Mass Transfer from Nanofluid Single Drops in LiquidâLiquid Extraction

Article pubs.acs.org/IECR

Mass Transfer from Nanofluid Single Drops in Liquid−Liquid Extraction Process Javad Saien* and Hamid Bamdadi Department of Applied Chemistry, Bu-Ali Sina University, 65174 Hamedan, Iran ABSTRACT: This investigation is focused on the behavior of nanofluid single drops in the liquid−liquid extraction process. The chemical system of toluene−acetic acid−water was used, and the drops were organic nanofluids containing magnetite or alumina nanoparticles. Synthesized nanoparticles were modified with fatty acids for hydrophobicity and ease of dispersion in the organic phase and were then characterized using different methods. Maximum enhancements in the rate of mass transfer of 157% and 121% were achieved using about 0.002 wt % magnetite and alumina nanoparticles, respectively; however, a decreasing variation was observed at higher concentrations. The microconvection and particle aggregation due to the interpenetration layers can provide this kind of variation. For the aim of modeling, the determined enhancement factors were correlated with an empirical expression that can be used, together with the Newman equation, for the prediction of the overall mass-transfer coefficient. al.4 and Nagy et al.,9 for instance, reported that mass transfer in oxygen bubbles is enhanced by up to 600% upon addition of 1 vol % Fe3O4 and by up to 200% upon addition of 10 vol % 65nm n-hexadecane nanoparticles in the liquid phase. Despite these favorable results, Wen et al.10 reported that gas−liquid mass transfer was unexpectedly reduced in the presence of TiO2 nanoparticles. This behavior was attributed to both a reduction of the residence time and a tendency for bubbles to coalesce, leading to a smaller total gas−liquid interfacial area. In most works that have reported mass-transfer enhancement, the results have been attributed to microconvection caused by Brownian motion. Despite its important role and wide application, there have been limited attempts to use nanofluids in liquid−liquid extraction. Recent studies include the work of Bahmanyar et al.,11 who investigated the effects of nanofluids on the performance of a pulsed liquid−liquid extraction column and found that the mass-transfer coefficient increased by 4−60% using 0.01−0.1 vol % SiO2 nanoparticles in kerosene, which was used as the dispersed phase in an aqueous continuous phase. A fundamental approach is attempted in this research to determine the influence of modified magnetite (Fe3O4) and alumina (Al2O3) nanoparticles on the liquid−liquid extraction process. Single-drop experiments in an extraction column were performed, and hydrodynamic characteristics such as drop size and terminal velocity were first determined while the physical properties were changed. The rate of mass transfer was then investigated by measuring the drop solute concentration for a specified distance in the column. The provided data were correlated for use in practical applications.

1. INTRODUCTION Nanofluids have attracted a great attention in recent years as effective working fluids in heat- and mass-transfer enhancement. A nanofluid consists of a base liquid and a suspended nanosize agent such as metallic or nonmetallic (Cu, Al2O3, SiO2, TiO2, Fe3O4, etc.) nanoparticles. In the past decade, with the aim of achieving lower operating costs, better performance, higher energy efficiency, and rapid advances in nanotechnology, a large number of investigations have been carried out using nanofluids in different heat- and mass-transfer applications. For instance, in the field of heat transfer, it has been shown that adding negligible amounts of nanoparticles (less than 1 vol %) can cause the thermal conductivity of fluids to increase by up to a factor of approximately 2.1 Meanwhile, increases in thermal conductivity within the range of 15−150% have been reported for the addition of 0.001−7.5 vol % nanoparticles.2 Lower enhancement levels in thermal conductivity with inorganic nanoparticles have also been reported. In this regard, Buongiorno et al.3 analyzed many data sets from different international sources. The potential application of nanofluids to mass transfer has not yet been exploited much.4 In fact, successes in applying nanoparticles to enhance heat transfer promote investigations into the potential application of nanofluids in mass transfer.5 Recent attempts include the work of Krishnamurthy et al.,6 who observed that diffusion of a dye droplet in water-based nanofluids increased upon use of 20-nm Al2O3 particles, and the work of Fang et al.,7 who used different volume fractions of florescent rhodamine B in Cu−water nanofluids at different temperatures and observed that mass diffusion in water with 0.5 vol % Cu nanoparticles increased by up to 10.71 times compared to that in just deionized water. Similarly, Veilleux and Coulombe studied the mass diffusion of rhodamine 6G in water-based alumina nanofluids and repoted a mass diffusivity enhancement that reached an order of magnitude.8 In a majority of studies dealing with gas−liquid systems, advantages of using nanofluids have been reported.3,7−10 Olle et © 2012 American Chemical Society

Received: Revised: Accepted: Published: 5157

February 3, 2012 March 15, 2012 March 20, 2012 March 20, 2012 dx.doi.org/10.1021/ie300291k | Ind. Eng. Chem. Res. 2012, 51, 5157−5166

Industrial & Engineering Chemistry Research

Article

2. EXPERIMENTAL SECTION 2.1. Materials. The chemical system of toluene−acetic acid−water,11,12 which has a high interfacial tension, was used. Toluene and acetic acid were Merck products with purities of more than 99.9%. Deionized water of high quality was used as the continuous phase. For Fe3O4 nanoparticle preparation, ferric chloride anhydrous (FeCl3), ferrous chloride tetrahydrate (FeCl2·4H2O), ammonium hydroxide (28−30% NH3), and oleic acid (ultrapure) were all purchased from Merck. Alumina (γ-type) nanoparticles with a full particle size range of 5−150 nm were supplied by Plasmachem GmbH. For alumina modification, chloroform with a purity of 99.9% and palmitic acid (ultrapure) were purchased from Merck and BDH, respectively. 2.2. Synthesis of Single-Layer-Coated Fe3O4 Nanoparticles. Metal or metal oxide nanoparticles exhibit unique features compared to their equivalent larger-scale materials. However, the surface of oxide nanoparticles is hydrophilic and incompatible with nonpolar organic liquids. For applications, it is therefore important to stabilize or functionalize such nanoparticles. Hydrophobic particles are usually achieved by attaching long-chain molecules, particularly those containing a polar group and a tail with dielectric properties, to the surface of nanoparticles.13,14 The resulting product is easily dispersed in nonpolar carrier liquids.15 According to the procedure of Ramirez and Landfester,16 the magnetite particles were first produced by coprecipitation from an aqueous Fe3+/Fe2+ solution, using concentrated ammonium hydroxide in excess. Samples of 14.6 g of FeCl3 and 12.0 g of FeCl2·4H2O were dissolved in 50 mL of distilled water, and 40 mL of ammonium hydroxide was added rapidly. After coprecipitation of magnetite particles, 3 g of oleic acid was added, and the suspension was heated to 70 °C for 30 min. Then, the temperature was increased to 110 °C to evaporate the water and excess ammonium. The black lump-like residuum was cooled to room temperature and then washed several times with distilled water and with ethanol to remove the excess oleic acid. The modified product was obtained after the samples had completed drying. 2.3. Synthesis of Single-Layer-Coated Al2O3 Nanoparticles. A measured 0.25 g of palmitic acid was dissolved in 200 mL of chloroform at room temperature, and the solution was added to a three-necked distillation flask. Then, 5 g of nanoalumina was added, and mixing was initiated. The modified product was obtained by filtering, drying, and grinding. Finally, the chloroform solvent was evaporated and recycled from the filtrate that mainly contained chloroform and unreacted modifier.17 2.4. Analysis and Characterization of Nanoparticles. The product morphology was observed by scanning electron microscopy (SEM, WEGA II TESCAN). For this purpose, a 0.01 wt % particle suspension was placed on a coated gold grid and dried in air before SEM observations. The crystal structure of the magnetic particles was also determined using X-ray diffraction (XRD, ITAL-Structures-APD 2000, Cu Kα1 X-ray source). The bonding structure of the covering oleic and palmitic acids on the nanoparticle surface was investigated by Fourier transform infrared (FT-IR) spectrometry (PerkinElmer Spectrum 65). Meanwhile, all nanoparticles, both before and after modification, were dried and pelletized with KBr powder for the FT-IR study. Furthermore, the colloidal stability of the nanofluids (toluene + nanoparticle) was investigated by

monitoring the change in sample UV absorbance with time. A UV−visible spectrophotometer (JASCO V-630) was used in the beam absorbance at maximum wavelengths of 300 and 302 nm for magnetite and alumina nanofluids, respectively. 2.5. Preparation of Nanofluids. The two-step nanofluid preparation method18 was used, because it works well for oxide nanopowders. In this method, the prepared nanoparticles are dispersed in toluene containing acetic acid. The nanofluids are then sonicated to break up any potential clusters of nanoparticles. Nanoparticles were used with concentrations of either magnetite or alumina of 0.0005, 0.001, 0.002, 0.003, 0.004, and 0.005 wt %. 2.6. Physical Properties of the Chemical System. The physical properties of the systems at 20 °C are given in Table 1. Table 1. Physical Properties of the Chemical Systems at 20 °Ca dispersed phase with property ρ (kg·m−3) μ (mPa·s−1) D × 1010 b (m2·s−1) a b

Fe3O4

Al2O3

873.05−876.69 0.589−0.597 30.5

873.05−876.36 0.589−0.595

continuous phase 998.17 1.003 11.9

Interfacial tension of the pure toluene/water system, γ = 39.5 mN/m. For the pure chemical system.

Molecular diffusivities were calculated from the correlation by Wilke and Chang.19 The drop weight method was used to measure the interfacial tensions.20 The interfacial tension did not vary markedly within the range of nanoparticle concentrations used, in agreement with the results reported recently by Fan et al.21 Regarding the variation of viscosity with nanoparticle addition, this property was measured for the dispersed phase. An Ubbleohde viscometer with an uncertainty of ±2 × 10−3 mPa·s was used. The equation for viscosity, according to Poiseuille’s law, is22 ⎛ c⎞ μ = ρ⎜kt − ⎟ ⎝ t⎠

(1)

where μ, ρ, and t are the dynamic viscosity, density and efflux time, respectively, and k and c are the viscometer constants. A calibrated Anton Parr DMA 4500 instrument, provided with automatic viscosity correction was used to measure the densities of the pure compounds. The uncertainty for density measurements was ±0.01 kg·m−3. The temperature in the cell was regulated to ±0.01 °C with a solid-state thermostat. The k and c parameters were obtained by measurements on deionized water and benzene. To obtain the densities of the nanofluids, the equation for density of two-phase mixtures of nanofluids23 was used ρnf = ρpϕ + ρ bf (1 − ϕ)

(2)

where ρnf is the density of the nanofluid, ϕ is the particle volume concentration, ρp is the density of the particles (5160 kg·m−3 for magnetite16 and 3580 kg·m−3 for alumina24), and ρbf 5158

dx.doi.org/10.1021/ie300291k | Ind. Eng. Chem. Res. 2012, 51, 5157−5166


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is the density of the base fluid (867.51 kg·m−3). The volume fraction (ϕ) was calculated as ⎡ ⎤ ω pρ bf ⎥ ϕ=⎢ ⎢⎣ ω pρ bf + ρp(1 − ω p) ⎥⎦

system agree well with the previously reported results.25 Adding nanoparticles to the organic phase leads the acetic acid to have a higher tendency toward the organic phase. 2.8. Experimental Setup and Operating Procedure. The experimental setup was described in our previous works.22,26,27 A Pyrex glass column (11.4-cm diameter and 51-cm height) was used as the contactor. Formation of different drop sizes was provided using a variety of glass nozzles. The outside diameter of the nozzles was typically about 0.3 mm. The toluene-phase nanofluid was held in a glass syringe, using an adjustable syringe pump (JMS SP-500) and flowed through a glass nozzle into the column while filled with aqueous phase. A small inverted glass funnel connected to a pipet was used to catch samples of about 1 mL of dispersed phase at the top of the column with 33 cm from the initial point. The interfacial area in the funnel was minimized at the level of the pipet inlet. Three samples were prepared for each concentration and were immediately analyzed by titration with NaOH. To omit the influence of unsteady mass transfer during drop formation and its transient rise velocity, the initial drop concentration was considered for a location of moving drops at 6.5 cm above the nozzles’ tip. Drop motion was observed to reach steady movement after about 40 mm of travel. To determine the initial concentrations, a small column equipped with the same nozzle was used. Drops were collected at the same distance of 6.5 cm and under the same conditions and drop sizes as in the main column. Experiments were conducted in the mass-transfer direction from the dispersed phase to the continuous phase. The syringe and connection tube to the nozzle tip were first filled with toluene + acetic acid to produce drops. The initial and final acetic acid concentrations were in the ranges 1.8−2.5 and 0.4−1.36 wt %, respectively. For each experimental run, the initial and final concentrations, drop size, and contact time were obtained. Moving drops were spaced more than 60 mm apart. The size of drops was determined by knowing the flow rate and the number of drops per a specified period. All equipment and glassware were cleaned with deionized water prior to experiments. The contact time of drops from the initial point to the collection point was measured several times with a stopwatch. The terminal velocity was calculated using the time required for drops to travel the distance in the apparatus. All experiments were conducted at the ambient temperature of 20 ± 2 °C. It has to be mentioned that separate experiments with nanofluids and acetic acid in a batch flask showed no change in acetic acid content at different times. This indicates that no solute adsorption by modified nanoparticles occurred.

(3)

where ωp is the weight fraction of particles. The variation in solution viscosity with nanoparticle concentration is presented in Figure 1. The nanofluid viscosity shows a very low increase

Figure 1. Variation of nanofluid viscosity with concentration of nanoparticles at 20 °C.

upon particle addition. The total increase within the range of conditions used was less than 1%. 2.7. Equilibrium Solute Distribution. The acetic acid equilibrium distribution between phases and in the presence of different concentrations of nanoparticles was determined. A weighed amount of aqueous solution, containing a known quantity of acetic acid, was mixed with a known amount of solvent in a stopper funnel. Then, organic and aqueous samples were taken and analyzed by titration with NaOH titrant (Merck). The equilibrium distributions of acetic acid between phases in the pure system and in the presence of nanoparticles show nonlinear variations (Figure 2). Equilibrium data for the pure

3. RESULTS AND DISCUSSION 3.1. Material Characterizations. Figure 3 shows SEM images of the modified magnetite and alumina nanoparticles. A high uniformity in the spherical particles is observed. An average size of 17 nm for Fe3O4 and 30 nm for Al2O3 nanoparticles are relevant. Meanwhile, XRD spectra are presented in Figure 4. The XRD pattern of magnetite nanoparticles agrees with those in a previous report.28 The particle diameter calculated by Scherrer’s equation from the XRD results was 10 nm for Fe3O4 and 25 nm for Al2O3 nanoparticles. Different average particle sizes have been reported in previous works using these methods.29,30

Figure 2. Equilibrium distribution of acetic acid between phases at 20 °C. 5159



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Figure 3. SEM images of modified (a) magnetite and (b) alumina nanoparticles.

Figure 4. XRD patterns of the modified (a) magnetite and (b) alumina nanoparticles.

Figure 5a shows the FT-IR spectra of Fe3O4 nanoparticles modified with oleic acid as well as bare Fe3O4 nanoparticles. Three bands at 586, 1637, and 3400 cm−1 appeared for the bare Fe3O4 nanoparticles. The band at 586 cm−1 corresponds to the vibration of the Fe−O bond in the crystalline lattice of Fe3O4. During the preparation of Fe3O4 nanoparticles by chemical coprecipitation, the particle surfaces are readily covered with hydroxyl groups in the aqueous medium. Thus, the characteristic bands of hydroxyl groups, 1637 and 3400 cm−1, appeared in the FT-IR spectrum of the bare Fe3O4 nanoparticles.15 Compared with the spectrum of the bare Fe3O4 nanoparticles, five new bands at 1408.9, 1437, 1521, 2850, and 2920 cm−1 appeared in the spectrum of Fe3O4 nanoparticles modified with oleic acid. The band at 1408.9 cm−1 corresponds to the CH3 umbrella mode of oleic acid. The two bands at 1437 and 1521 cm−1 are attributable to the asymmetric (−COO¯) and symmetric (−COO¯) stretch vibration bands, respectively.15 The bands at 2850 and 2920 cm−1 are due to the asymmetric and symmetric CH2 stretches in oleic acid, respectively.15

Figure 5b shows the FT-IR spectra of Al2O3 nanoparticles modified with palmitic acid as well as bare Al2O3 nanoparticles. Alumina nanoparticles indicate a strong metal−oxygen (Al−O) adsorption band at 630.4 cm−1.31 Compared to bare nanoscale Al2O3, in addition to the characteristic adsorption peaks of palmitic acid, the strong peaks appearing at about 2850 and 2918 cm−1 are due to stretching vibrations of methyl and methylene from bonds on the surface of Al2O3.17 3.2. Nanofluid Stability. Nanofluids can experience a lack of stable dispersion as a result of sedimentation of nanoparticles. The stability of the nanofluids in this work was investigated with respect to the sediment time based on UV− vis absorbance values at the maximum wavelength (section 2.4). As illustrated in Figure 6, the relative absorbance, A/A0 (where A0 is the absorbance just after preparation of the nanofluid), decreases with increasing sediment time. However, the colloidal stability of the nanofluids was maintained at over 95% after 110 min, indicating a satisfactory stability of the nanofluids.11 The run times in this work did not exceed 25 min after preparation of the nanofluids. 5160



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Figure 5. FT-IR spectra of (a) modified magnetite (I) and its bare nanoparticles (II) and (b) modified alumina (I) and its bare nanoparticles (II).

3.3. Hydrodynamic Investigations. The generated drop sizes were within the ranges 2.9−4.1 mm with magnetite nanoparticles and 3.2−4.3 mm with alumina nanoparticles. The size of the drops did not change much when different concentrations of either type of nanoparticles were used

because of the nearly constant interfacial tension and other physical properties of the phases (Table 1). Meanwhile, the generated drops were slightly larger with alumina nanoparticles under similar conditions. The correlation of Grace et al.32 for terminal velocity (Vt) was used for comparison with experimental results μ Vt = c [(J − 0.857)/M 0.149] dρc (4) where d, μc, and ρc represent the drop size, viscosity, and density of the continuous phase, respectively. The parameter J is given by J = 3.42H 0.757

(H > 59.3)

(5)

⎛ μ ⎞−0.14 4 − 0.149 ⎜⎜ c ⎟⎟ H = Eo ̈ × M 3 ⎝ μw ⎠

(6)

and H is defined as

where μw is the viscosity of water at 4 °C. The Morton number (M) and Eötvös number (Eö) are two dimensionless numbers that are defined as M = gμc4Δρ/ρc2γ3 and Eö = gΔρd2/γ. The

Figure 6. Relative absorbance of nanofluids versus sediment time. 5161



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value of 59.3 for H corresponds, approximately, to the transition between circulating and oscillating drops. The H values for the drops in this work lie in the range 10.85 < H ≤ 32.66; the Weber number values (We = dVt2ρc/γ), within the range 0.36−0.72 (less than 3.58); and the values of the ratio Re/NPG0.15 (where NPG is the inverse of the Morton number), within the range 5.02−8.29 (less than 20). All of these criteria indicate circulating drops.32 For circulating drops, as the drop size increases, the terminal velocity increases. Figure 7 shows that the measured terminal

Figure 8. Overall mass-transfer coefficient versus concentration for both nanoparticles with similar nozzles.

the overall mass-transfer coefficient with nanoparticle concentration for typical nozzles that provide nearly the same drop sizes. The rate of mass transfer rises to an average of about 72% (157% for the smallest drop and 46% for the largest) with magnetite and 75% (121% for the smallest and 55% for the largest) with alumina, each with appropriate drop size ranges for concentrations up to about 0.002 wt %. A decreasing variation after this optimum point then occurred upon addition of extra amounts of nanoparticles. Note that the extraction fraction exhibited approximately the same variations as a function of the nanofluid concentration. The Kod variations can be discussed in terms of the microconvection induced by Brownian motion. Brownian motion is one of the factors affecting mass and heat transfer in nanofluids. It is basically the random dynamic mode of particles in a liquid where the particles move and collide with each other.34 Different processes have usually been introduced as the dominant mechanisms in nonofluid heat and mass transfer, namely, (i) Brownian motion of nanoparticles and subsequent microconvection and (ii) aggregation and clustering. A number of investigators have reported that Brownian motion of nanoparticles is the main mechanism controlling the thermal conductivity of nanofluids.35 It has also been confirmed that nanofluids composed of smaller particles experience greater enhancement in thermal conductivity than larger particles.35,36 Smaller particles display a higher level of Brownian motion than larger particles, because of easier movement. In a quiescent liquid, small particles are expected to fluctuate about a mean path because of Brownian motion. The movement of particles subsequently causes momentum transfer and a continuous change in velocity with distance. Thus, the disturbance field created by the motion of the nanoparticles causes a convective motion. Considering this liquid flow around the moving particles and its possible effect on mass transport, some researchers, among them Krishnamorty et al.6 and Fang et al.,6 measured the diffusion coefficients of particles in liquids. In the mass-transfer field, Krishnamorty et al.7 and Prasher et al.37,38 pointed out that the Brownian motion of particles, by itself, could not contribute directly to the mass-transfer enhancement; however, the main reason for mass-transfer enhancement has been introduced as the microconvection caused by Brownian motion.

Figure 7. Comparison between experimental terminal velocities and the Grace correlation for both nanofluids.

velocities are to some extent less than those predicted by the Grace correlation. This difference can be attributed to the masstransfer situation. Henschke and Pfennig33 demonstrated the influence of mass transfer on the terminal velocity and explained, as a more plausible reason, that mass-transferinduced turbulence inside the drops leads to a stochastic and irregular movement of the interface, which causes the drops to slow. Another reason is that the Grace equation might not be consistent for nanofluids. 3.4. Mass-Transfer Investigations. The rate of mass transfer for a drop of size d can be obtained from the overall mass-transfer coefficient. Considering mass transfer during the measured contact time, the overall dispersed-phase masstransfer coefficient is calculated from the equation K od = −

d ln(1 − E) 6t

(7)

where E is the extraction fraction, defined as E=

Cdi − Cdf Cdi − Cd*

(8)

where Cdi, Cdf, and Cd* are the drop-side initial, final, and equilibrium solute concentrations, respectively. The extraction fraction (E) is the ratio of the amount of material transferred to the maximum amount transferable. For dispersed-to-continuous phase mass transfer, Cd* = 0, because the solute concentration in the aqueous phase is zero. 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 7 is, in fact, a time-averaged mass-transfer coefficient over the contact time. The obtained Kod values are within the ranges 32.9−211.3 μm·s−1 with magnetite nanoparticles and 46.1−210.4 μm·s−1 with alumina nanoparticles. Figure 8 presents the variations of 5162



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A similar type of variations was recently reported for the mass diffusion of rhodamine 6G and attributed to significant interactions among nanoparticles and the resulting reduction in the particles’ root-mean-square velocity, which, in turn, causes a lower contribution of the nanoparticle Brownian motion to mass transfer.8 The variation of the mass-transfer coefficient with drop size is presented in Figure 9 for both nanofluids. As shown, the mass transfer increases with drop size within the investigated range. This behavior can be explained in terms of eqs 7 and 8. Larger drops provide more internal circulation or turbulence and, therefore, easier mass transfer per unit time. At the same time, a higher terminal velocity results in a lower residence time for a specified length of traveling in the column, so a higher overall mass-transfer coefficient is expected. As is obvious in Figure 8, using magnetite nanoparticles provides better performance for concentrations less than about 0.002 wt %, and the opposite is true for concentrations greater than this value. 3.5. Modeling of Results. The effect of nanoparticles on the rate of mass transfer can be expressed in terms of masstransfer-coefficient equations. A widely used procedure is to employ Whitman two-film theory where individual masstransfer coefficients are related through the slope of equilibrium solute distribution curve. Because of the negligible continuousphase resistance within the concentration range used (Cd < 2.5 wt %), mass-transfer resistance mostly existed in the dispersed phase (i.e., Kod ≈ kd) for the system in this work.40 In an attractive method in modeling, the molecular diffusivity (Dd) in the Newman equation

The root-mean-square velocity of a Brownian particle can be calculated as9

v=

3k bT mp

(9)

where kb, T, and mp are the Boltzmann constant, absolute temperature, and mass of a nanoparticle, respectively. According to this equation and the densities of the nanoparticles used in this work (higher for magnetite), the velocity of the magnetite particles was about twice that of the alumina particles; therefore, a higher mass-transfer rate was induced with magnetite nanoparticles, as reflected in Figure 9 in the

Figure 9. Variation of overall mass-transfer coefficient with drop size for different nanoparticle concentrations.

⎡ ∞ ⎛ −4π 2n2D t ⎞⎤ −d ⎢ 6 1 d ⎟⎥ kd = ln 2 ∑ 2 exp⎜⎜ ⎟⎥ 2 ⎢ 6t ⎣ π d ⎝ ⎠⎦ n=1 n

ascending variation of the curves. As stated by Nagy et al.,9 the distance between particles is much less than the thickness of the moving fluid boundary layer around each particle (even at very low particle volume fractions). Therefore, the flow fields around nanoparticles will interact; this can create increased momentum transfer because of increased velocity gradients in the boundary layers, and consequently, it can increase the mass transfer in a nanofluid. The rate of mass transfer exhibits a decrease above the optimum concentration of 0.002 wt %. One possible influencing mechanism is particle aggregation. An increase in concentration means a decrease in the particle-to-particle separation and a greater possibility of aggregation. As particles approach each other, the tails of the palmitic and oleic acids are physically absorbed on the primary layer by forming an interpenetrating layer with the tails of the primary layer.15 In this regard, Shen et al.39 detected a transition energy between different fatty acids with differential scanning calorimetry and reported that the transition temperature increases gradually with chain length. Increasing the mass through particle aggregation causes the particles to move slowly and decreases microconvection. In this work, we used C16 and C18 hydrocarbon chain fatty acids with different self-interpenetrations. Oleic acid with a longer chain length tends to self-interpenetrate more than palmitic acid. This fact and the higher density of magnetite nanoparticles reduces the velocity of the Brownian motion of magnetite more; therefore, the mass-transfer coefficient decreases more with magnetite than with alumina when the nanoparticle concentrations are more than about 0.002 wt %.

(10)

is replaced by an overall effective diffusivity, Doe = ℛDd, where ℛ is an enhancement factor that is based on experimental data and is usually derived from empirical correlations. Sherwood et al.41 were the first to use this approach, and they pointed out that the equation for radial diffusion in a rigid sphere42 can be used for mass transfer in all kinds of drops if the molecular diffusivity is multiplied by the empirical factor ℛ. Steiner et al.41,43 checked this method on numerous data points and correlated the effective diffusivity with the system properties. Recent works using this method include predictions of masstransfer coefficients in a pulsed packed extraction column44 and in a regular packed extraction column.40 Accordingly, each experimental mass-transfer coefficient value was used to determine the relevant enhancement factor when used in the Newman equation. The obtained ℛ values are within the ranges 2.4−24.9 with magnetite nanoparticles and 4.1−26.6 with alumina nanoparticles. A quick review of the enhancement factors revealed that this parameter depends nonlinearly on drop size and nanoparticle concentration, with trends similar to the variations observed in Kod. The relationship can be developed in dimensionless variables consistent with the enhancement factor. Two employed appropriate variables are the drop Reynolds number (Re = ρcVtd/μc), based on the continuous-phase physical properties, and the l/a ratio in the form45 ⎛ 4π ⎞1/3 l =⎜ ⎟ −2 a ⎝ 3ϕ ⎠ 5163

(11)



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have relative deviations (100 × |Kod,exp−Kod,cal|/Kod,exp) within ±18% (except for four data points) for both types of nanoparticles used (Figure 11). This deviation is thought to

where l is the average distance of nanoparticles from each other, a is the radius of the nanoparticles, and ϕ is the particle volume fraction (eq 3). The ratio l/a can be used as a direct indication of the nanoparticle concentration. A correlation with a thirdorder polynomial function for l/a and a simple quadratic function for Re is applicable in this regard and the provided data are nicely reproduced with the expression ⎡ ⎛l⎞ ⎛ l ⎞2 ⎛ l ⎞3⎤ 9 = ⎢c1 + c 2⎜ ⎟ + c3⎜ ⎟ + c4⎜ ⎟ ⎥Re 2 ⎝a⎠ ⎝a⎠ ⎝ a ⎠ ⎥⎦ ⎢⎣

(12)

where c1−c4 are the equation parameters. The third-order polynomial considered for the parameter l/a is due to the asymmetric parabola-like variation with this term. Equation 12 was fitted with the experimental data, and no correlation was imposed among the parameters considering their significance. The appropriate obtained values of the parameters along with the regression coefficients are reported in Table 2. Figure 10 shows the goodness of fit obtained with the data for the nanofluids. Table 2. Parameters of Equation 12 nanoparticle

c1 × 10−3

c2 × 10−4

c3 × 10−6

c4 × 10−8

R2

Fe3O4 Al2O3

−2.335 −4.917

1.473 3.931

−2.743 −9.802

1.635 7.933

0.966 0.968

Figure 11. Comparison of experimental and calculated overall masstransfer coefficients.

Equation 12 is applicable for circulating drops moving in an aqueous medium containing one of the nanoparticles. Use of the Newman model along with eq 12 provides Kod values that

be sufficient considering an experimental error of approximately 5% in Kod values. The model can therefore be used satisfactorily to predict the rate of mass transfer in the presence of nanoparticles.

4. CONCLUSIONS The advantage of using low-concentration organic nanofluids as the dispersed phase in liquid−liquid extraction was revealed. Drop sizes within the range 2.9−4.3 mm, with magnetite and alumina nanoparticle concentrations of 0.0005−0.005 wt %, were examined. The size of the generated drops was not found to be influenced much by the nanoparticles; however, the rate of mass transfer was found to exhibit an increasing and then decreasing variation due to microconvection induced by Brownian motion and presumably particle aggregation, respectively. The optimum mass-transfer enhancement was achieved at a nanoparticle concentration of 0.002 wt %, at which average enhancements of 72% and 75% were achieved with magnetite and alumina, respectively, compared with nanoparticle-free results. Small drops were found to experience greater enhancement in this regard. Magnetite was found to have a stronger effect than alumina for concentrations less than the optimum value; however, this order reversed for concentrations greater than the optimum value. A practical model for the drop mass-transfer coefficient, based on effective diffusivity, accurately predicted the rate of mass transfer over a wide range of drop sizes and nanoparticle concentrations.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +98 811 8282807. Fax: +98 811 8257407. E-mail: [email protected].

Figure 10. Variation of enhancement factor versus drop size and l/a parameter for (a) magnetite and (b) alumina nanoparticles.

Notes

The authors declare no competing financial interest. 5164



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We express thanks to the university authorities for providing the financial support to carry out this work.

a =radius of nanoparticles (nm) A =absorbance 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 Kod =overall mass-transfer coefficient (μm·s−1) l =avereage distance between nanoparticles (nm) m =distribution coefficient M =Morton dimensionless number (gμc4Δρ/ρc2γ3) NPG =inverse of the Morton dimensionless number R2 =coefficient of determination Re =drop Reynolds number (ρcutd/μc) t =drop contact time and efflux time in the viscometer (s) Vt =terminal velocity (m·s−1) We =drop Weber number (ρcut2d/γ)

Greek Symbols

γ =interfacial tension (mN·m−1) Δ =difference μ =viscosity (mPa·s−1) ρ =density (kg·m−3) ϕ =particle volume concentration ω =weight fraction Subscripts

bf =base fluid c =continuous phase d =dispersed phase f =final value i =initial value nf =nanofluid od =overall dispersed value p =particle w =water Superscript

* =equilibrium

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