvement Permanent Lent d’Une Sphere Liquide et Visqueuse dans un Liquide Visqueux. C. R. Acad. Sci. 1911, 152 (25), 1735. (27) Rybczynski, W. Uber die Fortschreitende Bewegung Einer Flussigen Kugel in Einem Zahen Medium. Bull. Acad. Sci. Cracov. Ser. A 1911, 1, 40. (28) Steiner, L.; Oezdemir, G.; Hartland, S. Single-Drop Mass Transfer in the Water−Toluene−Acetone System. Ind. Eng. Chem. Res. 1990, 29 (7), 1313.

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