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Ind. Eng. Chem. Res. 2006, 45, 1434-1440
Comparative Investigations on the Effects of Contamination and Mass Transfer Direction in Liquid-Liquid Extraction Javad Saien,*,† Maryam Riazikhah,† and Seyed Nezameddin Ashrafizadeh‡ Department of Applied Chemistry, UniVersity of Bu-Ali Sina, Hamadan 65174, Iran, and Research Lab for AdVanced Separation Processes, Department of Chemical Engineering, Iran UniVersity of Science and Technology, Narmak, Tehran 16846, Iran
The influence of different factors on the overall mass transfer coefficient of liquid-liquid extraction was investigated, employing single-drop experiments with mass transfer in either direction. The chemical system of toluene-acetone-water was used with the advantage of high accuracy and repeatability when using gas chromatography for analysis. Three different types of surfactants were used as contaminant agents, and their effectiveness in retarding the mass transfer appeared in the order cationic < anionic < nonionic. Addition of contaminants did not change the trend of variation with drop size for the concentration range investigated in this study; however, a number of small drops demonstrated rigid behavior at high contaminant concentrations. The rate of mass transfer is greater in the dispersed to continuous phase direction. An empirical correlation was developed here in conjunction with a combined model which describes the variations of the mass transfer coefficient. The variation of physical properties was also taken into account. Introduction Contaminants are usually present to an unknown extent in industrial materials. They accumulate at the interface between phases, inhibit circulation within the drops, cause hydrodynamic and adsorptive barriers to transfer across the interface, and change the pattern of drop behavior. Although a great deal of effort has been made to identify the influence of contamination in a systematic way,1-6 no consistent conclusion has been drawn so far, and for design or simulation purposes it is still promising to use mass transfer data from single drops in conjunction with a hydrodynamic model. The reduction in mass transfer, exerted by contaminants, has been attributed to the interfacial barrier layer and to the hydrodynamic revolutions in lowering interfacial mobilization which in turn cause changes in internal circulation of drops. Adsorption and desorption of contaminants to and from the surface are also involved in the change of the rate of mass transfer. For example, Stebe et al.7,8 have shown that, for surfactants with fast adsorption kinetics, the surface mobility of drops is decreased at lower surfactant concentrations. The change in interfacial movement due to the gradient of interfacial tension along the drop surface has also been studied, and a model named the “interfacial tension variation model” has been offered in a series of works initiated by Lochiel.9 Considering the relationship between interfacial tension and contaminant concentration, an equation has been derived for the continuous phase Sherwood number, including the effect of contamination. In an application point of view, there is a need in industrial mass transfer systems to have a single description of contamination; otherwise, a distinct value for the level of contamination may be defined for each of the phases. In this regard, Slater and Hughes10 and Slater2 have proposed using the ratio of average surface to terminal velocities to link the effect of * To whom correspondence should be addressed. Tel. and fax: +98811-8272404. E-mail:
[email protected]. † Bu-Ali Sina University. ‡ University of Science and Technology.
contamination in continuous and dispersed phases. In this way a “combined mass transfer model” has been provided. A number of authors6,11 have used this model with the help of a mathematical assumption. In their works, sodium dodecyl sulfate (SDS) has been used as contaminant in the mass transfer direction of dispersed phase to continuous phase. Recently, Chen and Lee4 have compared the influence of different types of surfactants in reducing the rate of mass transfer. They have introduced a procedure to determine the equilibrium adsorption parameters, examined for only a specified drop size and one direction of mass transfer. In our previous work12 the simultaneous effect of contamination and agitation on the mass transfer of liquid-liquid extraction was investigated. In the present work, the influence of three types of surfactants (as different contaminants) on the rate of mass transfer of different single drops was studied and both directions of mass transfer were considered. These mass transfer data, obtained from single-drop experiments, can be used directly in the design of different extraction contactors, with high confidence.11,13 The “combined mass transfer coefficient model” was assessed in accordance with experimental results to evaluate its adequacy for the conditions employed in this study. Enhanced diffusivity for transport inside drops in an overall diffusivity model was applied. Experimental Section Materials. The chemical system of toluene-acetone-water, a recommended system for liquid-liquid extraction studies,14 was chosen. The main specification of this system is its high interfacial tension. Toluene and acetone were Merck products with purities of more than 99% and 99.5%, respectively. Distilled and deionized water was produced from a new still and was used for the continuous phase. The following surfactants, as simulating industrial contaminants, have been used to investigate the influence of different types of contaminants: the anionic surfactant sodium dodecyl sulfate (SDS), the cationic surfactant dodecyl trimethylammonium chloride (DTMAC), and the nonionic surfactant octylphe-
10.1021/ie0508379 CCC: $33.50 © 2006 American Chemical Society Published on Web 01/20/2006
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1435 Table 1. Physical Properties of Chemical System Toluene-Acetone-Water at 20 °C property
dispersed phase
F [kg/m3] µ [kg/m‚s]
866.7 0.628 × 10-3
D [m2/s] γ [mN/m]
2.55 × 10-9
Table 2. Range of Drop Diameter (mm) Generated by Nozzles
continuous phase 998.2 DTMAC: (1.012-1.040) × 10-3 SDS: (1.012-1.069) × 10-3 Triton: (1.012-1.024) × 10-3 1.09 × 10-9 DTMAC: 23.60-33.25 SDS: 20.79-33.25 Triton: 18.16-33.25
nol decaethylene glycol ether (Triton X-100). SDS, DTMAC, and Triton X-100 are products of Merck, Fluka, and Merck with purities of more than 99%, 99%, and 99.5%, respectively. The average (with respect to solute concentration) and the range of physical properties of the chemical system at 20 °C (ambient temperature) are given in Table 1. The physical properties were measured using a self-adjustable temperature density meter (Anton Parr DMA 4500), a calibrated automatic ring method tensiometer (Sigma 70), and an Ostwald viscometer. Regarding the sensitivity of mass transfer equations to the viscosity, this property was measured for the continuous phase while surfactants were added at the appropriate concentrations. The viscosity of the aqueous phase increases by adding surfactants, having a significant variation for SDS (Figure 1). Deo et al.15 have reported a similar variation for the viscosity of aqueous SDS solutions. Organic and aqueous molecular diffusivities also were applied from those reported by Baldauf and Knapp.16 The values of equilibrium distribution of acetone between the phases at 20 °C, within the concentration range used (1 < Cc < 35 g/L), were examined and correlated by
C*d ) 0.832Cc
(1)
where C/d and Cc are equilibrium dispersed phase (organic) and continuous phase (aqueous) concentrations (g/L), respectively, of acetone. The equilibrium data are in agreement with those reported by Brodkorb et al.,17 which include data in either the presence or absence of phenol. The presence of surfactants, within the concentration range used in this work, shows no significant influence on the equilibrium distribution. Setup. A Pyrex glass column (11.4 cm diameter and 51 cm height) was used as the contactor. Drop forming was provided using a variety of glass nozzles located at the bottom of this column. The toluene phase was held in a glass syringe conducted by an adjustable syringe pump (Phoenix M-CP) and flowed through a rigid tube to the glass nozzle. The column was filled with aqueous phase.
Figure 1. Viscosity of continuous phase as a function of surfactant concentration at 20 °C.
nozzle no.
cfd
dfc
1 2 3 4 5
2.57-2.99 2.99-3.25 3.11-3.39 3.84-4.34 4.24-4.65
2.17-2.49 2.52-2.90 2.67-3.09 3.65-4.04 3.97-4.34
A small inverted glass funnel attached to a pipet and vacuum bulb was used to catch a sample of 1-2 mL of dispersed phase at the top of the column with 31.2 cm distance from the initial point. The interfacial area in the funnel was minimized by occasionally pulling toluene into the pipet. Two or three samples were prepared for each concentration and were kept in closed sample tubes at a cold medium until gas chromatographic (GC) analysis. To omit the influence of unsteady mass transfer during the drop formation and its transient velocity, the initial drop concentration was considered for a location of moving drops to be at 6.5 cm above the nozzles’ tips. Drop motion was observed to reach steady movement after traveling about 40 mm. In this regard, Slater et al.1 have reported a distance of about 30 mm for the chemical system of cumene-acetic acidwater. To determine the initial concentrations at that location, an empty small column equipped with the nozzle at the bottom was used. Drops were collected at the same distance of 6.5 cm, under the same conditions and drop size of the main column. Procedure and Analysis. The syringe and the connection tube to the nozzle tip were first filled with toluene or toluene + acetone to produce drops and the column was then filled with distilled water, as the continuous phase. To determine the size of drops, the syringe pump was initially calibrated with respect to the specified volume scale on the calibrated syringe. By knowing the flow rate and the number of drops per a particular period, drop volume was easily calculated. Toluene drops of diameters from 2.17 to 4.65 mm were generated. The range of drop sizes, generated by each nozzle, is listed in Table 2. The size of each drop formed at the nozzle tip was influenced by contaminant concentration, mainly due to the decrease of interfacial tension (Figure 2). Drops of larger sizes were obtained when the direction of mass transfer was from the continuous to dispersed phase. Variation in drop size was achieved by using different glass nozzles. The outside diameter of the nozzles was typically on the order of 0.3 mm. The contact time of drops from the initial to the collection point was measured several times with a stopwatch, and its average was considered. The terminal velocity of drops was
Figure 2. Variation of generated drop sizes with contaminant concentration, nozzle 5.
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tension will be higher than that of the surroundings. The interfacial layer of the drop exerts a Marangoni stress due to this variation of interfacial tension and thus increases the drag resistance of the interfacial flow. As a consequence, the mass transfer rate will be decreased. Lochiel and Calderbank20 developed a model describing the transfer of solute around a spherical drop when the Schmidt number is large (Sc . 1), in the form
Sh )
Figure 3. Variation of interfacial tension with surfactant concentrations at 20 °C.
obtained with respect to the average times. Drops were typically spaced more than 60 mm apart (with a range of flow rates between 40.91 and 196.35 mL/h). Skelland and Vasti18 have shown that interactions are negligible for this distance. Concentration of acetone in the collected samples was measured using a GC (Shimadzu, 14B) with a flame ionization detector (FID), calibrated with reference substances of toluene and acetone (Merck) for gas chromatography. The number of samples, used for the calibration curve experiments, was seven to ten, and the concentration of acetone in the known samples was within the range of 0.5-45 g/L. The maximum error of the measurements did not exceed (5.5%, with a mean value (2.4% for all the experiments. Experiments were conducted in both mass transfer directions of dispersed to continuous phase and vice versa. Acetone was dissolved in the aqueous or the organic phase at initial concentrations between 29.9 and 43.3 g/L, depending on the direction of mass transfer. Surfactants, as the contaminating agents, were added to the continuous phase at predetermined amounts from 6.25 to 100 mg/L. The formation of critical micelle concentration (cmc) did not occur within these concentrations, since the interfacial tension tends to decrease by adding surfactants (Figure 3); the cmc is expected to appear when the interfacial tension remains constant with surfactant concentration.4 The aqueous phase was frequently changed to avoid any change in its original solute concentration. It was also changed at the beginning of every series of experiments with a new nozzle. At such occasions, all of the equipment and glassware were cleaned with Decon 90 solution, followed by several rinses with distilled water. The ambient temperature was within 20 ( 2 °C. Theoretical Model The range of drops used in this work is within the conditions of circulating drops, since the values of dimensionless group H, defined in the model by Grace et al.,19 are in the range of 11.6-39.3 (2 < H < 59.3, corresponding to circulating drops), unless the presence of contaminants changes them to rigid behavior. The range of drop Weber numbers is also within 0.42.7 (We < 3.58). When a drop moves in a contaminated solution, contaminant molecules that have been adsorbed on the interface are convected toward the rear of the drop, where they reduce the local interfacial tension. At the leading pole of the drops, the contaminant concentration is lower and, thus, the local interfacial
2 0.5 0.5 0.5 R Re Sc xπ
(2)
where R ) Vi/Vt is the ratio of averaged tangential velocity component at the interface to the terminal velocity. Subsequently, for contaminated chemical systems, Lochiel9 assumed that the adsorption of contaminants at the interface provides a contamination concentration gradient. This gradient will provide a tangential velocity gradient at the interface with respect to polar angle, relative to the axis of drop movement. A model like eq 2 was developed and the parameter m, named by Slater2 as the “contamination factor”, was included in the equation of R:
R)1-
2 + 3(µd/µc) + m 1.45 Fdµd 0.5 Re0.5 1+ Fc µc
( )
(3)
Slater2 proposed an alteration to the equation of R, to extend the range of usefulness of this equation to a wide range of Reynolds number, using the approximation (valid at low values of x):
R ) 1 - x = (1 + x)-1
(4)
For mass transfer inside drops, the well-known “Newman equation” is frequently used. The Newman equation is based on the diffusion equation in the spherical drops and in spherical coordinates when the continuous phase resistance is absent:
kd )
-d 6t
ln
[∑ 6
∞
1
π2n)1 n2
exp
]
-4π2n2Dt d2
(5)
where d is the drop size, t is the contact time, and D is the molecular diffusivity. An overall effective diffusivity (Doe) can be used for drop behavior envisaging both molecular and eddy diffusion in a sphere and using it in the Newman equation. The eddy diffusion contribution increases as drop size (and therefore its velocity) increases. Young and Korchinsky,21 Slater,2 Ghalehchian and Slater,11 and Saien and Barani12 have proposed alternative effective diffusivity models to be used in overall effective diffusivity. It has been attempted to describe the effect of contamination in both phases with a single parameter. This has a significant industrial implication especially when resistance exists in both phases. In this regard and as the “combined model”, Slater and co-workers2,6,11 have used the contribution of effective diffusivity based on that used by Handlos and Baron:22
De )
dVt 2048(1 + κ)
(6)
where κ ) µd/µc; they add the molecular diffusivity to give the overall effective diffusivity in the form
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1437
Doe ) D + RDe
(7)
This Doe is used in eq 5 instead of D. Therefore, the term R, which represents the effect of interfacial tension gradient together with the retardation effect of contamination, is also applied to the drop-side mass transfer coefficient and the effect of contamination is linked to both film coefficients. Whitman two-film theory is used to add the individual mass transfer resistances in continuous and dispersed phases obtained from appropriate equations, and the overall mass transfer coefficient is calculated:
φ 1 1 ) + Kod kc kd
(8)
where φ is the solute equilibrium distribution coefficient obtained from eq 1. The parameter m, which represents the level of contamination in eq 3, is a function of surface and bulk diffusivity of contaminant, film thickness, and parameters for adsorption of contaminant. Due to difficulties in measuring these properties, the value of parameter m has been determined by fitting with experimental data.2,6,10,11 The empirical equation given by Steiner23 is used to verify whether drops reach rigid conditions by adding the contaminants:
Shr ) 2.43 + 0.775Re0.5Sc0.33 + 0.0103Re Sc0.33
Figure 4. Variation of overall mass transfer coefficient with contaminant concentration, nozzle 5.
(9)
The combined model is to be applied to calculate the overall mass transfer coefficient with reference to experimental results. Figure 5. Variation of overall mass transfer coefficient with drop size for surfactant concentration of 25 mg/L.
Results and Discussion Ninety series of experimental data including initial and final concentrations, drop size, and contact time were obtained for each mass transfer direction. The experimental overall mass transfer coefficient values were calculated using
Kod ) -
d ln(1 - E) 6t
(10)
where t is the contact time and E is the extraction fraction, defined by
E)
Cdf - Cdi C*d - Cdi
(11)
where Cdi, Cdf, and C/d are the initial, final, and equilibrium solute concentrations, respectively, in the drop phase. For the d f c mass transfer direction C/d is zero, because the solute concentration in aqueous phase is zero for this case. The continuous phase is considered uniform in the bulk phase and thus has a unique bulk concentration. The overall mass transfer coefficient obtained from eq 10 is in fact an overall timeaveraged mass transfer coefficient. Effect of Contaminants. Figure 4 shows the variation of overall mass transfer with contaminant concentration. As it is shown, the overall mass transfer coefficient decreases rapidly with low amounts of surfactant and reaches a nearly constant value at concentrations around 12 mg/L depending on the type of surfactant and the drop size. The influence of Triton X-100 is more significant compared with that of the other two surfactants, while the influence of DTMAC is less for both mass transfer directions. The order of effectiveness of surfactants, acting as contaminants, increases in the order DTMAC < SDS
< Triton X-100, i.e., cationic surfactant < anionic surfactant < nonionic surfactant. Chen and Lee4 have used these surfactants for the chemical system of carbon tetrachloride-acetic acid-water. In their work, the effectiveness of SDS and and the effectiveness of Triton X-100 are close with minor effects on the mass transfer coefficient for concentrations greater than about 10 mg/L; however, for lower concentration, the order of effectiveness is in agreement with the results of this work. Different behavior of surfactants in the mass transfer of drops could be attributed to the adsorption rate and surface concentration on the interface. Chen and Lee4 have obtained a significantly greater adsorption constant for Triton X-100 in their chemical system, and therefore, a greater surface activity of this surfactant is concluded. Effect of Drop Size. As Figure 5 shows, the mass transfer coefficient increases with drop size. On the other hand, addition of contaminants has not altered this trend of increasing with drop size. There is a similar variation for other contaminant concentrations. Drops tend to higher circulation with increasing size and enhancing mass transfer. Meanwhile, large drops move faster with low contact times. Table 3 shows the variation of the maximum (with surfactant concentration of 100 mg/L) percentage of Kod reduction, compared with a clean system for both mass transfer directions. The important observation, revealed from this set of results, is that small drops are more affected by the retarding effect of contamination, particularly at high contaminant concentrations. The higher contact times for small drops, during which the adsorption of surfactants is continued, can be a reason for this effect. It should be noted that the smaller drops provide a greater
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Table 3. Maximum Percentage of Kod Reduction for Drops of Different Nozzles in Both Mass Transfer Directions Triton
SDS
DTMAC
nozzle no.
dfc
cfd
dfc
cfd
dfc
cfd
1 2 3 4 5
97.3 94.2 91.8 79.9 77.1
98.8 94.6 91.9 72.0 66.7
91.9 83.6 82.1 73.5 65.7
93.3 85.4 76.1 61.4 56.3
83.4 76.1 75.1 61.5 58.1
86.6 68.3 67.9 61.9 53.7
surface for a specified volume of the dispersed phase, thus providing an enhancement of the mass flux in this point of view. The low difference between the results for nozzles 2 and 3 in Table 3 is due to the closeness of drop sizes generated by them. Effect of Mass Transfer Direction. From Figures 4 and 5 it is obvious that the mass transfer coefficient is greater in the d f c direction for all cases under similar conditions. It is notable that the range of Kod values is from 2.9 to 198.7 µm/s for the d f c direction and from 0.81 to 140.3 µm/s for the c f d direction. As it appears in these figures, the difference is greater for the clean chemical system and it remains nearly constant with increasing contaminant concentration. When investigating the difference between the reverse mass transfer directions, the variation of contact time (hydrodynamic term) and the extraction fraction (mass transfer term), included in eq 10, becomes useful. In this regard, Figures 6 and 7 show that both the contact time and the extraction fraction are higher for the d f c direction. Although these two terms oppose each other, the more important difference in the extraction fraction would provide the higher mass transfer coefficient in this direction.
Figure 8. Comparison between experimental terminal velocity and the model of Grace et al.19 Table 4. Drop Size (d) and Surfactant Concentration (c) of Rigid Drops in Both Mass Transfer Directions dfc surfactant Triton
SDS
DTMAC
nozzle no.
d (mm)
c (mg/L)
d (mm)
c (mg/L)
1
2.26 2.20 2.17
25 50 100
2
2.55 2.52
50 100
3
2.69 2.67
50 100
1
2.45 2.44
50 100
2
2.68
100
3
2.77
100
1
2.45
100
2.79 2.69 2.61 2.57 3.12 3.06 3.02 2.99 3.19 3.11 3.10 2.76 2.70 2.67 2.82 2.74 2.69 3.14 3.09 2.81 2.77 3.02 3.11
12.5 25 50 100 12.5 25 50 100 25 50 100 25 50 100 25 50 100 50 100 50 100 100 100
2 3
Figure 6. Variation of contact time with surfactant concentration, nozzle 5.
Figure 7. Variation of extraction fraction with surfactant concentration, nozzle 5.
cfd
The kind of variation of contact time with surfactant concentration, presented in Figure 6, is due to the reduction of terminal velocity which is influenced by the reduction in drop size (Figure 2) and the increase in viscosity of the continuous phase by adding the surfactants for a specified nozzle (Figure 1). Application of the Combined Model. The mass transfer model, described above, was applied in accordance with the experimental conditions. The appropriate R values were first obtained by adjusting its value until measured and calculated overall mass transfer coefficients agree while all other variables remained fixed. The accuracy was set at a tolerance of (0.1 µm/s to give solutions correct to five or six decimal places. Higher R values are expected for higher Kod values (low contaminant concentrations and/or large drops) and an extreme limit when the model is used for clean systems. To assess part of the calculations, the measured values of terminal velocity of drops, used in eqs 2, 6, and 9, were compared with the model of Grace et al.19 using the appropriate physical properties. The agreement is excellent (maximum relative deviation of (5.3%), as is represented by Figure 8 for the c f d direction for instance.
Ind. Eng. Chem. Res., Vol. 45, No. 4, 2006 1439 Table 5. Parameters of eq 12 mass transfer direction surfactant dfc cfd
Figure 9. Variation of R with surfactant concentration for nozzle 5.
Triton SDS DTMAC Triton SDS DTMAC
a1
a2
a3 × 103
n1
n2
R2
-1.051 -0.612 -0.671 -0.471 -0.503 -0.381
1.421 1.092 1.120 0.639 0.702 0.711
6.512 8.489 7.812 6.120 6.511 7.014
-0.086 -0.148 -0.132 -0.129 -0.113 -0.227
2.701 2.678 2.865 2.591 2.588 2.738
0.98 0.97 0.98 0.98 0.98 0.96
appropriate variables. Dependence on drop size implies dependence on contact time, during which the surface adsorption of the contaminant is continued. From presented variations in Figures 9 and 10, it is obvious that the changes of R, under the conditions studied, are attributed to the nonlinear influences of contaminant concentration (c) and drop size (d). As a simplified correlation, applicable in the combined model, the data are nicely reproduced with the following equation:
R ) a1 + a2cn1 + a3dn2
Figure 10. Variation of R with drop size for surfactant concentration of 6.25 mg/L.
The values of R required to fit the combined model to experimental data are less than 0.72 (0.091-0.713 for d f c and 0.078-0.553 for c f d) for contaminated systems. Therefore, the alteration proposed by Slater2 for using the modified Lochiel equation (eq 4) is not consistent for conditions used in this work. Some Kod values lie below the rigid drop limit at high concentrations of contamination; i.e., Sh becomes less than Shr (eq 9). The number of these drops is greater in the c f d direction, since the mass transfer coefficient required to agree with experimental data is lower. Table 4 gives the specification of these drops, falling in the region of rigid behavior due to the presence of contaminants. For a small number of clean experiments (large drops produced from nozzles 3, 4, and 5) with the mass transfer direction of d f c, the values of R exceed 1. Therefore, the combined model with the appropriate drop and continuous phase mass transfer coefficients predicts a lower overall mass transfer coefficient for them and R should be higher. Other parts of the model may have influence in this matter. For example, Beitel and Heideger24 have shown that the drop mass transfer coefficient can exceed that predicted by the Handlos and Baron equation even with surfactant present. For the c f d direction, the values of R never reach 1 and the model predicts higher values of overall mass transfer coefficient even without the presence of surfactants. The lower value of µd/µc (Table 1) in the equation of Handlos and Baron is probably the main reason to predict the higher mass transfer coefficient in this direction. Figures 9 and 10 present typical variations of R versus surfactant concentration and drop size, respectively. The trend of variation is nearly similar to the variation of Kod with the
(12)
where a1, a2, a3, n1, and n2 are the equation parameters. This equation was fitted with the experimental data using Table 3D software. No correlation was imposed among the parameters, and the higher significance was provided for the exponents n2 and n1. Due to the different level of R values for each mass transfer direction and different physical properties for different surfactant types, each series of data was processed separately. The appropriate obtained values of parameters along with the regression coefficients are given in Table 5, when c is in mg/L and d is in mm. Equation 12, with the appropriate parameters in this table, is applicable for circulating drops moving in aqueous medium, contaminated with one of the surfactants. The maximum of relative deviation (100 × |Rexp - Rcal|/ Rexp) for experiments with the mass transfer direction of c f d is (9.6% (except five experiments with higher deviations) and for the d f c direction is (12% (except four experiments). Applying the combined model with the help of eq 12 provides Kod values that have relative deviations within (8.5% for both mass transfer directions (except three experiments in each direction with higher deviations). This deviation is thought to be sufficient considering an experimental error of approximately 5% in Kod values. The combined model in its new form can therefore be used satisfactorily to predict the overall mass transfer coefficient. Conclusions The experimental results demonstrate that different types of surfactants provide differing effectiveness in the rate of mass transfer for single-drop extraction systems. For all cases, the overall mass transfer coefficient decreases markedly when only a tiny amount of surfactants is added and approaches a constant value for concentrations greater than 12 mg/L. The direction of mass transfer itself influences the rate of mass transfer, no matter the presence or absence of contaminants. However, the trend of variation of the overall mass transfer coefficient is similar. The mass transfer in drops of different sizes is not equally influenced by contaminants, and the percentage in reduction of mass transfer coefficient is higher for small drops particularly under high concentrations. The combined mass transfer model, with the advantage of incorporating only one parameter for contamination, can be used to describe the variation of the overall mass transfer coefficient.
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However, the mathematical assumption already used for this model cannot be applied. Increasing contaminant concentration could result in changing the circulating behavior to the rigid one, even for concentrations less than 100 mg/L. An empirical equation was developed for the ratio of interfacial velocity to drop terminal velocity that is used to link the film mass transfer coefficients of both sides. The influence of physical properties, drop size, and contaminant concentration are taken into account in this empirical equation. Nomenclature a1, a2, a3 ) constant and coefficients in eq 12 c ) continuous phase c ) contaminant concentration (mg/L) C ) solute concentration (g/L) d ) dispersed phase d ) drop diameter (mm) D ) diffusivity (m2/s) E ) extraction fraction defined by eq 11 H ) dimensionless group defined in the model by Grace et al.19 k ) phase mass transfer coefficient (µm/s) K ) overall mass transfer coefficient (µm/s) m ) contamination factor in eq 3 n1, n2 ) exponents in eq 12 Re ) drop Reynolds number (FcVtd/µc) Sc ) Schmidt number for continuous phase (µc/FcDc) Sh ) Sherwood number for continuous phase (kcd/Dc) t ) contact time (s) Vi ) average interfacial velocity (m/s) Vt ) terminal velocity of a drop (m/s) We ) drop Weber number (FcVt2d/γ) Greek Symbols R ) ratio of drop surface interfacial velocity to terminal velocity γ ) interfacial tension (mN/m) κ ) viscosity ratio (µd/µc) µ ) viscosity (kg/m‚s) φ ) solute equilibrium distribution coefficient F ) density (kg/m3) Subscripts c ) continuous phase cal ) calculated d ) dispersed phase e ) effective value exp ) experimental i ) initial value f ) final value o ) overall value r ) rigid condition Superscript / ) equilibrium Literature Cited (1) Slater, M. J.; Baird, M. H. I.; Liang, T.-B. Drop Phase Mass Transfer Coefficients for Liquid-Liquid Systems and the Influence of Packings. Chem. Eng. Sci. 1988, 43, 233.
(2) Slater, M. J. A Combined Model of Mass Transfer Coefficients for Contaminated Drop Liquid-Liquid Systems. Can. J. Chem. Eng. 1995, 73, 462. (3) Lee, Y. L.; Maa, J. R.; Yang, Y. M. The Effects of Surfactant on the Mass Transfer in Extraction Column. J. Chem. Eng. Jpn. 1998, 31 (3), 340. (4) Chen, L. H.; Lee, Y. L. Adsorption Behavior of Surfactants and Mass Transfer in Single-Drop Extraction. AIChE J. 2000, 46 (1), 160. (5) Lohner, H.; Czisch, C.; Lehrnann, P.; Bauchange, K. Mass Transfer Processes in Liquid-Liquid Systems with Surfactants. Chem. Eng. Technol. 2001, 11, 1157. (6) Brodkorb, M. J.; Bosse, D.; von Reden, C.; Gorak, A.; Slater, M. J. Single Drop Mass Transfer in Ternary and Quaternary Liquid-Liquid Extraction Systems. Chem. Eng. Process. 2003, 42, 825. (7) Stebe, K. J.; Lin, S. Y.; Maldarelli, C. Remobilizing Surfactant Retarded Fluid Particle Interface I. Phys. Fluids 1991, A3, 3. (8) Stebe, K. J.; Maldarelli, C. Remobilizing Surfactant Retarded Fluid Particle Interface II. J. Colloid Interface Sci. 1994, 163, 177. (9) Lochiel, A. C. The Influence of Surfactants on Mass Transfer Around Spheres. Can. J. Chem. Eng. 1965, 43, 40. (10) Slater, M. J.; Hughes, K. C. The Application of a New Combined Film Mass Transfer Coefficient Model to the n-Butanol/Succinic Acid/Water System. In Proceedings of International SolVent Extraction Conference ISEC 93, York; Logsdail, D. H., Slater, M. J., Eds.; Elsevier Applied Science: London, 1993. (11) Ghalehchian, J. S.; Slater, M. J. A Possible Approach to Improving Rotating Disc Contactor Design for Drop Breakage and Mass Transfer with Contamination. Chem. Eng. J. 1999, 75, 131. (12) Saien, J.; Barani, M. A Combined Mass Transfer Coefficient Model for Liquid-Liquid Systems under Simultaneous Effect of Contamination and Agitation. Can. J. Chem. Eng. 2005, 83 (2), 224. (13) Qi, M. Z.; Haverland, H.; Vogelpohl, A. Design of Pulsed Sieve Plate Extraction Columns for Extraction on the Basis of Single Drop Experiments. Chem.-Ing.-Tech. 2000, 72 (3), 203. (14) Misek, T.; Berger, R.; Schroter, J. Standard Test Systems for Liquid Extraction Studies. EFCE Publ. Ser. 1985, No. 46. (15) Deo, P.; Jockusch, S.; Ottaviani, M. F.; Moscatelli, A.; Turro, N. J.; Somasundaran, P. Interactions of Hydrophobically Modified Polyelectrolytes with Surfactants of the Same Charge. Langmuir 2003, 19, 10747. (16) Baldauf, W.; Knapp, H. Experimental Determination of Diffusion Coefficients, Viscosities, Densities and Refractive Indexes of 11 Binary Liquid Systems. Ber. Bunsen-Ges. Phys. Chem. 1983, 87, 304. (17) Brodkorb, M. J., Gomis, V., Slater, M. J. Determination of Phase Equilibria and Densities for the Quaternary System Toluene + Acetone + Phenol + Water. J. Chem. Eng. Data 1999, 44, 591. (18) Skelland, A. H. P.; 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, 390. (19) Grace, J. R.; Wairegi, T.; Nguyen, T. H. Shapes and Velocities of Single Drops and Bubbles Moving Freely Through Immiscible Liquids. Trans. Inst. Chem. Eng. 1976, 54, 167. (20) Lochiel, A. C.; Calderbank, P. H. Mass Transfer in the Continuous Phase Around Axisymmetric Bodies of Revolution. Chem. Eng. Sci. 1964, 19, 471. (21) Young, C. H.; Korchinsky, W. J. Modelling Drop Side Mass Transfer in Agitated Polydispersed Liquid-Liquid Systems. Chem. Eng. Sci. 1989, 44, 2355. (22) Handlos, A. S. E.; Baron, T. Mass and Heat Transfer from Drops in Liquid-Liquid Extraction. AIChE J. 1957, 3, 127. (23) Steiner, L. Mass Transfer Rates from Spherical Drops and Drop Swarms. Chem. Eng. Sci. 1986, 41, 1979. (24) Beitel, A.; Heideger, W. J. Surfactant Effects on Mass Transfer from Drops Subject to Interfacial Instability. Chem. Eng. Sci. 1971, 26, 711.
ReceiVed for reView July 16, 2005 ReVised manuscript receiVed November 8, 2005 Accepted December 28, 2005 IE0508379
