Mass Transfer from Single Drops and the Influence of Temperature

Article pubs.acs.org/IECR

Mass Transfer from Single Drops and the Influence of Temperature Javad Saien* and Shabnam Daliri Department of Applied Chemistry, Bu-Ali Sina University, Hamedan 65174, Iran ABSTRACT: Temperature can alter the performance of conventional liquid−liquid extraction columns in which one phase is dispersed inside another phase. In this research, the influence of temperature on the extraction process was investigated using a toluene−acetic acid−water chemical system with dominant mass transfer resistance in the organic phase. Single drop experiments with a range of drop size within 2.49−3.77 mm and temperature within 15−40 °C were performed. Results demonstrate significant impact of temperature on the rate of mass transfer with an average enhancement of 93.6% in overall mass transfer coefficient while small drops are benefited more. Having lower contributions by drop size and terminal velocity, the extraction efficiency is the most effective term in this regard which itself is increased by increasing molecular diffusivity in the organic dispersed phase. For the aim of modeling, effective diffusivity was substituted for molecular diffusivity in Newman’s equation and consequently, a reliable empirical equation was derived for the enhancement factor of diffusivity as a function of dimensionless variables.

1. INTRODUCTION Liquid−liquid extraction has found wide applications in different industries such as petroleum refining, metal extraction, and nuclear fuel processing, and since the design of contactors for this process is often connected with expensive experimental investigations, studies on pilot plants and laboratory-scale apparatuses are inevitable. So far, the effects of different parameters such as aqueous phase pH, contamination, and the presence of salts on single drop behavior have been investigated;1−4 however, it is still difficult to predict the rate of mass transfer as a function of major physical parameters, even for single drops. Temperature is one important parameter that makes significant changes in the physical property of liquids and can be easily employed for the performance improvement of a unit operation. Nevertheless, investigations around this effect on liquid−liquid extraction are scarce. It can be due to conventional operation of this process under ambient temperature. Recently, the effect of temperature on batch liquid−liquid extraction of phenol from aqueous solutions has been investigated by Palma et al.5 A benchscale mixed contactor was employed and the influence of temperature, phase volumes, and rotational speed on phenol removal was investigated using methyl isobutyl ketone as the extracting solvent. The overall effect of temperature was difficult to interpret due to its simultaneous influence on a large number of parameters. It should be noted that the mutual solubility of phases more or less increases with temperature, providing a negative impact on subsequent separations; however, an optimum temperature balancing mass transfer and separation efficiencies can be relevant. Because of its wide application, corresponding to a variety of contactors that accommodate a steady flow of dispersed phase through continuous phase, the study about the influence of temperature on single drops can be memorable as a fundamental approach. In this study, the effect of temperature on the rate of mass transfer, within the usual temperature range of 15−40 °C is determined. An enhancement in the rate of mass transfer is expected because of molecular diffusivity enhancement which strongly depends on temperature. Other variations due © 2012 American Chemical Society

to temperature in physical properties such as viscosity and interfacial tension can alter the mass transfer as well. The findings from this study provide a scientific basis to understand the role of temperature or to choose an optimum operating temperature to suit higher mass transfer requirements in extraction process.

2. EXPERIMENTAL SECTION 2.1. Chemical System and Physical Properties. The chemical system of toluene−acetic acid−water, often used in liquid−liquid extraction studies,6−8 was chosen. The important properties of this system are the relatively high interfacial tension and the existence of mass transfer resistance in the organic phase. Meanwhile, equilibrium data of this system indicate that increasing temperature to 40 °C does not provide noticeable increase in solubility of organic and aqueous phases.9 Deionized water (electrical conductivity of 0.06 μS·cm−1) was used as continuous phase. Toluene and acetic acid were Merck products with purities of more than 99.9% and 100%, respectively. The analysis of collected samples containing acetic acid solute was carried out through a simple titration method using O.1 M NaOH titrant (Merck) solutions. The physical properties of aqueous (continuous) and organic (dispersed) phases are given in Table 1. Densities were measured using a self-adjustable temperature density-meter (Anton Parr DMA 4500) equipped with automatic viscosity correction. The uncertainty for density measurements was ±0.01 kg·m−3. The apparatus was calibrated with dry air and deionized water prior to experiments. The temperature in the cell was regulated to ±0.01 °C with a solid-state thermostat. Owing to appeared changes in viscosity with temperature, this property was measured at different temperatures for continuous and dispersed phases. An Ubbleohde viscometer with an uncertainty Received: Revised: Accepted: Published: 7364

March 14, 2012 April 28, 2012 May 9, 2012 May 9, 2012 dx.doi.org/10.1021/ie300649d | Ind. Eng. Chem. Res. 2012, 51, 7364−7372

Industrial & Engineering Chemistry Research

Article

Table 1. Physical Properties of the Chemical System within Temperature Range of 15−40 °C phase dispersed continuous

ρ [kg·m−3] 848.2−871.9 992.1−999.1

μ [kg·m−1·s−1] −3

(0.458−0.628) × 10 (1.140−0.653) × 10−3

γ [mN·m−1]

Dm [m2·s−1]

28.68−33.48

(2.58−3.85) × 10−9

Figure 1. Variation of viscosity of water and toluene (containing 8.62 g·L−1 acetic acid) with temperature.

Figure 2. Variation of interfacial tension of toluene (containing 8.62 g·L−1 acetic acid) + water with temperature.

of ±2 × 10−3 mPa·s was used. According to Poiseuille law, the viscosity equation is ⎛ t⎞ μ = ρ⎜kt − ⎟ ⎝ c⎠

were obtained by measurements on double distilled water and benzene. The viscosity of organic and aqueous phases decreases 27 and 42% with temperature respectively, as presented in Figure 1. The measured density and viscosity values agree well with data which previously investigated and reported for number of temperatures.10 The measured values of interfacial tension with drop volume method showed that this property tends to decrease by increasing temperature (Figure 2)

(1)

where μ, ρ, and t are dynamic viscosity, density, and efflux time, and k and c are the viscometer constants, respectively. The k and c parameters 7365

dx.doi.org/10.1021/ie300649d | Ind. Eng. Chem. Res. 2012, 51, 7364−7372


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which has been previously reported.11 The average initial concentration of acetic acid in toluene drops was 12.21 g·L−1 (∼1.3 wt %). So, an average concentration of 8.62 g·L−1 (1.0 wt %) was used in measuring density, viscosity, and interfacial tension. Molecular diffusivity coefficient (Dm) was calculated from the correlation by Wilke and Chang.12 According to the data given in Table 1, the significant increase in molecular diffusivity of acetic acid in toluene (49.2%) is relevant as temperature increases from 15 to 40 °C. This variation has been predicted in its correlation with a direct dependency to absolute temperature and inversely to the solvent viscosity. 2.2. Setup and Operating Procedure. A corrugated wall (high heat transfer area) and jacketed Pyrex column (9 cm diameter and 51 cm height) was used as the contactor (Figure 3).

pulling drops into the pipet. Three samples were collected for each temperature and kept in closed sample tubes until titration with O.1 M NaOH to determine acetic acid concentration. To avoid the effect of unsteady mass transfer during drop formation and drops’ transient velocity, the location for determining initial drop concentration was considered at 6.5 cm above the nozzle tip. Drop motion was observed to reach steady movement after about 40 mm traveling. Slater et al.13 have reported a distance of about 30 mm for the chemical system of cumeneacetic acid−water to be adequate to have steady movement. To determine the initial concentrations, a separate small jacketed column, working with the same nozzles, was used. Drops were collected at that distance of 6.5 cm, under the same operating conditions (temperature, solute concentration and drop size) of the main column. Mass transfer direction was from dispersed to continuous phase. Accordingly, acetic acid was dissolved in toluene (saturated with deionized water). The acetic acid concentration was within 5.34−22.75 g·L−1 for initial concentrations (at 6.5 cm above nozzles) and 0.99−11.86 g·L−1 for final (at top of the column) concentrations. To determine the size of drops for each nozzle and temperature, the syringe pump was initially calibrated with respect to the specified volume scale on the calibrated syringe. Knowing the flow rate and the number of generated drops per a particular time, drop volume was easily calculated. In other words, with measuring the related time to evacuation of a specified volume of syringe and also the time of generation of 10 drops with stopwatch, drop volume was obtained. The contact time of drops from the initial to the collection point was measured several times by a stopwatch and the average was considered. Drops were spaced typically more than 60 mm apart (with a range of flow-rate between 45 and 110 mL·h−1). Skelland and Vasti14 have shown that interactions are negligible for this distance. All the equipment and glassware were cleaned with several rinses with deionized water prior to experiments.

3. RESULTS AND DISCUSSION 3.1. Hydrodynamic Investigations. The range of drop size, generated by each nozzle is listed in Table 2. The size of drops, formed at each nozzle tip, is mildly decreased by increasing temperature (Figure 4) mainly due to the interfacial tension decrease. Toluene drops ranging from 2.49 to 3.77 mm were generated. Drops generated in this work are consistent with circulating conditions. There are a number of criteria for circulating drops, including the dimensionless group H defined by Grace et al.,15 Eötvös number and Morton number (H = 4/3EöM−0.149(μo/ μw)−0.14, Eö = gΔρd2/γ and M = gμc4Δρ/(ρc2γ3)), the range of the drops Weber number16 (We = dut2ρc/γ), Reynolds number (Re = ρcutd/μc),17 and the range of Re/NPG0.15 (NPG is the inverse of the Morton number),18 and criterion of critical drop size, dc,d⟨dc = 0.33 μ0.30γ0.43/(ρ0.14Δρ0.43) are also stated.19 As reflected in Table 3, all criteria confirm the circulating condition of drops. The upper limits given for the criteria in Table 3, indicate the onset of oscillation in drops.18

Figure 3. Details of experimental setup.

Generation of different size drops was provided using a variety of glass nozzles located at the bottom of this column. The organic phase was held in a glass syringe conducted by an adjustable syringe pump (JMS SP-500, Japan) and flowed through a rigid tube to the glass nozzle. The column containing aqueous phase and conducting tubes was thermostatted to reach the desired temperature (15, 20, 25, 30, 35, and 40 °C), with an uncertainty of ±0.1 °C. This was established using an adjustable safe and calibrated thermostat (Julabo F12, German), the syringe and the connection tube to the nozzle tip were first filled with organic phase to produce drops, and the column was then filled with deionized water as the continuous phase. A small inverted glass funnel attached to a pipet and vacuum bulb was used to catch a sample of 1 to 2 mL of dispersed phase at top of the column with 33 cm distance from initial point. The interfacial area in the funnel was minimized by occasionally Table 2. the Range of Generated Drop Diameters by the Nozzles

d (mm)

nozzle no. 1

nozzle no. 2

nozzle no. 3

nozzle no. 4

nozzle no. 5

2.49−2.62

2.53−2.65

2.85−2.96

3.49−3.65

3.65−3.77

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Figure 4. Variation of generated drop size with temperature for different nozzles.

Table 3. Different Criteria to Indicate Circulating Conditions of Drops in This Work range in this work

2 < H < 59.3

We < 3.58

Re/NPG0.15 < 20

200 < Re < 500

d < dc (mm)

12.37−39.51

0.59−1.38

5.75 −13.20

198.4−580.8*

2.49−3.77 < 3.76−4.86

*

Three data with Re > 500 and one with Re < 200.

Figure 5. Variation of experimental and predicted (Grace et al.15) terminal velocities with temperature.

The obtained experimental terminal velocities are compared with those predicted by Grace et al.15 There is an excellent agreement between measured and predicted values (Figure 5). Surely, terminal velocity is higher for larger drops produced from bigger size nozzles while temperature is maintained

constant; however, terminal velocity itself increases with temperature for a specified drop size. This matter is in agreement with predicted values from the Grace equation which is presented in Figure 5 for the largest, mean, and biggest generated drops in this work. 7367



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Figure 6. Variation of overall mass transfer coefficient with temperature for different nozzles.

Figure 7. Variation of extraction fraction versus temperature for different nozzles.

where Cdi, Cdf, and C*d are the initial, final, and equilibrium solute concentrations corresponding to the dispersed phase, respectively. For dispersed to continuous phase mass transfer direction Cd* is zero, since the solute concentration in aqueous phase is zero for this case. The overall mass transfer coefficient obtained from eq 2 is in fact an overall time−averaged mass transfer coefficient. The obtained Kod values are within 74.51−324.61 μm·s−1. Figure 6 shows the variation of this parameter with temperature for different nozzles. As it is obvious, the overall mass transfer coefficient increases significantly with temperature. The average

3.2. Mass Transfer Investigations. The overall mass transfer coefficient, Kod, can be obtained from Kod = −

d ln(1 − E) 6t

(2)

where t is the contact time and E is the extraction fraction, defined by E=

Cdf − Cdi Cd* − Cdi

(3) 7368



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Figure 8. Variation of overall mass transfer coefficient with drop size at different temperatures.

Figure 9. Variations of drops contact time with temperature for different nozzles.

largest). The most corresponding parameter for this enhancement is the molecular diffusivity which depends directly on the absolute temperature of the liquid media and inversely to the viscosity of solvent,12 which decreases with temperature (Figure 1). Compared with ordinary conditions temperature causes an increasing in diffusivity. This in turn can provide intensification in the Marangoni phenomenon and therefore mass transfer enhancement. As Figure 8 shows, the mass transfer coefficient increases with drop size as well. Drops tend to higher internal circulation or turbulence as their size increases, and therefore, easier mass transfer per unit time is attained. Meanwhile, larger drops have

enhancement is about 93.6% with a higher value achieved for small drops. The variation of extraction fraction, E should be taken into account for this matter. As introduced in eq 3, E is the ratio of concentration difference to its maximum achievable concentration difference. So, when drops lose higher solute during movement, higher E values will be provided. As Figure 7 shows, the extraction fraction increases significantly with increasing temperature (an average enhancement is about 44.8% with temperature from 15 to 40 °C); whereas drop size reduction was not significant (Figure 4). Small drops benefit more in this regard (about 51.5% for the smallest drops compared with 38.7% for the 7369



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Figure 10. Comparison between experimental and calculated overall mass transfer coefficients.

lower contact time along the column and thus, higher overall mass transfer coefficients are provided. The variation of contact time with temperature, presented in Figure 9, is due to the increasing of terminal velocity (Figure 5) which is influenced by the variation of physical properties of phases (Table 1). In calculating overall mass transfer coefficient from eq 2, contact time reduction with temperature compensates the low level reduction of the size of generated drops. The above discussions indicate that the extraction fraction plays more important role in mass transfer enhancement; that is, the contribution of mass transfer term is higher than hydrodynamic terms even though these parameters have interactions with each other. 3.3. Modeling the Mass Transfer Coefficient. Effect of temperature on the rate of mass transfer can mainly be explained by expressions giving the variation of mass transfer coefficient. A well-adopted procedure uses Whitman two-film theory where individual mass transfer coefficients are related via the slope of equilibrium solute distribution curve (m): 1 m 1 = + Kod kc kd

kd =

− d ⎡⎢ 6 ln 6t ⎣⎢ π 2

∞

∑ n=1

− 4π 2n2Ddt ⎤ 1 ⎥ exp ⎥⎦ n2 d2

(5)

is replaced by an overall effective diffusivity, Doe = 9Dd where 9 is the enhancement factor and empirical correlations are presented to predict its value. Sherwood et al.21 were first to use this approach, pointing out that the equation for radial diffusion in a rigid sphere22 may be used for mass transfer in all kinds of drops if the molecular diffusivity is multiplied by an empirical factor (9 ). Steiner23,24 checked the method on numerous data points and correlated the effective diffusivity against the system properties. This correlation was for all experiments with a variety of properties such as mass transfer resistance and interfacial tension. Also Temos et al.,17 Mostaedi and Safdari,25 and recently Rahbar et al.8 proposed several empirical correlations for prediction of the enhancement factor in different extraction columns. The method has considerable advantage over direct correlation of the mass transfer coefficient, eliminating difficulties with time dependency and working on the effective diffusivity which is not usually dependent on contact time.23 Here, the overall diffusivity is replaced in eq 5 for Dd. The experimental mass transfer coefficient values were used to find each relevant enhancement factor (or directly overall effective diffusivity). The obtained 9 values are within 4.78 to 33.19. Steiner23,24 has presented a correlation for low transfer rates:

(4)

where kc and kd are local mass transfer coefficients in continuous and dispersed phases. As previously reported,9 the slope of equilibrium distribution curve (m = dC*d /dCc where Cc is solute aqueous phase concentration) at the solute average concentrations in toluene (8.62 g·L−1 ≈ 1.0 wt %), and within the temperature range, is nil; that is, acetic acid tends strongly to stay in the aqueous phase. Therefore, mass transfer resistance exists totally in the dispersed phase, that is, Kod ≈ kd.8,20 In an attractive method in modeling which has been adopted, the molecular diffusivity (Dd) in Newman’s equation:

9 = 1 + 0.177Re

⎡ μ ⎤0.89 c ⎢ ⎥ Scd 0.23 ⎢⎣ μc + μd ⎥⎦

0.43

(6)

where Scd = μd/ρdDd is the Schmidt number based on dispersed phase properties. This equation is applicable if the resulting effective diffusivity 9 is smaller than about 10. It is comparable to the empirical equation of Skelland and Wellek26 for direct correlation of the mass-transfer coefficient in nonoscillating drops. 7370



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For higher Reynolds numbers the effective diffusivity increases rapidly and can reach values up to 100. For high transfer rates the correlation given by Steiner is 1.42 ⎡ 2μc ⎤ ⎥ Scd 0.67Eo 0.12 9 = 5.56 × 10 ⎢Re ̈ ⎢⎣ μc + μd ⎥⎦

■

(7)

Using the above correlations would not provide a satisfactory agreement (maximum Kod relative deviation of ±41.5%). Keeping the dimensionless variables and the exponents, these correlations therefore were used for modeling 9 values in this work. The data were nicely reproduced with correlations: (for 9 < 10) (8)

⎡ 2μc ⎤ ⎥ 9 = 9.66 × 10−5⎢Re ⎢⎣ μc + μd ⎥⎦

1.42

Scd 0.67Eo 0.12 ̈

(for 9 < 10)

(9) 2

while the so-called coefficient of determination, R values were 0.957 and 0.922 for the above equations, respectively. The maximum relative deviation of these values is ±19.2% (except five data with more deviations). Applying the modified Newman equation accompanied with eqs 8 and 9 provides Kod values with R2 value of 0.933 and a maximum relative deviation of ±13.3% (except five data with more deviations). This deviation is thought to be sufficient, considering an experimental error of approximately ±5% in Kod values. Figure 10 shows the agreement between experimental and calculated values. The Newman equation in its new form can therefore be used satisfactorily to predict the overall mass transfer coefficient with the influence of temperature.

NOMENCLATURE C = solute concentration (g·L−1) c = viscometer constant d = drop diameter (mm) D = diffusivity (m2·s−1) E = extraction fraction Eö = Eötvös dimensionless number (gΔρd2/γ) H = dimensionless group defined by Grace et al. k = viscometer constant, local mass transfer coefficient (μm·s−1) Kod = overall mass transfer coefficient (μm·s−1) m = solute distribution coefficient M = Morton dimensionless number (gμc4Δρ/ρc2γ3) NPG = inverse of Morton dimensionless number R2 = coefficient of determination Re = drop Reynolds number (ρcutd/μc) Sc = Schmidt number based on dispersed phase (μd/ρdDd) T = temperature (°C) t = drops contact time and efflux time in viscometer (s) ut = terminal velocity (m·s−1) We = drop Weber number (ρcut2d/γ)

Greek Symbols 9 enhancement factor in diffusivity γ interfacial tension (mN·m−1) μ viscosity (mPa·s−1) ρ density (kg·m−3) Δ difference Subscripts c continuous phase, critical size d dispersed phase f final value i initial value m molecular o organic oe overall effective od overall dispersed value t terminal w water Superscript * equilibrium

4. CONCLUSIONS The overall mass transfer coefficient of drops significantly increases (average 93.6%) with an increase of temperature from 15 to 40 °C. Therefore, employing higher available temperatures in extraction columns will cause a more effective extraction process. The most responsible parameter for this enhancement is the molecular diffusivity in drops which increases significantly with temperature. With a less pronounced effect, an increase in temperature alters the hydrodynamic performance, including a decrease in both drop size and contact time, which can be attributed to the variations in the system's physical properties. Modeling based on experimental data can be done using an effective diffusivity in Newman’s equation for accurate prediction of the overall mass transfer coefficient, and an empirical correlation for the prediction of the enhancement factor in diffusivity was developed based on Steiner’s previous model. This study looks at the significant influence of temperature on these processes. The remaining important job will be to find an optimum operating temperature while economic criteria is taken into account.

■

ACKNOWLEDGMENTS

The authors wish to acknowledge the university authorities for providing the financial support to carry out this work.

−5

⎡ μ ⎤0.89 c ⎥ Scd 0.23 9 = 1 + 1.529Re 0.43⎢ ⎢⎣ μc + μd ⎥⎦

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REFERENCES

(1) Saien, J.; Daliri, S. Mass transfer coefficient in liquid−liquid extraction and the influence of aqueous phase pH. Ind. Eng. Chem. Res. 2008, 47, 171−175. (2) Saien, J.; Riazikhah, M.; Ashrafizadeh, S. N. Comparative investigations on the effects of contamination and mass transfer direction in liquid−liquid extraction. Ind. Eng. Chem. Res. 2006, 45, 1434−1440. (3) Saien, J.; Rezabeigy, S. Alternative influence of binary surfactant mixtures on the rate of mass transfer in a liquid−liquid extraction process. Ind. Eng. Chem. Res. 2011, 50, 6925−6932. (4) Saien, J.; Ashrafi, F. Mass transfer enhancement in liquid− liquid extraction with very dilute aqueous salt solutions. Ind. Eng. Chem. Res. 2009, 48, 10008−10014. (5) Palma, M. S. A.; Shibata, C.; Paiva, J. L.; Zilli, M.; Converti, A. Batch liquid−liquid extraction of phenol from aqueous solutions. Chem. Eng. Technol. 2010, 33, 39−43.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +98 811 8282807. Fax: +98 811 8257407. E-mail: saien@ basu.ac.ir. Notes

The authors declare no competing financial interest. 7371



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Mass Transfer from Single Drops and the Influence of Temperature

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