- Email: [email protected]
Investigation the effect of super hydrophobic titania nanoparticles on the mass transfer performance of single drop liquid-liquid extraction process
Separation and Purification Technology 176 (2017) 107–119
Contents lists available at ScienceDirect
Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Investigation the effect of super hydrophobic titania nanoparticles on the mass transfer performance of single drop liquid-liquid extraction process Ashkan Hatami a,⇑, Dariush Bastani a, Farhood Najafi b a b
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Department of Resin and Additives, Institute for Color Science and Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 23 May 2016 Received in revised form 13 November 2016 Accepted 20 November 2016 Available online 27 November 2016 Keywords: Liquid-liquid extraction Titania nanoparticles Single drop Synthesis Mass transfer
a b s t r a c t Hydrophobic titania nanoparticles were synthesized by a novel in situ sol-gel method and applied in a single drop liquid-liquid extraction column to enhance the overall dispersed-phase mass transfer coefficient (Kod). The chemical system of toluene, acetic acid and water was used, and the direction of solute (acetic acid) mass transfer was from dispersed phase, including: toluene and acetic acid to the continuous phase of water. For such system, much of the mass transfer resistance exists in the dispersed phase, which is nonpolar organic liquid. Hence, modified titania nanoparticles (MTNP’s), prepared by sol-gel route, in five different concentrations of 0.001–0.005 wt.% were added in the dispersed phase. Also, the impact of MTNP’s at the different solute concentrations and nozzles was investigated. Results indicated an anomalous enhancement in the overall dispersed-phase mass transfer coefficient at 0.002 wt.% of MTNP’s. A maximum enhancement of 70% in the overall mass transfer coefficient was found in droplets formed from a nozzle of 2.5 mm inner diameter, containing 3 wt.% of solute. Eventually, based on the theoretical model of Newman, a semi-empirical model was presented, that is capable to predict the overall dispersed-phase mass transfer coefficient of nanofluids with an average absolute relative error of 8.6%. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Fluids which contain well-dispersed particles with an average size of less than 100 nm, are called nanofluids [1]. Recently, effects of their presence on the transfer phenomena such as heat and mass transfer have been attracted great attention [2]. Once, the improvement of both conductive and convective heat transfer due to the use of nanoparticles was shown [3–6]. Similarity between heat and mass transfer has caused a stimulus for investigating the effect of nanoparticles in the mass transfer operation. Several works have been done on the systems which dealing with the gas and liquid phase, and various improvement effects have been seen due to use of the nanoparticles. Whereas, in case of liquid-liquid extraction process fewer studies have been coducted [2], that have reported increase in the mass transfer coefficients of nanofluids. Bahmanyar et al. [7], used kerosene based SiO2 nanofluids in a pulsed liquid–liquid extraction column (PLLEC). Their chemical system was kerosene, acetic ⇑ Corresponding author. E-mail address: [email protected] (A. Hatami). http://dx.doi.org/10.1016/j.seppur.2016.11.063 1383-5866/Ó 2016 Elsevier B.V. All rights reserved.
acid (solute) and water and solute mass transfer was from the kerosene to the water. Based on the pulsation intensity and the nanoparticles concentration, an increase of 4–60% was found in their work. Saien and Bamdadi [8], investigated the effect of Fe3O4 and Al2O3 nanoparticles in a single drop liquid-liquid extraction column. In their study chemical system was toluene-acetic acid (solute)-water, at the nanoparticles concentration of 0.002 wt.%, the enhancement of solute transfer from dispersed nanofluids (toluene + nanoparticles) was 157% and 121% for magnetite and alumina nanoparticles, respectively. Mirzazadeh Ghanadi et al. [9], used carbon nanotube, ZnO and TiO2 nanoparticles with different concentration in the water, and investigated mass transfer of succinic acid from n-butanol (dispersed phase) to water. They found that, nanoparticles can play a role as a mass transfer promoter in the laminar flow regime of the dispersed phase. Nematbakhsh and RahbarKelishami [10], studied the effect of hydrophobic SiO2 nanoparticles with different particle size of 10, 30 and 80 nm in an irregular packed column with the chemical system of toluene-acetic acid-water. They used various concentrations of those nanoparticles in water, and found that the maximum enhancement in the
108
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Nomenclature dp C C⁄ V Kod k d de dei t E Vt Vnp KB R Dd Doe Re Renf ni
nanoparticle size (nm) solute concentration (mol/m3) equilibrium concentration of solute in dispersed phase (mol/m3) total volume of 200 dropts (m3) overall dispersed mass transfer coefficient (lm=sÞ local mass transfer coefficient droplet diameter (m) equivalent diameter of drop (m) equivalent diameter of drop of ith drop (m) contact time (s) extraction fraction terminal velocity (m/s) velocity of nanoparticles (m/s) Boltzmann constant, =1.3807 1023 J/K enhancement factor, dimensionless molecular diffusivity (m2/s) effective molecular diffusivity (m2/s) drop Reynolds dimensionless number nanofluid Reynolds dimensionless number number of droplets with dei
overall mass transfer coefficient was 42% in 0.05 vol% of the smallest nanoparticles. Ashrafmansouri and Nasr Esfahany [11], investigated the effect of toluene based SiO2 nanofluids on the mass transfer and hydrodynamics characteristics of a spray liquid-liquid extraction column. They observed that, nanofluids have not any sensible effect on the hydrodynamic performance of toluene-acetic acid-water system. However, in 0.001 vol% of that nanoparticles a maximum enhancement of 47% in the overall mass transfer coefficient was detected. Recently, Goodarzi and Nasr Esfahany [12], investigated the effects of the hydrophilic SiO2 nanoparticles in the aqueous phase of toluene-acetic acidwater systems. They reported that when toluene and acetic acid are the dispersed phase, using SiO2 nanoparticles in the water couldn’t enhance the mass transfer rate, even at the concentration of 0.1 vol% of that nanoparticles the overall dispersed phase mass transfer reduced up to 22% in their work. In all the studies in this field, microconvection created due to the Brownian motion of nanoparticles is the most reported possible reason for the anomalous enhancement of mass transfer rate [7–14]. So, it can be more efficient if the nanoparticles would be used in the phase with higher mass transfer resistance. In this investigation, a single drop liquid-liquid extractor as a simple study column, which provides easy and accurate control over the main specification of the extraction process, was chosen and we have focused on the toluene, acetic (solute) and water chemical systems. Solute transfer was from the toluene as the dispersed phase to the water as the continuous phase. In this system major resistance of the mass transfer exists in the dispersed phase [11,12], so nanoparticles should have a good distribution in the toluene. To this end, titania (TiO2) nanoparticles, which has not been used in the dispersed phase, have synthesized and then functionalized through an in situ sol-gel method with using of a silane coupling agent. Aside the titania nanoparticles concentration, the effect of solute concentration and nozzle tip size on the mass transfer performance of the single drop experiments has been investigated. At the end of this work, with modification of the Newman model by experimental data, a semi-empirical model has been proposed for predicting the overall dispersedphase mass transfer coefficient.
E1 CD Sos Ss g
ratio of the major to the minor axis of the oblate spheroid drag coefficient, dimensionless area of an oblate spheroid (m2) area of a sphere which has equal volume of an oblate spheroid (m2) gravity, (m/s2)
Greek symbols l dynamic viscosity (Pa s) q density (kg/m3) c interfacial tension (N/m) m kinematic viscosity (m2/s) U volume fraction Subscripts 0 initial point nf nanofluid np nanoparticles c continuous phase d dispersed phase
2. Experimental 2.1. Materials Toluene and acetic acid with purity above 99.9% were purchased from Merck and ultrapure deionized water was prepared, these materials were used as the chemical extraction systems. To synthesis hydrophobic titania nanoparticles, ultrapure isopropyl alcohol, tetraethyl orthotitanate (purity higher than 95%), citric acid and ammonium hydroxide (25% NH4OH), all supplied from Merck, were used. For surface modifying of nanoparticles, trimethoxi (octyl) silane (octyltrimethoxysilane) with a purity of 96% was prepared from Aldrich.
2.2. Synthesis of super hydrophobic TiO2 nanoparticle Titanium dioxide (TiO2) due to its unusual structural, optical, electronic, magnetic and chemical properties, exhibits wide applications in pigments, UV protection creams, photo-catalysis, solar cells, water and air purification [15–17]. There are some different methods for synthesis of titania nanoparticles such as chemical precipitation, microemulsion, hydrothermal and sol-gel, which among them, sol-gel method is the most preferred procedure to synthesis titania nanoparticles [18]. There would be hydroxyl bonds on the titania nanoparticles synthesized through sol-gel method [19], which makes them as hydrophilic materials with no inclination to distribute in non-polar organic phase [20]. Although TiO2 nanoparticles due to high surface area to volume, have peculiar properties and advantage to bulk or micro sized particles [16], but for the same reason they tend to agglomerate [20,21]. In order to change the nanoparticles hydrophobicity and to prevent them from agglomeration, various methods have been used. Surface chemical modification with organic molecules can be utilized to stabilize nanoparticles efficiently in organic solution [21]. Surface treatment of nanoparticles can be performed during or after the synthesis process, the former one is more time and cost effective, so in this work they have been synthesized and functionalized during an in situ method. Silane coupling agents typically
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
have been applied to surface modificatio of nanoparticles [16,17,20,21]. Trimethoxi (octyl) silane (TMOS) which has nonpolar organic chain with a proper length has been chosen to use as titania functionalizing agent. Based on the literature [16,17,20,21], and our investigations, synthesis of titania nanoparticles follows this procedure: at first 10 g of tetraethyl orthotitanate as titania precursor together with 30.4 g of isopropyl alcohol as a solvent was added to the beaker, which it had been kept under magnetic stirring. After 1 min, to generate a stable colloidal solution, which is called sol, a second mixture of 0.2 g water, 0.05 g of citric acid and 5 g of isopropyl alcohol was added to the stirred solution. For the surface modification of titania nanoparticles, 0.36 g of octyltrimethoxysilane was added to the second mixture. For making polymeric structure which is called gel, pH of the solution was changed by dissolving 23 g of ammonia solution to the sol, so alcohol and water condensation reactions take place. Milky produced solution was stirred for 24 h under ambient air of 25 °C until all of the solvent was vaporized. The dried gel was ground in the form of powders and by using filter paper MTNP’s were washed with deionized water to remove unreacted citric acid. Finally, to achieve dried surface modified titania nanoparticles, they were dried in a vacuum oven at the 120 °C for 2 h. 2.3. Characterization of TiO2 nanoparticles A FT-IR spectrometer (Thermo Nicolet, Nexus670) was used to indicate functional groups. In order to investigate nanoparticles hydrophobicity, 1.5 g of MTNP’s were compressed as a pill and it was placed on a film sample holder, then a 4 ll of water droplet was placed on its surface, subsequently video-based optical contact angle measuring instruments (OCA 15 plus connected to a computer using SCA20 software) was used to measure the contact angle of MTNP’s pill with the water droplet. To determine the morphological structure and to measure the particle size of the magnetite nanoparticles, a scanning electron microscope (Fe-SEM, TESCAN, MIRA 3) was used. A helium pycnometer (AccuPyc 1330) was used to measure the powder density of nanoparticles. 2.4. Preparation of TiO2 nanofluids In order to prepare titania nanofluids, these nanoparticles at the five different concentrations of 0.001, 0.002, 0.003, 0.004 and 0.005 wt.% were added to the two mixtures of toluene and acetic acid. In one mixture acetic acid concentration was 3 wt.% and in another it was 6 wt.%, so in final 10 different titania nanofluids with this two-step method were prepared. Furthermore, an ultrasound bath (Fritsch Ultrasonic, Laborette 17 with frequency of 35 kHz) was used to provide better dispersion of nanoparticles. Each sample was sonicated in the bath for 40 min. 2.5. Nanofluids stability The colloidal stability of the nanofluids (toluene, acetic acid, nanoparticles) was measured by a UVvisible spectrophotometer (JASCO V-630). For each solution containing 3 or 6 wt.% of AA, five samples of nanofluids with different MTNP’s concentration (0.001– 0.005 wt.%) was sonicated and immediately the maximum UV absorbance of those samples was measured. According to the work of Jiand et al. [22], a relation between nanoparticles concentration (i.e. in wt.%) and corresponding peak absorbance was obtained as a linear calibration line. By using these cures (one for 3 wt.% of AA and another for 6 wt.% of it) the nanoparticles relative concentration, i.e. Cnp/Cnp,0 (nanoparticles concentration at each time/initial nanoparticles concentration just after preparation) versus sedimentation time can be determined.
109
2.6. Physical properties of the chemical system at 25 °C Density and viscosity of the chemical system are measured by Anton Paar DMA 4100 M instrument with an uncertainty of 0.05 kg m3 and LAUDA viscometer with an accuracy of 0.5%, respectively. An interfacial tension measuring instrument (IFT 700, Vinci) was applied to determine the interfacial tension of nanofluid drops and water. It measures the IFT in a range of 0.1– 100 mN/m. Based on the numerical solving Young-Laplace equation over to complete shape of drop. A slight increase in all the above mentioned properties was seen due to the presence of nanoparticles. The molecular diffusivity (diffusion coefficient) of acetic acid was taken from the experimental work of Change and Wilke [23]. Table 1 shows the physical properties of chemical systems at 25 °C. 2.7. Experimental setup and procedures Experimental setup is illustrated in Fig. 1. This setup consisted of a Pyrex glass column with internal diameter of 10 cm and height of 55 cm. Dispersed phase was injected into the column with a digital syringe pump through a glass nozzle located at the bottom of the column. During this work two glass nozzles with an inside diameter of 1.5 and 2.5 mm separately were used, which are referred to nozzle no. 1 and 2 respectively. Since the purpose of the present research was only the investigation of the solute mass transfer from the dispersed to continuous phase, there should be no mass transfer between toluene and water. Thus, before starting of mass transfer experiments these materials have been mutually saturated with the each other. The dispersed flow rate was kept at 100 ml/h. To ease of collecting the dispersed phase, an inverted glass funnel connected with a pipette was held on top of the column. The inner diameter of the funnel stem was only 3 mm, hence the interfacial surface area between the dispersed and continuous phase at the funnel was very small. In order to neglect the mass transfer during the drop formation on the nozzle tip and also the unsteady mass transfer, another column with a height of only 5 cm was used. The solute concentration at the top of the little column was considered as the initial concentration for the main column, it was in the range of 520–550 mol/ m3. Through the experiments for each kind of nanofluids, initial and final solute concentrations, the terminal velocity and the drop size were measured. The solute concentration of the collected dispersed phase was measured by titration of 2 ml of those with 0.5 M NaOH, this procedure was repeated five times for each mass transfer experiment and the solute concentration at the top of the column was in the range of 135–525 mol/m3. All the experiments have been conducted at 25 + 0.5 °C. To determine terminal velocity of drops, their contact time with the continuous phase, from initial and final point (t), was measured by stopwatch with an accuracy of 0.003%. Since, the distance between the two points is known (50 cm), terminal velocity of drops (Vt) can be easily measured by Vt = 50/t with uncertainty of 0.003%. The terminal velocity of each droplet was measured 10 times and the maximum deviations from the average value was less than 0.6%. The drop sizes were measured through two different methods. In one method, for each specified solution of nanofluids total volume of 200 drops was measured with the aid of a digital syringe pump (V), then by assumption of sphericity of drops their equivalent diameter (de Þ can be calculated from Eq. (1):
de ¼
1=3 6V 200 p
ð1Þ
For each of the nanofluids this method was repeated three times, the accuracy was 1% and the maximum deviation from the average value was less than 0.4%.
110
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 1 Physical properties of chemical systems at 25 °C. System’s name
qc (kg/m3)
qd (kg/m3)
T/W 997.10 862.2 T/AA(3 wt.%)/W 997.10 866.30 T/AA(6 wt.%)/W 997.10 869.50 T/AA(3 wt.%)/MTNP’s (0.001 wt.%)/W 997.10 866.30 T/AA(3 wt.%)/MTNP’s (0.002 wt.%)/W 997.10 866.31 T/AA(3 wt.%)/MTNP’s (0.003 wt.%)/W 997.10 866.31 T/AA(3 wt.%)/MTNP’s (0.004 wt.%)/W 997.10 866.32 T/AA(3 wt.%)/MTNP’s (0.005 wt.%)/W 997.10 866.33 T/AA(6 wt.%)/MTNP’s (0.001 wt.%)/W 997.10 869.5 T/AA(6 wt.%)/MTNP’s (0.002 wt.%)/W 997.10 869.51 T/AA(6 wt.%)/MTNP’s (0.003 wt.%)/W 997.10 869.52 T/AA(6 wt.%)/MTNP’s (0.004 wt.%)/W 997.10 869.52 T/AA(6 wt.%)/MTNP’s (0.005 wt.%)/W 997.10 869.53 Dd (Molecular diffusivity of Acetic acid in Toluene) = 2.265 109 m2/s T: Toluene; AA: Acetic Acid; W:Water; MTNP’s: Modified Titania Nanoparticles
lc (mP/s)
ld (mP/s)
c (mN/m)
0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890
0.555 0.560 0.575 0.562 0.562 0.564 0.566 0.569 0.577 0.577 0.579 0.581 0.583
36 27.9 21.2 27.9 27.9 27.9 28 28 21.2 21.2 21.3 21.3 21.3
Fig. 1. Schematic of the experimental setup.
In another one, a high resolution digital camera (Canon Powershot SX610 HS) was used to take photographs of droplets. A ruler ribbon was attached to the column as a dimensional scale, and by using Image J 1.5 software the photographs were analyzed and the size of the drops was calculated again. In this investigation all of the drops were oblate spheroidal, the surface area of the elliptical drop could be determined by Eq. (2):
SOS
1 e2 1þe 2 ¼ 2pb 1 þ ln 1e 2e
ð2Þ
where
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi c2 e¼ 1 2 b
ð3Þ
b and c are respectively the horizontal and vertical diameter of an oblate spheroidal drop. Surface area of a spherical drop which has the equal volume of the oblate spheroidal, can be calculated by following equation:
Sos 1 23 ¼ E1 þ 2 Ss
1 1
1
2E31 ðE21 1Þ2
1 ln E1 þ ðE21 1Þ2
ð4Þ
where E1 is the ratio of the horizontal to the vertical axis of the oblate spheroidal, finally the equivalent diameter of the drop was determined by Eq. (5):
de ¼
rffiffiffiffiffi Ss
p
ð5Þ
For each sample, measuring the drop diameter by photographic method was repeated 50 times and the maximum deviation with the average value was less than 3%. Then, based on the equivalent drop diameter calculated by photography method, the drop diameter was taken as the Sauter mean diameter by the following equation:
Pn 3 ni dei d32 ¼ Pi¼1 2 n i¼1 ni dei
ð6Þ
111
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Sauter mean diameter calculated by the photographic method was slightly larger than that was calculated by Eq. (1) (Less than 0.3 mm). The plausible reason is the refractive index of water and the column wall (glass), which causes the bodies behind them seem smaller than their actual size. The average values determined by two methods were reported. It should be noted that to ensure accuracy of results, all the mass transfer experiments were carried out twice and for some results, with little difference, the mean values are reported. Specification of the extraction column is listed in Table 2.
J ¼ 3:42H0:441
ðH > 59:3Þ
H is determined by following equation:
H¼
4 € EOMo0:149 3
lc lw
0:14 ð10Þ
€ (Eo €tvo € s number) and Mo (Morton number) are two In which EO € ¼ gDqd2 ; dimensionless number defined as EO c
Mo ¼ glqc2Dcq ; respectively and 4
c
3. Result and discussion 3.1. Material characterization Fig. 2 shows FT-IR spectra of three nanoparticles. The bands at 700, 1640 and 3420 are attributed to: TiAOATi bonding of TiO2, hydroxyl group attached on the TiO2 and stretching vibration group, respectively [24]. For the MTNP’s, five other bands can be recognized. Band at 940 cm1 is attributed to TiAOASi bonds [25] and bands at 1032 and 1111 cm1 correspond to SiAOASi [26]. Asymmetrical and symmetrical stretching vibrations of the CAH bonds in methylene group were detected by peaks at 2927 and 2860 cm1 [26]. These bands show that MTNP’s were functionalized by silane coupling agent. Fig. 3 demonstrates Fe-SEM images of Titan nanoparticles, from this figure one can see MTNP’s have an average particle size about of 25 nm. Fig. 4, Illustrates that these nanoparticles show super hydrophobic characteristics. Water Contact angle of MTNP’s is 150° ± 1°, and the main characteristics of the MTNP’s were listed in Table 3. The viscosity of nanofluids was illustrated in Fig. 5, as it is clear from this figure, adding MTNP’s leads viscosity to increase. Fig. 6 shows the colloidal stability of MTNP’s, in the toluene solutions containing 3 and 6 wt.% of the acetic acid. According to Fig. 6., however the stability of modified titania nanoparticles in the solution containing 3 wt.% of the acetic acid is higher, but, the colloidal stability of both fluids was maintained at over 96% after 60 min. Since the operation time of the mass transfer experiments was less than 20 min, it can be concluded that nanoparticles have a good stability in the dispersed phase during conducting the experiments. 3.2. Investigate hydrodynamic performance Hydrodynamic characteristics of a liquid-liquid extraction column can directly affect on the mass transfer performance of that process [27]. In the single drop experiments, the terminal velocity and droplet size are two important hydrodynamic parameters. Grace et al. [28] proposed a correlation (Eq. (7)) to predict the terminal velocity of contaminated drops:
lc J 0:857 ð7Þ dqc M0:149 In Eq. (7), d;lc ; qc are drop size, viscosity and density of the contin-
Vt ¼
uous phase, and J is calculated by Eqs. (8) or (9).
J ¼ 0:94H0:757
ð2 < H < 59:3Þ
ð8Þ
Table 2 Main specifications of the liquid-liquid extraction column. Column height (cm) Column internal diameter (cm) Dispersed flow rate (ml/h) Nozzle tip size (mm)
55 10 100 1.5,2.5
ð9Þ
lw is the viscosity of water at 4 °C.
Terminal velocities measured experimentally by the stopwatch method were compared with the correlation of Grace et al. [28] described in Fig. 7. As it can be seen from this figure, for binary system of toluene and water, all the drops in the present work have lower terminal velocity relative to calculated values by Eq. (7). A plausible reason for such behavior is the solute mass transfer from drops. As it was observed in the previous works [29–31], droplets which are loaded with the solute have lower terminal velocity than those are unloaded. The stochastic and irregular movement of the interface induced due to the solute mass transfer, leads to increase the drag coefficient and subsequently causes the terminal velocity of drops to slow [30]. Droplets due to internal flow pattern are categorized in three different groups of stagnant, circulating and oscillating drops [32]. There are several criteria to distinguish the flow regime of drops, Grace et al. [28] reported that in the condition of 2 < H < 59:3 drops are internally circulating and for H > 59:3 drops fall into oscillating group. In the present work, H was between 71 and 113, so it can be concluded that the drops are oscillating, moreover a critical diameter (dcr) size has been defined which above that drops transient to the oscillating regime. There are several correlations for prediction of this size, which are summarized in Table 4. The critical diameters based on these correlations were reported in the Table 5. As it is clear all of the drops formed in this work had a larger diameter than dcr determined by all correlations, thus drops fall into oscillating group. Furthermore, as it was shown in Fig. 8a, droplets generated from both nozzles were ellipsoidal and according to the work of Wegener et al. [36], for a system of toluene and water, droplets bigger than 4.5 mm are non-spherical oscillating drops. From Fig. 8b it is obvious that the terminal velocity of nanofluids is slightly less than the base fluid (only toluene and acetic acid). One possible reason for such behavior may be decreasing the density difference between the dispersed and continuous phase due to the use of nanoparticles. Another may attributed to the viscosity enhancement of droplets by adding the nanoparticles as it was shown in Fig. 5, Feng and Michaelides [37] reported that increasing the viscosity ratio l ¼ lld of drops in a range of Reynolds numc
ber (5 < Re < 1000, in this work 670 < Re < 846) enhance the drag coefficient (CD), which is subsequently leads to a reduction of the terminal velocity. Also, it is reported by Wegener et al. [38] that existing of impurities can form stagnant cap, which increases the drag force and subsequently decreases the terminal velocity. Furthermore, Fig. 8 shows dispersed phase with higher concentration of solute (acetic acid) has a lower terminal velocity. When solute concentration increased the amount of mass transfer increased too, so turbulence on the interface of the two phases increased which finally leads to a reduction of the terminal velocity [36,39]. Another possible reason is enhancing the Marangoni instability by adding more solute in the dispersed phase [40], according to the [36] in high interfacial tension systems like (toluene + water) existence of solute causes to the gradient of interfacial tension on the interface of drop followed by surface turbulency, which is subsequently leads to increasing the drag coefficient (CD).
112
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Fig. 2. FT-IR spectra of TiO2 nanoparticles: (a) uncoated (b) surface modified.
Fig. 3. SEM image of surface modified TiO2 nanoparticles.
In this work addition of nanoparticles had no any remarkable change on the drop size, because a very small quantity of nanoparticles is used in dispersed phase, this is in accordance with the work of AshrafMansouri and Nasr Esfahany [11]. But, droplet containing a higher solute concentration had smaller size. Droplets with 3 wt.% of acetic acid which are formed from nozzle no. 1 and 2 had a diameter of 5.7 and 7.1 mm respectively. On the other hand, the diameter of droplets containing a higher solute concentration which are generated from nozzle no. 1 and 2 are 5.6 and 6.5 mm, respectively. Reduction of the interfacial tension due to adding of solute, is the reason for such manner [41]. 3.3. Investigation of mass transfer performance Through this work to achieve a comprehensive understanding of mass transfer performance in the liquid-liquid extraction systems, the overall dispersed-phase mass transfer coefficient was studied. Applying the mass transfer balance around a drop with the diameter d, leads to Eq. (14) [39]:
p 3 dCd 2 d ¼ Kod pd cd cd 6 dt
ð14Þ
In Eq. (14) Cd and C⁄ are solute concentration of drop and the equilibrium solute concentration with the continuous phase, respectively. Integrating of Eq. (14) from initial to final point gives:
Fig. 4. Contact angle of surface modified TiO2 nanoparticles.
Table 3 Physical characteristics of synthesized nanoparticles.
Properties
Particle size (nm)
q
Titania nanoparticles
25
2443.4
Kod ¼
C d;f C d d ln 6ðtf t0 Þ C d;0 C d
kg m3
Hydrophobicity (contact angle) 150°
ð15Þ
In which Cd,f and Cd,0 are solute concentration in drop at the initial and final point, respectively, and t is contact time of the raising drops within the continuous phase. Eq. (15) can be rewritten as:
d Kod ¼ lnð1 EÞ 6t
ð16Þ
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Fig. 5. Dynamic viscosity of nanofluids stability versus MTNP’s concentration.
Fig. 6. Nanofluids stability versus sedimentation time.
Fig. 7. Comparison between experimental terminal velocities and those calculated by Grace correlation.
113
114
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 4 Correlations for prediction of the terminal velocity of drops. Author
Correlation
Klee and Treybal [33] Eq. (11) Yamaguchi et al. [34] Eq. (12)
0:24 dcr ¼ 0:33q0:14 Dq0:43 l0:3 c c c 0:5 196c 0:22 3 ; Mo ¼ gDql4c q2 dcr ¼ Dqg Mo c c rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Mersmann [35] Eq. (13)
dcr ¼ 14:1
0:28 c0:4 l0:8 c qd
Dq0:867 g0:8 qc0:613
where E is fraction extracted and calculated by Eq. (17):
E¼
C0 C C0 C
ð17Þ
The volume of continuous phase (about 4000 ml) is much higher than the drop (less than 0.1 ml) and the continuous phase is initially free of acetic acid, thus the solute concentration in continuous phase is negligible. Since the acetic acid equilibrium concentration in the water is much higher than toluene [43], the solute concentration in water (continuous phase) is negligible and C⁄ can be assumed to zero. From section 3.2 contact time and size of the drops were determined, so E and Kod can be calculated easily. In the chemical systems of toluene, acetic acid and water, the mass transfer resistance exists mainly in the organic phase [11,44–48]. For further explanation, in accord to the Whitman two film theory the overall mass transfer resistance is determined from the sum of the local mass transfer resistance in the both phases (i.e. 1/Kod = 1/kd + m/kc), where kd and kc are dispersed and continuous phase mass transfer coefficients calculated by Baron [49] and Higbie [50], respectively. In the chemical system used in this work at 25 °C, the slope of the equilibrium curve (m) is low (m 0.09) [43], and the values of kd and kc determined by Handlos and Baron [49] and Higbie [50], are in the range of 2.3 2.5 104 m/s and 2.3 2.4 104 m/s, respectively. Since, the value of m/kc is less than 0.09 of 1/kd, the mass transfer resistance of continuous phase is negligible in the other words, Kod kd. Fig. 9 shows the overall mass transfer coefficient of the dispersed phase formed from the various nozzles and contained different solute concentrations. In all cases, the uncertainty of measurements is less than 5%, and there is a peak in the mass transfer coefficient enhancement at the MTNP’s concentration of 0.002 wt.%. This trend was similar to the other results reported by Saien and Bamdadi [8] and Ashrafmansouri and Nasr Esfahany [11]. At the solute concentration of 3 and 6 wt.%, a maximum enhancement in the overall dispersed-phase mass transfer coefficient for drops generated from the bigger nozzle was 70% and 25%, respectively. Moreover, for those drops formed from smaller nozzle, maximum enhancement in Kod was 60.7% and 24%, respectively, for 3 and 6 wt.% of acetic acid. The reason for the anomalous enhancement of the mass transfer coefficients is attributed to the microconvections created by the Brownian motion [7,51,52]. As it is clearly mentioned, the maximum enhancement in the Kod due to use of MTNP’s is more obvious for the bigger drops, this is in accord with the work of Ashrafmansouri and Nasr Esfahany [11]. To explain why nanoparticles are more effective in the bigger drops, their internal regime
should be taken into account. It can be seen that, in the oscillating drops with increasing of droplet diameter internal circulation of drop decreased [53], so there would be a more proper opportunity for Brownian motion of nanoparticles to influence on the mass transfer performance. As it is shown in Fig. 9 adding nanoparticles excess than 0.002 wt.%, leads to a continuous reduction of the overall mass transfer coefficient. The possible reason for such behavior is the aggregation of nanoparticles, which it plays an obstacle role in the diffusion of solute and subsequently leads to increasing mass transfer resistance [7,54]. According to Eq. (26), it is clear that increasing the viscosity of dispersed phase causes to reduction of the mass transfer coefficient [42], so another possible reason for decreasing of mass transfer coefficient by adding excess amount of nanoparticles is the viscosity enhancement of dispersed phase by adding MTNP’s. The possible existence of nanoparticles on the interface of drops, can be mentioned as the last reason for the reduction of Kod at the higher concentration of MTNP’s [12]. As mentioned above, the mass transfer enhancement effect of nanoparticles is higher for drops with lower solute concentration. From Fig. 9, it is obvious that solute concentration has an adverse effect on the mass transfer improvement created by nanoparticles addition. For the initial solute concentration of 3 wt.%, the average of the overall mass transfer coefficient enhancement of nozzles 1 and 2 was 34.2% and 42.9%, respectively. Whereas at the concentration of 6% of solute, for above nozzles, this value was 16.4% and 13% respectively. Increasing the initial solute concentration leads to increase the amount of solute mass transfer [46], which it presumably disturbs the Brownian motion of nanoparticles, and reduces the mass transfer promoting effect of nanoparticles. Also, the viscosity of the dispersed phase were increased by adding higher amount of the acetic acid in the drops, this can be considered as another reason for the reduction of the mass transfer coefficient at higher solute concentration [12]. 3.4. Modeling of results To calculate the overall mass transfer coefficient as a basic parameter for designing of the liquid-liquid extractors [46], several models and correlations have been reported. Mass transfer coefficient of drops depends on their internal flow regime. It is recognized that, the drops can be internally stagnant, circulated or oscillating. Based on the intensity of drop circulation, there are three models which are described in Table 6. Eq. (18) derived by Newman et al. [55], describes the overall mass transfer for molecular diffusion in stagnant droplets. For drops with internal circulation Kronig and Brink [56] suggested Eq. (19). The last model was proposed by Handlos and Baron (Eq. (20)) [49], which is reliable when the mass transfer mechanism is eddy diffusion between internal toroidal streamlines. Further of these theoretical models, there are a lot of empirical correlations which some of them have been limited to a specific condition of flow regime or type of the extraction column. However, in 1999, Kumar and Hartland [42], introduced a general equation for prediction of the dispersed phase mass transfer coefficient (Eq. (21), Table 6), which is applicable for a various range of chemical systems and flow regimes. In the present investigation, experimental Kod for drops, which are free of nanoparticles were compared with their corresponding values derived from available
Table 5 Experimental drop diameter and calculated values of critical diameter. Nozzle
dexp (mm)
dcr (mm) [33]
dcr (mm) [34]
dcr (mm) [35]
No. 1
5.6 5.7 6.5 7.1
4.1 4.3 4.1 4.3
4.5 4.6 4.5 4.6
5.2 5.4 5.2 5.4
No. 2
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
115
Fig. 8. (a) Terminal velocity of drops versus MTNP’s concentration.
Fig. 9. Overall dispersed-phase mass transfer coefficient versus concentration of MTNP’s.
Table 6 Available models and correlation for dispersed phase mass transfer coefficient. Model and correlation Newman [55] Eq. (18) Kronig & Brink [56] Eq. (19) Handlos & Baron [49] Eq. (20) Kumar and Hartland [42] Eq. (21)
Equation K od ¼
d
K od ¼
d
K od
6t 6t
Description h
P1
2
d
i h P1 2 kn V t t ¼ d n¼1 Bn exp 128dð1þkÞ 6t ln 2
kd d Dd
i
ln p62 n¼1 n12 exp 4n p2 Dd t d h P i 2 64kn Dd t ln 38 1 2 n¼1 Bn exp 2
¼ 17:7 þ
1
3:19103 ReSc3d 1þ1:4310
2
1:7
1 ReSc3d
23 q 1 0:7 qd 2 c 1þk3
Molecular diffusion in stagnant spherical drops Laminar diffusion with circulation induced by relative motion of drop and continuous phase Turbulent circulation within the drops and eddy diffusion between internal toroidalstreamlines Empirical correlation for both circulating and oscillating drops
correlations in Table 7. This table indicated that measured overall dispersed phase mass transfer coefficient have a relatively poor agreement with those calculated by Kronig and Brink correlation (Eq. (19)). It is reported that Kronig and Brink model can be applied for drops with circulation regime and low Reynolds number (less than 1) [56], while in the present investigation drops were in oscillating condition and their Reynolds number was greater than 670. On the other hand, this experimental data were in a good agreement with those calculated by Handlos and Baron model (Eq. (20)) and
Kumar and Hartland correlation (Eq. (21)). For explaining this adaptation, it should be noted that Handlos and Baron model is based on the eddy diffusion, presumably developed from drop vibrations, which is similar to the present oscillating condition of drops. Moreover, Kumar and Hartland correlation is a completely empirical generalized correlation which is driven by fitting of a broad range of data points gathered from 21 sources. Table 7 also indicated that for the smaller drops Eq. (21) predicts experimental Kod better than Eq. (20) whilst in the case
116
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 7 Experimental and calculated Kod for Cnp = 0. System’s name Nozzle no. 1 Nozzle no. 2
T/AA(3 wt.%)/W T/AA(6 wt.%)/ W T/AA(3 wt.%)/ W T/AA(6 wt.%)/ W
Experimental
Eq. (13) (Kronig & Brink)
Error%
Eq. (14) (Handlos & Baron)
Error%
Eq. (15) (Kumar & Hartland)
Error%
187 189 254 228
41.7 41.4 40.3 40.2
77.5 78.0 84.0 82.3
250.6 248.88 2 C1 42.14 236.93
34.0 31,6 4.6 3.9
189.17 185.87 181.99 179.27
1.1 1.6 28.3 21.3
%AARE
80.5
18.5
of larger drops the agreement between measured Kod and those predicted by Eq. (20) was more evident. However, as it was demonstrated in Fig. 9, overall dispersedphase mass transfer coefficient of the nanofluids shows thoroughly special manner. Hence, a specific model to predict the mass transfer coefficient of dispersed phase nanofluids should be proposed. The proposed approach is applying the Newman model (Eq. (18)) with a modified molecular diffusivity, RDd, which is called overall effective (or enhanced, Doe ) diffusivity and R is the enhanced factor [57,58]. With regard to this modification, R includes both the effect of internal circulation and Brownian motion of nanoparticles, so overall dispersed-phase mass transfer coefficient is changed to the following form:
K od
" X # d 6 1 1 4n2 p2 Doe t ln 2 ¼ exp 2 6t p n¼1 n2 d
ð22Þ
To obtain R, several governing aspects, including internal circulation of drop, nanoparticles concentration and the magnitude of Brownian motion must be taken into account. Generally, the enhanced factor in this process depends on the viscosity and density of continuous and dispersed phase, velocity of drops and nanoparticles, size of drops and nanoparticles concentration. Therefore, general correlation can be written as:
fðR;qc ; qd ; lc ; ld ; Vt ; Vp ; d32 ; UÞ ¼ 0
ð23Þ
Based on Eq. (23) and pai theorem, five dimensionless groups can be defined. Thus, with the dimensional analysis R can be written as Eq. (24):
q l R ¼ f Re;U; Renp ; d ; d
ð24Þ
qc lc
To explain the origin of Eq. (24), it should be mentioned that the Reynolds number (Re) of drops plays a significant role on the flow regime of the drops, so it was selected as a parameter of the proposed correlation for enhanced factor. As it was seen in Fig. 9, Kod depends on the nanoparticles concentrations, so the volume fraction (UÞ of nanoparticles was used as the second parameter which has influence on the R. As it was mentioned in section 3.3, Brownian motion of nanoparticles has a major effect on the mass transfer performance of nanofluids. These motions are affected by the nanoparticle velocity (Vp). Furthermore, viscosity and density of dispersed phase are effective parameters on mass transfer and hydrodynamic characteristics, so the Reynolds number of nanoparticles within the
13.5
drop was chosen (Renf) as another effective variable in the enhanced factor, it is defined by Nagy et al. [51] in the form of Eq. (25):
Renf ¼
v np dp tnf
¼
1
tnf
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 18K B T pdp q
ð25Þ
Finally, as it was demonstrated in Eq. (21), density and viscosity ratios of dispersed and continuous phase are two other important variables. In the present investigation, for 20 nanofluids, R had various amounts of 33.3–150. The percentage of average absolute relative error (%AARE) was used to compare the predicted results with available models, it is defined as follows:
%AARE ¼
N 1X Model Experiment 100 N i¼1 Experiment
ð26Þ
In Eq. (26), N is the number of various drops, since there was 10 different nanofluids and also two different nozzles were used, there would be 20 different drops. The mathematical procedure for determining proper correlation and its constants is based on the regression analysis by use of Ordinary Least Square (OLS) method. In the OLS method, the final purpose is minimizing the sum of squares made by differences between the model and actual values, this was done by the DataFit 9.0 software. In order to analysis a fitted correlation, it is essential to define some statistical parameters, including R2, R2adj, Durbin Watson (D.W.T), Prob (t-statistic). The model’s ability in fitting the experimental data is determined by the R2 and R2adj, generally the value of these parameters is between 0.0 and 1.0 and the degree of fitting enhanced by increasing of these parameters. Another parameter which considers the difference between the predicted amount by model and real value is D.W.T, in a proper model this amount must be greater than 1. The last parameter is Prob (t) which shows the importance level of each model’s variable. The smaller the value of Prob (t), means the higher importance of parameter. Based on Eq. (23), a plausible type of model can be written in the form of Eq. (27):
R ¼ C 1 ReC 2 ReCnf3 UC 6
qd qc
C 4 C5 ld
lc
ð27Þ
Model parameters were determined by fitting the experimental data on Eq. (27), it was demonstrated in Table 8.
Table 8 The specification of Eq. (28). C 5 C 6 l R ¼ 10C 1 ReC 2 ReCnf3 UC 4 qqd ld Eq. (28) c c
C2 C3 C4 C5 C6
Coefficient 165.8985 4.6708 105.5066 0.1130 17.6242 93.4255
Prob(t) 0.0310 0.011 0.2869 0.8059 0.0332 0.0017
AARE%
8.4
r2
0.83
r 2adj
0.78
D.W.T
1.62
117
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119 Table 9 The specification of Eq. (29). C 4 l R ¼ 10C 1 ReC 2 ReCnf3 ld Eq. (29) c Coefficient 221.7870 5.4214 138.7525
Prob(t) 0.00026 0.0 0.00018
AARE%
8.6
C1 C2 C3
r2 r 2adj
0.82 0.78
C4
124.1335
0.00022
D.W.T
1.44
Table 10 Comparison of the models and correlation for dispersed phase mass transfer coefficient. Kod (lm s1)
System’s name
Experimental
Eq. (29) (Present work)
Eq. (19) (Kronig & Brink)
Eq. (20) (Handlos & Baron)
Eq. (26) (Kumar & Hartland)
Nozzle no. 1
T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s
(0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W (0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W
183.39 197.34 235.06 240.00 230.10 167.68 175.46 204.36 292.74 236.31
199.3 207.1 217.9 227.9 233.3 188.7 199.8 210.5 223.5 236.1
41.11 41.13 41.19 41.24 41.34 41.13 41.18 41.27 41.37 41.57
241.66 242.31 243.41 244.40 245.71 245.22 246.38 247.82 249.49 252.15
182.49 182.71 183.30 183.78 184.85 183.03 183.48 184.32 185.33 187.50
Nozzle no. 2
T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s
(0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W (0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W
227.62 240.87 266.50 432.52 392.15 219.71 233.72 260.80 286.00 253.52
218.68 266.1 325.1 400.2 350.3 199.9 208 250 303.9 270.4
39.59 39.64 39.71 39.78 39.89 39.73 39.77 39.82 39.91 40.00
235.87 236.88 237.97 239.05 240.59 231.42 232.19 233.03 234.33 235.63
177.86 178.37 179.10 179.82 180.90 175.64 175.97 176.51 177.41 178.34
8.6
82.8
16.8
24.5
%AARE
Analyzing the Prob (t) leads to omitU and ðqqd Þ, so after neglectc
ing volume fraction and density ratio, another type of equation with its regression parameters is listed in Table 9. Comparison between Tables 8 and 9, indicates that Eq. (29) has lower parameters than first model type, while the difference between the AARE% of two equations is not considerable. Thus, Eq. (29) is proposed as a proper model type for prediction the overall dispersed phase in the present investigation. Also, it is worth to note that this type of model satisfies the physical principles governing the process. It is reported in the various works that the enhancement in the transfer coefficients is directly proportional to Brownian motion [2,7–10], which is in adapt to the proposed model where it relates to Renf. Furthermore, in all of the published works addressed this issue, the enhancement factor is a function of the Reynolds number [59], which is in accordance to Eq. (29). In Table 10, the values of overall dispersed-phase mass transfer coefficient computed by different equations were listed, and a comparison between the proposed model with other conventional equations have been done. According to Table 10, both Kronig and Brink and Handlos and Baron equations, cannot be able to predict the overall dispersed-phase mass transfer coefficient appropriately, but predicted values by the new proposed model are in a good agreement with the experimental data. The AARE of Kod for Kronig & Brink and Handlos & Baron models are 82.8% and 16.8%, respectively, and it is 24.5% for Kumar and Hartland correlation, but its value for the new proposed model is only 8.6%, which indicates precise predictability of this approach. Fig. 10 shows that prediction of Kod from Eq. (29), is more satisfying than other works.
Fig. 10. Comparison of the experimental Kod with present and previous equations.
To explain why the traditional model (i.e. Kronig & Brink and Handlos & Baron models) as well as the Kumar and Hartland correlation cannot accurately estimate the overall dispersed-phase mass transfer coefficient, it should be mentioned that these equations
118
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
don’t take the Brownian motion of nanoparticles into account. In contrast, the influence of MTNP’s nanoparticles and other major parameters such as droplet size and terminal velocity, physical properties of both phases are considered in the proposed model.
4. Conclusion During this investigation, the super hydrophobic titania nanoparticles were prepared via a modified sol-gel method. Then nanoparticles were applied in the non-polar dispersed phase of a single drop liquid-liquid extraction column. It was found that the overall dispersed-phase mass transfer coefficient of solute is greatly affected by using this type of nanoparticles. Adding modified titania nanoparticles in concentration up to 0.002 wt.% led to a continuous mass transfer enhancement, but after this concentration the overall dispersed-phase mass transfer coefficient decreased to the extent which it was even lower than that of the base fluid. The mass transfer improvement due to the use of nanoparticles was more observable for bigger droplets containing a lower solute concentration. Finally, based on the Newman’s theoretical model and experimental data, a rigorous semi-empirical equation was proposed to predict the overall dispersed-phase mass transfer coefficient in terms of droplet’s Reynolds number, nanoparticle’s Reynolds number and viscosity ratio. For the chemical systems and extraction column studied in the present investigation the proposed model has higher accuracy and precision with the experimental data compared with other available models.
References [1] W. Duangthongsuk, S. Wongwises, An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime, Int. J. Heat. Mass Transfer 53 (1–3) (2010) 334–344. [2] S.S. Ashrafmansouri, M. Nasr Esfahany, Mass transfer in nanofluids: a review, Int. J. Therm. Sci. 82 (2014) 84–99. [3] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol based Nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (2001) 718–720. [4] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer 52 (2009) 3187–3196. [5] Z. Azizi, A. Alamdari, M.R. Malayeri, Convective heat transfer of Cu-water nanofluid in a cylindrical microchannel heat sink, Energ. Convers. Manage. 101 (2015) 515–524. [6] Z. Azizi, A. Alamdari, M.R. Malayeri, Thermal performance and friction factor of a cylindrical microchannel heat sink cooled by Cu-water nanofluid, Appl. Therm. Eng. 99 (2016) 970–978. [7] A. Bahmanyar, N. Khoobi, M.R. Mozdianfard, H. Bahmanyar, The influence of nanoparticles on hydrodynamic characteristics and mass transfer performance in a pulsed liquid–liquid extraction column, Chem. Eng. Process. 50 (2011) 1198–1206. [8] J. Saien, H. Bamdadi, Mass transfer from nanofluid single drops in liquid-liquid extraction process, Ind. Eng. Chem. Res. 51 (2012) 5157–5166. [9] A. Mirzazadeh Ghanadi, A. Heydari Nasab, D. Bastani, A.K. Seife Kordi, The effect of nanoparticles on the mass transfer in liquid–liquid extraction, Chem. Eng. Commun. 202 (5) (2015) 600–605. [10] G. Nematbakhsh, A. Rahbar-Kelishami, The effect of size and concentration of nanoparticles on the mass transfer coefficients in irregular packed liquid– liquid extraction columns, Chem. Eng. Commun. 202 (11) (2015) 1493–1501. [11] S.-S. Ashrafmansouri, M. Nasr Esfahany, The influence of silica nanoparticles on hydrodynamics and mass transfer in spray liquid–liquid extraction column, Sep. Purif. Technol. 151 (2015) 74–81. [12] H. Hasani Goodarzi, M. Nasr Esfahany, Experimental investigation of the effects of the hydrophilic silica nanoparticles on mass transfer and hydrodynamics of single drop extraction, Sep. Purif. Technol. 170 (2016) 130–137. [13] X. Fang, Y. Xuan, Q. Li, Experimental investigation on enhanced mass transfer in nanofluids, Appl. Phys. Lett. 95 (2009) 203103–203108. [14] S. Krishnamurthy, P. Bhattacharya, P.E. Phelan, R.S. Prasher, Enhanced mass transport in nanofluids, Nano Lett. 6 (3) (2006) 419–423. [15] V. Chaudhary, A.K. Srivastava, J. Kumar, On the sol-gel synthesis and characterization of titanium oxide nanoparticles, MRS Proc. (2011) 1352, http://dx.doi.org/10.1557/opl.2011.759. [16] H. Pan, X.D. Wang, S.S. Xiao, L.G. Yu, Z. Zhang, Preparation and characterization of TiO2 nanoparticles surface-modified by octadecyltrimethoxysilane, Indian. J. Eng. Mater. S 20 (2013) 561–567.
[17] J. Zhaoa, M. Milanovab, M.M.C.G. Warmoeskerkena, V. Dutschka, Surface modification of TiO2 nanoparticles with silane coupling agents, Colloids Surf. A: Physicochem. Eng. Aspects 413 (2012) 273–279. [18] F. Sayilkan, H. Sayilkan, M. akarsu, Characterization of TiO2 synthesized in alcohol by a sol-gel process: the effects of annealing temperature and acid catalyst, Turk. J. Chem. 29 (2005) 697–706. [19] W. Wu, Q. He, C. Jiang, Magnetic iron oxide nanoparticles: synthesis and surface functionalization strategies, Res Lett. 3 (11) (2008) 397–415. [20] S. Mallakpour, E. Nikkhoo, Surface modification of nano-TiO2 with trimellitylimido-amino acid-based diacids for preventing aggregation of nanoparticles, Adv. Powder Technol. 25 (2014) 348–353. [21] M. Sabzi, S.M. Mirabedini, J. Zohuriaan-Mehr, M. Atai, Surface modification of TiO2 nano-particles with silane coupling agent and investigation of its effect on the properties of polyurethane composite coating, Prog. Org. Coat. 65 (2) (2009) 222–228. [22] Jiand et al., Production of aqueous colloidal dispersions of carbon nanotubes, Colloid Interface Sci. (2003) 89–94. [23] P. Chang, C.R. Wilke, Some measurements of diffusion in liquids, J. Phys. Chem. 59 (7) (1955) 592–596. [24] Q. Chena, N.L. Yakovlevb, Adsorption and interaction of organosilanes on TiO2 nanoparticles, Appl. Surf. Sci. 257 (2010) 1395–1400. [25] Z. Li, B. Hou, Y. Xu, D. Wu, Y. Sun, W. Hu, F. Deng, Comparative study of sol–gel hydrothermal and sol–gel synthesis of titania–silica composite nanoparticles, J. Solid State Chem. 178 (2005) 1395–1405. [26] E. Ukaji, T. Furusawa, M. Sato, N. Suzuki, The effect of surface modification with silane coupling agent on suppressing the photo-catalytic activity of fine TiO2 particles as inorganic UV filter, Appl. Surf. Sci. 254 (2007) 563–569. [27] P.H. Calderbank, I.J.O. Korchinski, Circulation in liquid drops: a heat transfer study, Chem. Eng. Sci. 6 (1956) 65–78. [28] J.R. Grace, T. Wairegi, T.H. Nguyen, Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, T. I. Chem. Eng. – Lond. 54 (1976) 167–173. [29] F.W. Keith, A.N. Hixson, Liquid-liquid extraction spray columns-drop formation and interfacial transfer area, Ind. Eng. Chem. 47 (2) (1955) 264–266. [30] M. Henschke, A. Pfennig, Mass-transfer enhancement in single drop mextraction experiments, AIChE J. 45 (1999) 2079–2086. [31] T. Al-Hassan, C.J. Mumford, G.V. Jeffreys, Flow characteristics of large oscillating drops in liquid-liquid systems, Chem. Eng. Technol. 14 (1) (1991) 65–72. [32] B. Arendt, R. Eggers, Interaction of Marangoni convection with mass transfer effects at droplets, Int. J. Heat. Mass Trans. 50 (2007) 2805–2815. [33] A.J. Klee, R.E. Treybal, Rate of rise or fall of liquid drops, AIChE J. 2 (4) (1956) 444–447. [34] M. Yamaguchi, T. Fujimoto, T. Katayama, Experimental studies of mass transfer rate in the dispersed phase and moving behavior for single oscillating drops in liquid–liquid systems, J. Chem. Eng. Jpn. 8 (5) (1975), 366-361. [35] A. Mersmann, Zur stationären Bewegung fluider Partikel (in German), Chem. Ing. Technol. 46 (6) (1974) 251. [36] M. Wegener, N. Paul, M. Kraume, Fluid dynamics and mass transfer at single droplets in liquid/liquid systems, Int. J. Heat Mass Transfer 71 (2014) 475–495. [37] Z.G. Feng, E.E. Michaelides, Drag coefficients of viscous spheres at intermediate and high Reynolds numbers, J. Fluids Eng. 123 (2001) 841–849. [38] M. Wegener, Matthias Kraume, Anja R. Paschedag, Terminal and transient drop rise velocity of single toluene droplets in water, AIChE J. 56 (1) (2010) 1–10. [39] X. Li, Z.-S. Mao, W. Fei, Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems, Chem. Eng. Sci. 58 (2003) 3793–3806. [40] M. Wegener, M. Fevre, A.R. Paschedag, M. Kraume, Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets, Int. J. Heat Mass Transf. 52 (11–12) (2009) 2543–2551. [41] M. Torab Mostaedi, P. Khadiv Parsi, M. Moosavian, Experimental investigation of phase inversion of liquid-liquid systems in a spray extraction column, Iran. J. Chem. Chem. Eng 27 (2) (2008) 135–140. [42] A. Kumar, S. Hartland, Correlation for prediction of masstransfer coefficients in single drop system and liquid–liquid extraction columns, Chem. Eng. Res. Des. 77 (Part A) (1999) 372–384. [43] J. Saien, M. Mozafarvandi, S. Daliri, M. Norouzi, (Liquid + liquid) equilibria for the ternary (water+acetic acid+toluene) system at different temperatures: experimental data and correlation, J. Chem. Thermodynam. 57 (2013) 76–81. [44] J.C. Godfrey, M.J. Slater, Liquid-Liquid Extraction Equipment, Wiley, Chichester, UK/New York, 1994. [45] J. Temos, H. Pratt, G. Stevens, Mass transfer to freely-moving drops, Chem. Eng. Sci. 51 (1996) 27. [46] A. Rahbar, Z. Azizi, H. Bahmanyar, M.A. Moosavian, Prediction of enhancement factor for mass transfer coefficient in regular packed liquid–liquid extraction columns, Can. J. Chem. Eng. 89 (2011) 508–519. [47] Z. Azizi, M. Rezaeimanesh, H. Abolghasemi, H. Bahmanyar, Effective diffusivity in a structured packed column: experimental and Sherwood number correlating study, Chem. Eng. Res. Des. 92 (2014) 43–53. [48] Z. Azizi, M. Rezaeimanesh, Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid, Chem. Eng. Res. Des. 115 (2016) 44– 52. [49] A.E. Handlos, T. Baron, Mass and heat transfer from drops in liquid –liquid extraction, AIChE J. 3 (1957) 127–136. [50] R. Higbie, The rate of absorption of a pure gas into still liquid during short periods of exposure, Tram. Am. InPt. Chem. Eng. 31 (1935) 365.
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119 [51] E. Nagy, T. Feczkó, B. Koroknai, Enhancement of oxygen mass transfer rate in the presence of nano sized particles, Chem. Eng. Sci. 62 (2007) 7391–7398. [52] S.W. Park, B.S. Choi, J.W. Lee, Effect of elasticity of aqueous colloidal silica solution on chemical absorption of carbon dioxide with 2-amino-2-methyl-1propanol, KoreaeAust. Rheol. J. 18 (2006) 133–141. [53] P.M. Rose, R.C. Kintner, Mass transfer from large oscillating drops, A.1.Ch.E. J. 12 (3) (1966) 530–534. [54] C. Gerardi, D. Cory, J. Buongiorno, L.W. Hu, T. McKrell, Nuclear magnetic resonance-based study of ordered layering on the surface of alumina nanoparticles in water, Appl. Phys. Lett. 95 (25) (2009) 253104. [55] A.B. Newamn, The drying of porous solids. Diffusion and surface emission effects, Trans. Am. Inst. Chem. Eng. 27 (1931) 203–220.
119
[56] R. Kronig, J.C. Brink, On the theory of extraction from falling drops, Appl. Sci. Res. 2 (1) (1951) 142–154. [57] M.J. Slater, A combined model of mass transfer coefficients for contaminated drop liquid-liquid systems, Can. J. Chem. Eng. 73 (1997) 462. [58] A.M. Dehkordi, S. Ghasemian, D. Bastani, Model for excess mass-transfer resistance of contaminated liquidliquid systems, Ind. Eng. Chem. Res. 46 (5) (2007) 1563–1571. [59] L. Steiner, Mass transfer rates from single drops and drop swarms, Chem. Eng. Sci. 41 (8) (1986) 1979–1986.
Contents lists available at ScienceDirect
Separation and Purification Technology journal homepage: www.elsevier.com/locate/seppur
Investigation the effect of super hydrophobic titania nanoparticles on the mass transfer performance of single drop liquid-liquid extraction process Ashkan Hatami a,⇑, Dariush Bastani a, Farhood Najafi b a b
Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran Department of Resin and Additives, Institute for Color Science and Technology, Tehran, Iran
a r t i c l e
i n f o
Article history: Received 23 May 2016 Received in revised form 13 November 2016 Accepted 20 November 2016 Available online 27 November 2016 Keywords: Liquid-liquid extraction Titania nanoparticles Single drop Synthesis Mass transfer
a b s t r a c t Hydrophobic titania nanoparticles were synthesized by a novel in situ sol-gel method and applied in a single drop liquid-liquid extraction column to enhance the overall dispersed-phase mass transfer coefficient (Kod). The chemical system of toluene, acetic acid and water was used, and the direction of solute (acetic acid) mass transfer was from dispersed phase, including: toluene and acetic acid to the continuous phase of water. For such system, much of the mass transfer resistance exists in the dispersed phase, which is nonpolar organic liquid. Hence, modified titania nanoparticles (MTNP’s), prepared by sol-gel route, in five different concentrations of 0.001–0.005 wt.% were added in the dispersed phase. Also, the impact of MTNP’s at the different solute concentrations and nozzles was investigated. Results indicated an anomalous enhancement in the overall dispersed-phase mass transfer coefficient at 0.002 wt.% of MTNP’s. A maximum enhancement of 70% in the overall mass transfer coefficient was found in droplets formed from a nozzle of 2.5 mm inner diameter, containing 3 wt.% of solute. Eventually, based on the theoretical model of Newman, a semi-empirical model was presented, that is capable to predict the overall dispersed-phase mass transfer coefficient of nanofluids with an average absolute relative error of 8.6%. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Fluids which contain well-dispersed particles with an average size of less than 100 nm, are called nanofluids [1]. Recently, effects of their presence on the transfer phenomena such as heat and mass transfer have been attracted great attention [2]. Once, the improvement of both conductive and convective heat transfer due to the use of nanoparticles was shown [3–6]. Similarity between heat and mass transfer has caused a stimulus for investigating the effect of nanoparticles in the mass transfer operation. Several works have been done on the systems which dealing with the gas and liquid phase, and various improvement effects have been seen due to use of the nanoparticles. Whereas, in case of liquid-liquid extraction process fewer studies have been coducted [2], that have reported increase in the mass transfer coefficients of nanofluids. Bahmanyar et al. [7], used kerosene based SiO2 nanofluids in a pulsed liquid–liquid extraction column (PLLEC). Their chemical system was kerosene, acetic ⇑ Corresponding author. E-mail address: [email protected] (A. Hatami). http://dx.doi.org/10.1016/j.seppur.2016.11.063 1383-5866/Ó 2016 Elsevier B.V. All rights reserved.
acid (solute) and water and solute mass transfer was from the kerosene to the water. Based on the pulsation intensity and the nanoparticles concentration, an increase of 4–60% was found in their work. Saien and Bamdadi [8], investigated the effect of Fe3O4 and Al2O3 nanoparticles in a single drop liquid-liquid extraction column. In their study chemical system was toluene-acetic acid (solute)-water, at the nanoparticles concentration of 0.002 wt.%, the enhancement of solute transfer from dispersed nanofluids (toluene + nanoparticles) was 157% and 121% for magnetite and alumina nanoparticles, respectively. Mirzazadeh Ghanadi et al. [9], used carbon nanotube, ZnO and TiO2 nanoparticles with different concentration in the water, and investigated mass transfer of succinic acid from n-butanol (dispersed phase) to water. They found that, nanoparticles can play a role as a mass transfer promoter in the laminar flow regime of the dispersed phase. Nematbakhsh and RahbarKelishami [10], studied the effect of hydrophobic SiO2 nanoparticles with different particle size of 10, 30 and 80 nm in an irregular packed column with the chemical system of toluene-acetic acid-water. They used various concentrations of those nanoparticles in water, and found that the maximum enhancement in the
108
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Nomenclature dp C C⁄ V Kod k d de dei t E Vt Vnp KB R Dd Doe Re Renf ni
nanoparticle size (nm) solute concentration (mol/m3) equilibrium concentration of solute in dispersed phase (mol/m3) total volume of 200 dropts (m3) overall dispersed mass transfer coefficient (lm=sÞ local mass transfer coefficient droplet diameter (m) equivalent diameter of drop (m) equivalent diameter of drop of ith drop (m) contact time (s) extraction fraction terminal velocity (m/s) velocity of nanoparticles (m/s) Boltzmann constant, =1.3807 1023 J/K enhancement factor, dimensionless molecular diffusivity (m2/s) effective molecular diffusivity (m2/s) drop Reynolds dimensionless number nanofluid Reynolds dimensionless number number of droplets with dei
overall mass transfer coefficient was 42% in 0.05 vol% of the smallest nanoparticles. Ashrafmansouri and Nasr Esfahany [11], investigated the effect of toluene based SiO2 nanofluids on the mass transfer and hydrodynamics characteristics of a spray liquid-liquid extraction column. They observed that, nanofluids have not any sensible effect on the hydrodynamic performance of toluene-acetic acid-water system. However, in 0.001 vol% of that nanoparticles a maximum enhancement of 47% in the overall mass transfer coefficient was detected. Recently, Goodarzi and Nasr Esfahany [12], investigated the effects of the hydrophilic SiO2 nanoparticles in the aqueous phase of toluene-acetic acidwater systems. They reported that when toluene and acetic acid are the dispersed phase, using SiO2 nanoparticles in the water couldn’t enhance the mass transfer rate, even at the concentration of 0.1 vol% of that nanoparticles the overall dispersed phase mass transfer reduced up to 22% in their work. In all the studies in this field, microconvection created due to the Brownian motion of nanoparticles is the most reported possible reason for the anomalous enhancement of mass transfer rate [7–14]. So, it can be more efficient if the nanoparticles would be used in the phase with higher mass transfer resistance. In this investigation, a single drop liquid-liquid extractor as a simple study column, which provides easy and accurate control over the main specification of the extraction process, was chosen and we have focused on the toluene, acetic (solute) and water chemical systems. Solute transfer was from the toluene as the dispersed phase to the water as the continuous phase. In this system major resistance of the mass transfer exists in the dispersed phase [11,12], so nanoparticles should have a good distribution in the toluene. To this end, titania (TiO2) nanoparticles, which has not been used in the dispersed phase, have synthesized and then functionalized through an in situ sol-gel method with using of a silane coupling agent. Aside the titania nanoparticles concentration, the effect of solute concentration and nozzle tip size on the mass transfer performance of the single drop experiments has been investigated. At the end of this work, with modification of the Newman model by experimental data, a semi-empirical model has been proposed for predicting the overall dispersedphase mass transfer coefficient.
E1 CD Sos Ss g
ratio of the major to the minor axis of the oblate spheroid drag coefficient, dimensionless area of an oblate spheroid (m2) area of a sphere which has equal volume of an oblate spheroid (m2) gravity, (m/s2)
Greek symbols l dynamic viscosity (Pa s) q density (kg/m3) c interfacial tension (N/m) m kinematic viscosity (m2/s) U volume fraction Subscripts 0 initial point nf nanofluid np nanoparticles c continuous phase d dispersed phase
2. Experimental 2.1. Materials Toluene and acetic acid with purity above 99.9% were purchased from Merck and ultrapure deionized water was prepared, these materials were used as the chemical extraction systems. To synthesis hydrophobic titania nanoparticles, ultrapure isopropyl alcohol, tetraethyl orthotitanate (purity higher than 95%), citric acid and ammonium hydroxide (25% NH4OH), all supplied from Merck, were used. For surface modifying of nanoparticles, trimethoxi (octyl) silane (octyltrimethoxysilane) with a purity of 96% was prepared from Aldrich.
2.2. Synthesis of super hydrophobic TiO2 nanoparticle Titanium dioxide (TiO2) due to its unusual structural, optical, electronic, magnetic and chemical properties, exhibits wide applications in pigments, UV protection creams, photo-catalysis, solar cells, water and air purification [15–17]. There are some different methods for synthesis of titania nanoparticles such as chemical precipitation, microemulsion, hydrothermal and sol-gel, which among them, sol-gel method is the most preferred procedure to synthesis titania nanoparticles [18]. There would be hydroxyl bonds on the titania nanoparticles synthesized through sol-gel method [19], which makes them as hydrophilic materials with no inclination to distribute in non-polar organic phase [20]. Although TiO2 nanoparticles due to high surface area to volume, have peculiar properties and advantage to bulk or micro sized particles [16], but for the same reason they tend to agglomerate [20,21]. In order to change the nanoparticles hydrophobicity and to prevent them from agglomeration, various methods have been used. Surface chemical modification with organic molecules can be utilized to stabilize nanoparticles efficiently in organic solution [21]. Surface treatment of nanoparticles can be performed during or after the synthesis process, the former one is more time and cost effective, so in this work they have been synthesized and functionalized during an in situ method. Silane coupling agents typically
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
have been applied to surface modificatio of nanoparticles [16,17,20,21]. Trimethoxi (octyl) silane (TMOS) which has nonpolar organic chain with a proper length has been chosen to use as titania functionalizing agent. Based on the literature [16,17,20,21], and our investigations, synthesis of titania nanoparticles follows this procedure: at first 10 g of tetraethyl orthotitanate as titania precursor together with 30.4 g of isopropyl alcohol as a solvent was added to the beaker, which it had been kept under magnetic stirring. After 1 min, to generate a stable colloidal solution, which is called sol, a second mixture of 0.2 g water, 0.05 g of citric acid and 5 g of isopropyl alcohol was added to the stirred solution. For the surface modification of titania nanoparticles, 0.36 g of octyltrimethoxysilane was added to the second mixture. For making polymeric structure which is called gel, pH of the solution was changed by dissolving 23 g of ammonia solution to the sol, so alcohol and water condensation reactions take place. Milky produced solution was stirred for 24 h under ambient air of 25 °C until all of the solvent was vaporized. The dried gel was ground in the form of powders and by using filter paper MTNP’s were washed with deionized water to remove unreacted citric acid. Finally, to achieve dried surface modified titania nanoparticles, they were dried in a vacuum oven at the 120 °C for 2 h. 2.3. Characterization of TiO2 nanoparticles A FT-IR spectrometer (Thermo Nicolet, Nexus670) was used to indicate functional groups. In order to investigate nanoparticles hydrophobicity, 1.5 g of MTNP’s were compressed as a pill and it was placed on a film sample holder, then a 4 ll of water droplet was placed on its surface, subsequently video-based optical contact angle measuring instruments (OCA 15 plus connected to a computer using SCA20 software) was used to measure the contact angle of MTNP’s pill with the water droplet. To determine the morphological structure and to measure the particle size of the magnetite nanoparticles, a scanning electron microscope (Fe-SEM, TESCAN, MIRA 3) was used. A helium pycnometer (AccuPyc 1330) was used to measure the powder density of nanoparticles. 2.4. Preparation of TiO2 nanofluids In order to prepare titania nanofluids, these nanoparticles at the five different concentrations of 0.001, 0.002, 0.003, 0.004 and 0.005 wt.% were added to the two mixtures of toluene and acetic acid. In one mixture acetic acid concentration was 3 wt.% and in another it was 6 wt.%, so in final 10 different titania nanofluids with this two-step method were prepared. Furthermore, an ultrasound bath (Fritsch Ultrasonic, Laborette 17 with frequency of 35 kHz) was used to provide better dispersion of nanoparticles. Each sample was sonicated in the bath for 40 min. 2.5. Nanofluids stability The colloidal stability of the nanofluids (toluene, acetic acid, nanoparticles) was measured by a UVvisible spectrophotometer (JASCO V-630). For each solution containing 3 or 6 wt.% of AA, five samples of nanofluids with different MTNP’s concentration (0.001– 0.005 wt.%) was sonicated and immediately the maximum UV absorbance of those samples was measured. According to the work of Jiand et al. [22], a relation between nanoparticles concentration (i.e. in wt.%) and corresponding peak absorbance was obtained as a linear calibration line. By using these cures (one for 3 wt.% of AA and another for 6 wt.% of it) the nanoparticles relative concentration, i.e. Cnp/Cnp,0 (nanoparticles concentration at each time/initial nanoparticles concentration just after preparation) versus sedimentation time can be determined.
109
2.6. Physical properties of the chemical system at 25 °C Density and viscosity of the chemical system are measured by Anton Paar DMA 4100 M instrument with an uncertainty of 0.05 kg m3 and LAUDA viscometer with an accuracy of 0.5%, respectively. An interfacial tension measuring instrument (IFT 700, Vinci) was applied to determine the interfacial tension of nanofluid drops and water. It measures the IFT in a range of 0.1– 100 mN/m. Based on the numerical solving Young-Laplace equation over to complete shape of drop. A slight increase in all the above mentioned properties was seen due to the presence of nanoparticles. The molecular diffusivity (diffusion coefficient) of acetic acid was taken from the experimental work of Change and Wilke [23]. Table 1 shows the physical properties of chemical systems at 25 °C. 2.7. Experimental setup and procedures Experimental setup is illustrated in Fig. 1. This setup consisted of a Pyrex glass column with internal diameter of 10 cm and height of 55 cm. Dispersed phase was injected into the column with a digital syringe pump through a glass nozzle located at the bottom of the column. During this work two glass nozzles with an inside diameter of 1.5 and 2.5 mm separately were used, which are referred to nozzle no. 1 and 2 respectively. Since the purpose of the present research was only the investigation of the solute mass transfer from the dispersed to continuous phase, there should be no mass transfer between toluene and water. Thus, before starting of mass transfer experiments these materials have been mutually saturated with the each other. The dispersed flow rate was kept at 100 ml/h. To ease of collecting the dispersed phase, an inverted glass funnel connected with a pipette was held on top of the column. The inner diameter of the funnel stem was only 3 mm, hence the interfacial surface area between the dispersed and continuous phase at the funnel was very small. In order to neglect the mass transfer during the drop formation on the nozzle tip and also the unsteady mass transfer, another column with a height of only 5 cm was used. The solute concentration at the top of the little column was considered as the initial concentration for the main column, it was in the range of 520–550 mol/ m3. Through the experiments for each kind of nanofluids, initial and final solute concentrations, the terminal velocity and the drop size were measured. The solute concentration of the collected dispersed phase was measured by titration of 2 ml of those with 0.5 M NaOH, this procedure was repeated five times for each mass transfer experiment and the solute concentration at the top of the column was in the range of 135–525 mol/m3. All the experiments have been conducted at 25 + 0.5 °C. To determine terminal velocity of drops, their contact time with the continuous phase, from initial and final point (t), was measured by stopwatch with an accuracy of 0.003%. Since, the distance between the two points is known (50 cm), terminal velocity of drops (Vt) can be easily measured by Vt = 50/t with uncertainty of 0.003%. The terminal velocity of each droplet was measured 10 times and the maximum deviations from the average value was less than 0.6%. The drop sizes were measured through two different methods. In one method, for each specified solution of nanofluids total volume of 200 drops was measured with the aid of a digital syringe pump (V), then by assumption of sphericity of drops their equivalent diameter (de Þ can be calculated from Eq. (1):
de ¼
1=3 6V 200 p
ð1Þ
For each of the nanofluids this method was repeated three times, the accuracy was 1% and the maximum deviation from the average value was less than 0.4%.
110
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 1 Physical properties of chemical systems at 25 °C. System’s name
qc (kg/m3)
qd (kg/m3)
T/W 997.10 862.2 T/AA(3 wt.%)/W 997.10 866.30 T/AA(6 wt.%)/W 997.10 869.50 T/AA(3 wt.%)/MTNP’s (0.001 wt.%)/W 997.10 866.30 T/AA(3 wt.%)/MTNP’s (0.002 wt.%)/W 997.10 866.31 T/AA(3 wt.%)/MTNP’s (0.003 wt.%)/W 997.10 866.31 T/AA(3 wt.%)/MTNP’s (0.004 wt.%)/W 997.10 866.32 T/AA(3 wt.%)/MTNP’s (0.005 wt.%)/W 997.10 866.33 T/AA(6 wt.%)/MTNP’s (0.001 wt.%)/W 997.10 869.5 T/AA(6 wt.%)/MTNP’s (0.002 wt.%)/W 997.10 869.51 T/AA(6 wt.%)/MTNP’s (0.003 wt.%)/W 997.10 869.52 T/AA(6 wt.%)/MTNP’s (0.004 wt.%)/W 997.10 869.52 T/AA(6 wt.%)/MTNP’s (0.005 wt.%)/W 997.10 869.53 Dd (Molecular diffusivity of Acetic acid in Toluene) = 2.265 109 m2/s T: Toluene; AA: Acetic Acid; W:Water; MTNP’s: Modified Titania Nanoparticles
lc (mP/s)
ld (mP/s)
c (mN/m)
0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890 0.890
0.555 0.560 0.575 0.562 0.562 0.564 0.566 0.569 0.577 0.577 0.579 0.581 0.583
36 27.9 21.2 27.9 27.9 27.9 28 28 21.2 21.2 21.3 21.3 21.3
Fig. 1. Schematic of the experimental setup.
In another one, a high resolution digital camera (Canon Powershot SX610 HS) was used to take photographs of droplets. A ruler ribbon was attached to the column as a dimensional scale, and by using Image J 1.5 software the photographs were analyzed and the size of the drops was calculated again. In this investigation all of the drops were oblate spheroidal, the surface area of the elliptical drop could be determined by Eq. (2):
SOS
1 e2 1þe 2 ¼ 2pb 1 þ ln 1e 2e
ð2Þ
where
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi c2 e¼ 1 2 b
ð3Þ
b and c are respectively the horizontal and vertical diameter of an oblate spheroidal drop. Surface area of a spherical drop which has the equal volume of the oblate spheroidal, can be calculated by following equation:
Sos 1 23 ¼ E1 þ 2 Ss
1 1
1
2E31 ðE21 1Þ2
1 ln E1 þ ðE21 1Þ2
ð4Þ
where E1 is the ratio of the horizontal to the vertical axis of the oblate spheroidal, finally the equivalent diameter of the drop was determined by Eq. (5):
de ¼
rffiffiffiffiffi Ss
p
ð5Þ
For each sample, measuring the drop diameter by photographic method was repeated 50 times and the maximum deviation with the average value was less than 3%. Then, based on the equivalent drop diameter calculated by photography method, the drop diameter was taken as the Sauter mean diameter by the following equation:
Pn 3 ni dei d32 ¼ Pi¼1 2 n i¼1 ni dei
ð6Þ
111
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Sauter mean diameter calculated by the photographic method was slightly larger than that was calculated by Eq. (1) (Less than 0.3 mm). The plausible reason is the refractive index of water and the column wall (glass), which causes the bodies behind them seem smaller than their actual size. The average values determined by two methods were reported. It should be noted that to ensure accuracy of results, all the mass transfer experiments were carried out twice and for some results, with little difference, the mean values are reported. Specification of the extraction column is listed in Table 2.
J ¼ 3:42H0:441
ðH > 59:3Þ
H is determined by following equation:
H¼
4 € EOMo0:149 3
lc lw
0:14 ð10Þ
€ (Eo €tvo € s number) and Mo (Morton number) are two In which EO € ¼ gDqd2 ; dimensionless number defined as EO c
Mo ¼ glqc2Dcq ; respectively and 4
c
3. Result and discussion 3.1. Material characterization Fig. 2 shows FT-IR spectra of three nanoparticles. The bands at 700, 1640 and 3420 are attributed to: TiAOATi bonding of TiO2, hydroxyl group attached on the TiO2 and stretching vibration group, respectively [24]. For the MTNP’s, five other bands can be recognized. Band at 940 cm1 is attributed to TiAOASi bonds [25] and bands at 1032 and 1111 cm1 correspond to SiAOASi [26]. Asymmetrical and symmetrical stretching vibrations of the CAH bonds in methylene group were detected by peaks at 2927 and 2860 cm1 [26]. These bands show that MTNP’s were functionalized by silane coupling agent. Fig. 3 demonstrates Fe-SEM images of Titan nanoparticles, from this figure one can see MTNP’s have an average particle size about of 25 nm. Fig. 4, Illustrates that these nanoparticles show super hydrophobic characteristics. Water Contact angle of MTNP’s is 150° ± 1°, and the main characteristics of the MTNP’s were listed in Table 3. The viscosity of nanofluids was illustrated in Fig. 5, as it is clear from this figure, adding MTNP’s leads viscosity to increase. Fig. 6 shows the colloidal stability of MTNP’s, in the toluene solutions containing 3 and 6 wt.% of the acetic acid. According to Fig. 6., however the stability of modified titania nanoparticles in the solution containing 3 wt.% of the acetic acid is higher, but, the colloidal stability of both fluids was maintained at over 96% after 60 min. Since the operation time of the mass transfer experiments was less than 20 min, it can be concluded that nanoparticles have a good stability in the dispersed phase during conducting the experiments. 3.2. Investigate hydrodynamic performance Hydrodynamic characteristics of a liquid-liquid extraction column can directly affect on the mass transfer performance of that process [27]. In the single drop experiments, the terminal velocity and droplet size are two important hydrodynamic parameters. Grace et al. [28] proposed a correlation (Eq. (7)) to predict the terminal velocity of contaminated drops:
lc J 0:857 ð7Þ dqc M0:149 In Eq. (7), d;lc ; qc are drop size, viscosity and density of the contin-
Vt ¼
uous phase, and J is calculated by Eqs. (8) or (9).
J ¼ 0:94H0:757
ð2 < H < 59:3Þ
ð8Þ
Table 2 Main specifications of the liquid-liquid extraction column. Column height (cm) Column internal diameter (cm) Dispersed flow rate (ml/h) Nozzle tip size (mm)
55 10 100 1.5,2.5
ð9Þ
lw is the viscosity of water at 4 °C.
Terminal velocities measured experimentally by the stopwatch method were compared with the correlation of Grace et al. [28] described in Fig. 7. As it can be seen from this figure, for binary system of toluene and water, all the drops in the present work have lower terminal velocity relative to calculated values by Eq. (7). A plausible reason for such behavior is the solute mass transfer from drops. As it was observed in the previous works [29–31], droplets which are loaded with the solute have lower terminal velocity than those are unloaded. The stochastic and irregular movement of the interface induced due to the solute mass transfer, leads to increase the drag coefficient and subsequently causes the terminal velocity of drops to slow [30]. Droplets due to internal flow pattern are categorized in three different groups of stagnant, circulating and oscillating drops [32]. There are several criteria to distinguish the flow regime of drops, Grace et al. [28] reported that in the condition of 2 < H < 59:3 drops are internally circulating and for H > 59:3 drops fall into oscillating group. In the present work, H was between 71 and 113, so it can be concluded that the drops are oscillating, moreover a critical diameter (dcr) size has been defined which above that drops transient to the oscillating regime. There are several correlations for prediction of this size, which are summarized in Table 4. The critical diameters based on these correlations were reported in the Table 5. As it is clear all of the drops formed in this work had a larger diameter than dcr determined by all correlations, thus drops fall into oscillating group. Furthermore, as it was shown in Fig. 8a, droplets generated from both nozzles were ellipsoidal and according to the work of Wegener et al. [36], for a system of toluene and water, droplets bigger than 4.5 mm are non-spherical oscillating drops. From Fig. 8b it is obvious that the terminal velocity of nanofluids is slightly less than the base fluid (only toluene and acetic acid). One possible reason for such behavior may be decreasing the density difference between the dispersed and continuous phase due to the use of nanoparticles. Another may attributed to the viscosity enhancement of droplets by adding the nanoparticles as it was shown in Fig. 5, Feng and Michaelides [37] reported that increasing the viscosity ratio l ¼ lld of drops in a range of Reynolds numc
ber (5 < Re < 1000, in this work 670 < Re < 846) enhance the drag coefficient (CD), which is subsequently leads to a reduction of the terminal velocity. Also, it is reported by Wegener et al. [38] that existing of impurities can form stagnant cap, which increases the drag force and subsequently decreases the terminal velocity. Furthermore, Fig. 8 shows dispersed phase with higher concentration of solute (acetic acid) has a lower terminal velocity. When solute concentration increased the amount of mass transfer increased too, so turbulence on the interface of the two phases increased which finally leads to a reduction of the terminal velocity [36,39]. Another possible reason is enhancing the Marangoni instability by adding more solute in the dispersed phase [40], according to the [36] in high interfacial tension systems like (toluene + water) existence of solute causes to the gradient of interfacial tension on the interface of drop followed by surface turbulency, which is subsequently leads to increasing the drag coefficient (CD).
112
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Fig. 2. FT-IR spectra of TiO2 nanoparticles: (a) uncoated (b) surface modified.
Fig. 3. SEM image of surface modified TiO2 nanoparticles.
In this work addition of nanoparticles had no any remarkable change on the drop size, because a very small quantity of nanoparticles is used in dispersed phase, this is in accordance with the work of AshrafMansouri and Nasr Esfahany [11]. But, droplet containing a higher solute concentration had smaller size. Droplets with 3 wt.% of acetic acid which are formed from nozzle no. 1 and 2 had a diameter of 5.7 and 7.1 mm respectively. On the other hand, the diameter of droplets containing a higher solute concentration which are generated from nozzle no. 1 and 2 are 5.6 and 6.5 mm, respectively. Reduction of the interfacial tension due to adding of solute, is the reason for such manner [41]. 3.3. Investigation of mass transfer performance Through this work to achieve a comprehensive understanding of mass transfer performance in the liquid-liquid extraction systems, the overall dispersed-phase mass transfer coefficient was studied. Applying the mass transfer balance around a drop with the diameter d, leads to Eq. (14) [39]:
p 3 dCd 2 d ¼ Kod pd cd cd 6 dt
ð14Þ
In Eq. (14) Cd and C⁄ are solute concentration of drop and the equilibrium solute concentration with the continuous phase, respectively. Integrating of Eq. (14) from initial to final point gives:
Fig. 4. Contact angle of surface modified TiO2 nanoparticles.
Table 3 Physical characteristics of synthesized nanoparticles.
Properties
Particle size (nm)
q
Titania nanoparticles
25
2443.4
Kod ¼
C d;f C d d ln 6ðtf t0 Þ C d;0 C d
kg m3
Hydrophobicity (contact angle) 150°
ð15Þ
In which Cd,f and Cd,0 are solute concentration in drop at the initial and final point, respectively, and t is contact time of the raising drops within the continuous phase. Eq. (15) can be rewritten as:
d Kod ¼ lnð1 EÞ 6t
ð16Þ
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Fig. 5. Dynamic viscosity of nanofluids stability versus MTNP’s concentration.
Fig. 6. Nanofluids stability versus sedimentation time.
Fig. 7. Comparison between experimental terminal velocities and those calculated by Grace correlation.
113
114
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 4 Correlations for prediction of the terminal velocity of drops. Author
Correlation
Klee and Treybal [33] Eq. (11) Yamaguchi et al. [34] Eq. (12)
0:24 dcr ¼ 0:33q0:14 Dq0:43 l0:3 c c c 0:5 196c 0:22 3 ; Mo ¼ gDql4c q2 dcr ¼ Dqg Mo c c rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Mersmann [35] Eq. (13)
dcr ¼ 14:1
0:28 c0:4 l0:8 c qd
Dq0:867 g0:8 qc0:613
where E is fraction extracted and calculated by Eq. (17):
E¼
C0 C C0 C
ð17Þ
The volume of continuous phase (about 4000 ml) is much higher than the drop (less than 0.1 ml) and the continuous phase is initially free of acetic acid, thus the solute concentration in continuous phase is negligible. Since the acetic acid equilibrium concentration in the water is much higher than toluene [43], the solute concentration in water (continuous phase) is negligible and C⁄ can be assumed to zero. From section 3.2 contact time and size of the drops were determined, so E and Kod can be calculated easily. In the chemical systems of toluene, acetic acid and water, the mass transfer resistance exists mainly in the organic phase [11,44–48]. For further explanation, in accord to the Whitman two film theory the overall mass transfer resistance is determined from the sum of the local mass transfer resistance in the both phases (i.e. 1/Kod = 1/kd + m/kc), where kd and kc are dispersed and continuous phase mass transfer coefficients calculated by Baron [49] and Higbie [50], respectively. In the chemical system used in this work at 25 °C, the slope of the equilibrium curve (m) is low (m 0.09) [43], and the values of kd and kc determined by Handlos and Baron [49] and Higbie [50], are in the range of 2.3 2.5 104 m/s and 2.3 2.4 104 m/s, respectively. Since, the value of m/kc is less than 0.09 of 1/kd, the mass transfer resistance of continuous phase is negligible in the other words, Kod kd. Fig. 9 shows the overall mass transfer coefficient of the dispersed phase formed from the various nozzles and contained different solute concentrations. In all cases, the uncertainty of measurements is less than 5%, and there is a peak in the mass transfer coefficient enhancement at the MTNP’s concentration of 0.002 wt.%. This trend was similar to the other results reported by Saien and Bamdadi [8] and Ashrafmansouri and Nasr Esfahany [11]. At the solute concentration of 3 and 6 wt.%, a maximum enhancement in the overall dispersed-phase mass transfer coefficient for drops generated from the bigger nozzle was 70% and 25%, respectively. Moreover, for those drops formed from smaller nozzle, maximum enhancement in Kod was 60.7% and 24%, respectively, for 3 and 6 wt.% of acetic acid. The reason for the anomalous enhancement of the mass transfer coefficients is attributed to the microconvections created by the Brownian motion [7,51,52]. As it is clearly mentioned, the maximum enhancement in the Kod due to use of MTNP’s is more obvious for the bigger drops, this is in accord with the work of Ashrafmansouri and Nasr Esfahany [11]. To explain why nanoparticles are more effective in the bigger drops, their internal regime
should be taken into account. It can be seen that, in the oscillating drops with increasing of droplet diameter internal circulation of drop decreased [53], so there would be a more proper opportunity for Brownian motion of nanoparticles to influence on the mass transfer performance. As it is shown in Fig. 9 adding nanoparticles excess than 0.002 wt.%, leads to a continuous reduction of the overall mass transfer coefficient. The possible reason for such behavior is the aggregation of nanoparticles, which it plays an obstacle role in the diffusion of solute and subsequently leads to increasing mass transfer resistance [7,54]. According to Eq. (26), it is clear that increasing the viscosity of dispersed phase causes to reduction of the mass transfer coefficient [42], so another possible reason for decreasing of mass transfer coefficient by adding excess amount of nanoparticles is the viscosity enhancement of dispersed phase by adding MTNP’s. The possible existence of nanoparticles on the interface of drops, can be mentioned as the last reason for the reduction of Kod at the higher concentration of MTNP’s [12]. As mentioned above, the mass transfer enhancement effect of nanoparticles is higher for drops with lower solute concentration. From Fig. 9, it is obvious that solute concentration has an adverse effect on the mass transfer improvement created by nanoparticles addition. For the initial solute concentration of 3 wt.%, the average of the overall mass transfer coefficient enhancement of nozzles 1 and 2 was 34.2% and 42.9%, respectively. Whereas at the concentration of 6% of solute, for above nozzles, this value was 16.4% and 13% respectively. Increasing the initial solute concentration leads to increase the amount of solute mass transfer [46], which it presumably disturbs the Brownian motion of nanoparticles, and reduces the mass transfer promoting effect of nanoparticles. Also, the viscosity of the dispersed phase were increased by adding higher amount of the acetic acid in the drops, this can be considered as another reason for the reduction of the mass transfer coefficient at higher solute concentration [12]. 3.4. Modeling of results To calculate the overall mass transfer coefficient as a basic parameter for designing of the liquid-liquid extractors [46], several models and correlations have been reported. Mass transfer coefficient of drops depends on their internal flow regime. It is recognized that, the drops can be internally stagnant, circulated or oscillating. Based on the intensity of drop circulation, there are three models which are described in Table 6. Eq. (18) derived by Newman et al. [55], describes the overall mass transfer for molecular diffusion in stagnant droplets. For drops with internal circulation Kronig and Brink [56] suggested Eq. (19). The last model was proposed by Handlos and Baron (Eq. (20)) [49], which is reliable when the mass transfer mechanism is eddy diffusion between internal toroidal streamlines. Further of these theoretical models, there are a lot of empirical correlations which some of them have been limited to a specific condition of flow regime or type of the extraction column. However, in 1999, Kumar and Hartland [42], introduced a general equation for prediction of the dispersed phase mass transfer coefficient (Eq. (21), Table 6), which is applicable for a various range of chemical systems and flow regimes. In the present investigation, experimental Kod for drops, which are free of nanoparticles were compared with their corresponding values derived from available
Table 5 Experimental drop diameter and calculated values of critical diameter. Nozzle
dexp (mm)
dcr (mm) [33]
dcr (mm) [34]
dcr (mm) [35]
No. 1
5.6 5.7 6.5 7.1
4.1 4.3 4.1 4.3
4.5 4.6 4.5 4.6
5.2 5.4 5.2 5.4
No. 2
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
115
Fig. 8. (a) Terminal velocity of drops versus MTNP’s concentration.
Fig. 9. Overall dispersed-phase mass transfer coefficient versus concentration of MTNP’s.
Table 6 Available models and correlation for dispersed phase mass transfer coefficient. Model and correlation Newman [55] Eq. (18) Kronig & Brink [56] Eq. (19) Handlos & Baron [49] Eq. (20) Kumar and Hartland [42] Eq. (21)
Equation K od ¼
d
K od ¼
d
K od
6t 6t
Description h
P1
2
d
i h P1 2 kn V t t ¼ d n¼1 Bn exp 128dð1þkÞ 6t ln 2
kd d Dd
i
ln p62 n¼1 n12 exp 4n p2 Dd t d h P i 2 64kn Dd t ln 38 1 2 n¼1 Bn exp 2
¼ 17:7 þ
1
3:19103 ReSc3d 1þ1:4310
2
1:7
1 ReSc3d
23 q 1 0:7 qd 2 c 1þk3
Molecular diffusion in stagnant spherical drops Laminar diffusion with circulation induced by relative motion of drop and continuous phase Turbulent circulation within the drops and eddy diffusion between internal toroidalstreamlines Empirical correlation for both circulating and oscillating drops
correlations in Table 7. This table indicated that measured overall dispersed phase mass transfer coefficient have a relatively poor agreement with those calculated by Kronig and Brink correlation (Eq. (19)). It is reported that Kronig and Brink model can be applied for drops with circulation regime and low Reynolds number (less than 1) [56], while in the present investigation drops were in oscillating condition and their Reynolds number was greater than 670. On the other hand, this experimental data were in a good agreement with those calculated by Handlos and Baron model (Eq. (20)) and
Kumar and Hartland correlation (Eq. (21)). For explaining this adaptation, it should be noted that Handlos and Baron model is based on the eddy diffusion, presumably developed from drop vibrations, which is similar to the present oscillating condition of drops. Moreover, Kumar and Hartland correlation is a completely empirical generalized correlation which is driven by fitting of a broad range of data points gathered from 21 sources. Table 7 also indicated that for the smaller drops Eq. (21) predicts experimental Kod better than Eq. (20) whilst in the case
116
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
Table 7 Experimental and calculated Kod for Cnp = 0. System’s name Nozzle no. 1 Nozzle no. 2
T/AA(3 wt.%)/W T/AA(6 wt.%)/ W T/AA(3 wt.%)/ W T/AA(6 wt.%)/ W
Experimental
Eq. (13) (Kronig & Brink)
Error%
Eq. (14) (Handlos & Baron)
Error%
Eq. (15) (Kumar & Hartland)
Error%
187 189 254 228
41.7 41.4 40.3 40.2
77.5 78.0 84.0 82.3
250.6 248.88 2 C1 42.14 236.93
34.0 31,6 4.6 3.9
189.17 185.87 181.99 179.27
1.1 1.6 28.3 21.3
%AARE
80.5
18.5
of larger drops the agreement between measured Kod and those predicted by Eq. (20) was more evident. However, as it was demonstrated in Fig. 9, overall dispersedphase mass transfer coefficient of the nanofluids shows thoroughly special manner. Hence, a specific model to predict the mass transfer coefficient of dispersed phase nanofluids should be proposed. The proposed approach is applying the Newman model (Eq. (18)) with a modified molecular diffusivity, RDd, which is called overall effective (or enhanced, Doe ) diffusivity and R is the enhanced factor [57,58]. With regard to this modification, R includes both the effect of internal circulation and Brownian motion of nanoparticles, so overall dispersed-phase mass transfer coefficient is changed to the following form:
K od
" X # d 6 1 1 4n2 p2 Doe t ln 2 ¼ exp 2 6t p n¼1 n2 d
ð22Þ
To obtain R, several governing aspects, including internal circulation of drop, nanoparticles concentration and the magnitude of Brownian motion must be taken into account. Generally, the enhanced factor in this process depends on the viscosity and density of continuous and dispersed phase, velocity of drops and nanoparticles, size of drops and nanoparticles concentration. Therefore, general correlation can be written as:
fðR;qc ; qd ; lc ; ld ; Vt ; Vp ; d32 ; UÞ ¼ 0
ð23Þ
Based on Eq. (23) and pai theorem, five dimensionless groups can be defined. Thus, with the dimensional analysis R can be written as Eq. (24):
q l R ¼ f Re;U; Renp ; d ; d
ð24Þ
qc lc
To explain the origin of Eq. (24), it should be mentioned that the Reynolds number (Re) of drops plays a significant role on the flow regime of the drops, so it was selected as a parameter of the proposed correlation for enhanced factor. As it was seen in Fig. 9, Kod depends on the nanoparticles concentrations, so the volume fraction (UÞ of nanoparticles was used as the second parameter which has influence on the R. As it was mentioned in section 3.3, Brownian motion of nanoparticles has a major effect on the mass transfer performance of nanofluids. These motions are affected by the nanoparticle velocity (Vp). Furthermore, viscosity and density of dispersed phase are effective parameters on mass transfer and hydrodynamic characteristics, so the Reynolds number of nanoparticles within the
13.5
drop was chosen (Renf) as another effective variable in the enhanced factor, it is defined by Nagy et al. [51] in the form of Eq. (25):
Renf ¼
v np dp tnf
¼
1
tnf
sffiffiffiffiffiffiffiffiffiffiffiffiffiffi 18K B T pdp q
ð25Þ
Finally, as it was demonstrated in Eq. (21), density and viscosity ratios of dispersed and continuous phase are two other important variables. In the present investigation, for 20 nanofluids, R had various amounts of 33.3–150. The percentage of average absolute relative error (%AARE) was used to compare the predicted results with available models, it is defined as follows:
%AARE ¼
N 1X Model Experiment 100 N i¼1 Experiment
ð26Þ
In Eq. (26), N is the number of various drops, since there was 10 different nanofluids and also two different nozzles were used, there would be 20 different drops. The mathematical procedure for determining proper correlation and its constants is based on the regression analysis by use of Ordinary Least Square (OLS) method. In the OLS method, the final purpose is minimizing the sum of squares made by differences between the model and actual values, this was done by the DataFit 9.0 software. In order to analysis a fitted correlation, it is essential to define some statistical parameters, including R2, R2adj, Durbin Watson (D.W.T), Prob (t-statistic). The model’s ability in fitting the experimental data is determined by the R2 and R2adj, generally the value of these parameters is between 0.0 and 1.0 and the degree of fitting enhanced by increasing of these parameters. Another parameter which considers the difference between the predicted amount by model and real value is D.W.T, in a proper model this amount must be greater than 1. The last parameter is Prob (t) which shows the importance level of each model’s variable. The smaller the value of Prob (t), means the higher importance of parameter. Based on Eq. (23), a plausible type of model can be written in the form of Eq. (27):
R ¼ C 1 ReC 2 ReCnf3 UC 6
qd qc
C 4 C5 ld
lc
ð27Þ
Model parameters were determined by fitting the experimental data on Eq. (27), it was demonstrated in Table 8.
Table 8 The specification of Eq. (28). C 5 C 6 l R ¼ 10C 1 ReC 2 ReCnf3 UC 4 qqd ld Eq. (28) c c
C2 C3 C4 C5 C6
Coefficient 165.8985 4.6708 105.5066 0.1130 17.6242 93.4255
Prob(t) 0.0310 0.011 0.2869 0.8059 0.0332 0.0017
AARE%
8.4
r2
0.83
r 2adj
0.78
D.W.T
1.62
117
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119 Table 9 The specification of Eq. (29). C 4 l R ¼ 10C 1 ReC 2 ReCnf3 ld Eq. (29) c Coefficient 221.7870 5.4214 138.7525
Prob(t) 0.00026 0.0 0.00018
AARE%
8.6
C1 C2 C3
r2 r 2adj
0.82 0.78
C4
124.1335
0.00022
D.W.T
1.44
Table 10 Comparison of the models and correlation for dispersed phase mass transfer coefficient. Kod (lm s1)
System’s name
Experimental
Eq. (29) (Present work)
Eq. (19) (Kronig & Brink)
Eq. (20) (Handlos & Baron)
Eq. (26) (Kumar & Hartland)
Nozzle no. 1
T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s
(0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W (0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W
183.39 197.34 235.06 240.00 230.10 167.68 175.46 204.36 292.74 236.31
199.3 207.1 217.9 227.9 233.3 188.7 199.8 210.5 223.5 236.1
41.11 41.13 41.19 41.24 41.34 41.13 41.18 41.27 41.37 41.57
241.66 242.31 243.41 244.40 245.71 245.22 246.38 247.82 249.49 252.15
182.49 182.71 183.30 183.78 184.85 183.03 183.48 184.32 185.33 187.50
Nozzle no. 2
T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(3 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s T/AA(6 wt.%)/MTNP’s
(0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W (0.005 wt.%)/W (0.004 wt.%)/W (0.003 wt.%)/W (0.002 wt.%)/W (0.001 wt.%)/W
227.62 240.87 266.50 432.52 392.15 219.71 233.72 260.80 286.00 253.52
218.68 266.1 325.1 400.2 350.3 199.9 208 250 303.9 270.4
39.59 39.64 39.71 39.78 39.89 39.73 39.77 39.82 39.91 40.00
235.87 236.88 237.97 239.05 240.59 231.42 232.19 233.03 234.33 235.63
177.86 178.37 179.10 179.82 180.90 175.64 175.97 176.51 177.41 178.34
8.6
82.8
16.8
24.5
%AARE
Analyzing the Prob (t) leads to omitU and ðqqd Þ, so after neglectc
ing volume fraction and density ratio, another type of equation with its regression parameters is listed in Table 9. Comparison between Tables 8 and 9, indicates that Eq. (29) has lower parameters than first model type, while the difference between the AARE% of two equations is not considerable. Thus, Eq. (29) is proposed as a proper model type for prediction the overall dispersed phase in the present investigation. Also, it is worth to note that this type of model satisfies the physical principles governing the process. It is reported in the various works that the enhancement in the transfer coefficients is directly proportional to Brownian motion [2,7–10], which is in adapt to the proposed model where it relates to Renf. Furthermore, in all of the published works addressed this issue, the enhancement factor is a function of the Reynolds number [59], which is in accordance to Eq. (29). In Table 10, the values of overall dispersed-phase mass transfer coefficient computed by different equations were listed, and a comparison between the proposed model with other conventional equations have been done. According to Table 10, both Kronig and Brink and Handlos and Baron equations, cannot be able to predict the overall dispersed-phase mass transfer coefficient appropriately, but predicted values by the new proposed model are in a good agreement with the experimental data. The AARE of Kod for Kronig & Brink and Handlos & Baron models are 82.8% and 16.8%, respectively, and it is 24.5% for Kumar and Hartland correlation, but its value for the new proposed model is only 8.6%, which indicates precise predictability of this approach. Fig. 10 shows that prediction of Kod from Eq. (29), is more satisfying than other works.
Fig. 10. Comparison of the experimental Kod with present and previous equations.
To explain why the traditional model (i.e. Kronig & Brink and Handlos & Baron models) as well as the Kumar and Hartland correlation cannot accurately estimate the overall dispersed-phase mass transfer coefficient, it should be mentioned that these equations
118
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119
don’t take the Brownian motion of nanoparticles into account. In contrast, the influence of MTNP’s nanoparticles and other major parameters such as droplet size and terminal velocity, physical properties of both phases are considered in the proposed model.
4. Conclusion During this investigation, the super hydrophobic titania nanoparticles were prepared via a modified sol-gel method. Then nanoparticles were applied in the non-polar dispersed phase of a single drop liquid-liquid extraction column. It was found that the overall dispersed-phase mass transfer coefficient of solute is greatly affected by using this type of nanoparticles. Adding modified titania nanoparticles in concentration up to 0.002 wt.% led to a continuous mass transfer enhancement, but after this concentration the overall dispersed-phase mass transfer coefficient decreased to the extent which it was even lower than that of the base fluid. The mass transfer improvement due to the use of nanoparticles was more observable for bigger droplets containing a lower solute concentration. Finally, based on the Newman’s theoretical model and experimental data, a rigorous semi-empirical equation was proposed to predict the overall dispersed-phase mass transfer coefficient in terms of droplet’s Reynolds number, nanoparticle’s Reynolds number and viscosity ratio. For the chemical systems and extraction column studied in the present investigation the proposed model has higher accuracy and precision with the experimental data compared with other available models.
References [1] W. Duangthongsuk, S. Wongwises, An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime, Int. J. Heat. Mass Transfer 53 (1–3) (2010) 334–344. [2] S.S. Ashrafmansouri, M. Nasr Esfahany, Mass transfer in nanofluids: a review, Int. J. Therm. Sci. 82 (2014) 84–99. [3] J.A. Eastman, S.U.S. Choi, S. Li, W. Yu, L.J. Thompson, Anomalously increased effective thermal conductivities of ethylene glycol based Nanofluids containing copper nanoparticles, Appl. Phys. Lett. 78 (2001) 718–720. [4] S. Kakaç, A. Pramuanjaroenkij, Review of convective heat transfer enhancement with nanofluids, Int. J. Heat Mass Transfer 52 (2009) 3187–3196. [5] Z. Azizi, A. Alamdari, M.R. Malayeri, Convective heat transfer of Cu-water nanofluid in a cylindrical microchannel heat sink, Energ. Convers. Manage. 101 (2015) 515–524. [6] Z. Azizi, A. Alamdari, M.R. Malayeri, Thermal performance and friction factor of a cylindrical microchannel heat sink cooled by Cu-water nanofluid, Appl. Therm. Eng. 99 (2016) 970–978. [7] A. Bahmanyar, N. Khoobi, M.R. Mozdianfard, H. Bahmanyar, The influence of nanoparticles on hydrodynamic characteristics and mass transfer performance in a pulsed liquid–liquid extraction column, Chem. Eng. Process. 50 (2011) 1198–1206. [8] J. Saien, H. Bamdadi, Mass transfer from nanofluid single drops in liquid-liquid extraction process, Ind. Eng. Chem. Res. 51 (2012) 5157–5166. [9] A. Mirzazadeh Ghanadi, A. Heydari Nasab, D. Bastani, A.K. Seife Kordi, The effect of nanoparticles on the mass transfer in liquid–liquid extraction, Chem. Eng. Commun. 202 (5) (2015) 600–605. [10] G. Nematbakhsh, A. Rahbar-Kelishami, The effect of size and concentration of nanoparticles on the mass transfer coefficients in irregular packed liquid– liquid extraction columns, Chem. Eng. Commun. 202 (11) (2015) 1493–1501. [11] S.-S. Ashrafmansouri, M. Nasr Esfahany, The influence of silica nanoparticles on hydrodynamics and mass transfer in spray liquid–liquid extraction column, Sep. Purif. Technol. 151 (2015) 74–81. [12] H. Hasani Goodarzi, M. Nasr Esfahany, Experimental investigation of the effects of the hydrophilic silica nanoparticles on mass transfer and hydrodynamics of single drop extraction, Sep. Purif. Technol. 170 (2016) 130–137. [13] X. Fang, Y. Xuan, Q. Li, Experimental investigation on enhanced mass transfer in nanofluids, Appl. Phys. Lett. 95 (2009) 203103–203108. [14] S. Krishnamurthy, P. Bhattacharya, P.E. Phelan, R.S. Prasher, Enhanced mass transport in nanofluids, Nano Lett. 6 (3) (2006) 419–423. [15] V. Chaudhary, A.K. Srivastava, J. Kumar, On the sol-gel synthesis and characterization of titanium oxide nanoparticles, MRS Proc. (2011) 1352, http://dx.doi.org/10.1557/opl.2011.759. [16] H. Pan, X.D. Wang, S.S. Xiao, L.G. Yu, Z. Zhang, Preparation and characterization of TiO2 nanoparticles surface-modified by octadecyltrimethoxysilane, Indian. J. Eng. Mater. S 20 (2013) 561–567.
[17] J. Zhaoa, M. Milanovab, M.M.C.G. Warmoeskerkena, V. Dutschka, Surface modification of TiO2 nanoparticles with silane coupling agents, Colloids Surf. A: Physicochem. Eng. Aspects 413 (2012) 273–279. [18] F. Sayilkan, H. Sayilkan, M. akarsu, Characterization of TiO2 synthesized in alcohol by a sol-gel process: the effects of annealing temperature and acid catalyst, Turk. J. Chem. 29 (2005) 697–706. [19] W. Wu, Q. He, C. Jiang, Magnetic iron oxide nanoparticles: synthesis and surface functionalization strategies, Res Lett. 3 (11) (2008) 397–415. [20] S. Mallakpour, E. Nikkhoo, Surface modification of nano-TiO2 with trimellitylimido-amino acid-based diacids for preventing aggregation of nanoparticles, Adv. Powder Technol. 25 (2014) 348–353. [21] M. Sabzi, S.M. Mirabedini, J. Zohuriaan-Mehr, M. Atai, Surface modification of TiO2 nano-particles with silane coupling agent and investigation of its effect on the properties of polyurethane composite coating, Prog. Org. Coat. 65 (2) (2009) 222–228. [22] Jiand et al., Production of aqueous colloidal dispersions of carbon nanotubes, Colloid Interface Sci. (2003) 89–94. [23] P. Chang, C.R. Wilke, Some measurements of diffusion in liquids, J. Phys. Chem. 59 (7) (1955) 592–596. [24] Q. Chena, N.L. Yakovlevb, Adsorption and interaction of organosilanes on TiO2 nanoparticles, Appl. Surf. Sci. 257 (2010) 1395–1400. [25] Z. Li, B. Hou, Y. Xu, D. Wu, Y. Sun, W. Hu, F. Deng, Comparative study of sol–gel hydrothermal and sol–gel synthesis of titania–silica composite nanoparticles, J. Solid State Chem. 178 (2005) 1395–1405. [26] E. Ukaji, T. Furusawa, M. Sato, N. Suzuki, The effect of surface modification with silane coupling agent on suppressing the photo-catalytic activity of fine TiO2 particles as inorganic UV filter, Appl. Surf. Sci. 254 (2007) 563–569. [27] P.H. Calderbank, I.J.O. Korchinski, Circulation in liquid drops: a heat transfer study, Chem. Eng. Sci. 6 (1956) 65–78. [28] J.R. Grace, T. Wairegi, T.H. Nguyen, Shapes and velocities of single drops and bubbles moving freely through immiscible liquids, T. I. Chem. Eng. – Lond. 54 (1976) 167–173. [29] F.W. Keith, A.N. Hixson, Liquid-liquid extraction spray columns-drop formation and interfacial transfer area, Ind. Eng. Chem. 47 (2) (1955) 264–266. [30] M. Henschke, A. Pfennig, Mass-transfer enhancement in single drop mextraction experiments, AIChE J. 45 (1999) 2079–2086. [31] T. Al-Hassan, C.J. Mumford, G.V. Jeffreys, Flow characteristics of large oscillating drops in liquid-liquid systems, Chem. Eng. Technol. 14 (1) (1991) 65–72. [32] B. Arendt, R. Eggers, Interaction of Marangoni convection with mass transfer effects at droplets, Int. J. Heat. Mass Trans. 50 (2007) 2805–2815. [33] A.J. Klee, R.E. Treybal, Rate of rise or fall of liquid drops, AIChE J. 2 (4) (1956) 444–447. [34] M. Yamaguchi, T. Fujimoto, T. Katayama, Experimental studies of mass transfer rate in the dispersed phase and moving behavior for single oscillating drops in liquid–liquid systems, J. Chem. Eng. Jpn. 8 (5) (1975), 366-361. [35] A. Mersmann, Zur stationären Bewegung fluider Partikel (in German), Chem. Ing. Technol. 46 (6) (1974) 251. [36] M. Wegener, N. Paul, M. Kraume, Fluid dynamics and mass transfer at single droplets in liquid/liquid systems, Int. J. Heat Mass Transfer 71 (2014) 475–495. [37] Z.G. Feng, E.E. Michaelides, Drag coefficients of viscous spheres at intermediate and high Reynolds numbers, J. Fluids Eng. 123 (2001) 841–849. [38] M. Wegener, Matthias Kraume, Anja R. Paschedag, Terminal and transient drop rise velocity of single toluene droplets in water, AIChE J. 56 (1) (2010) 1–10. [39] X. Li, Z.-S. Mao, W. Fei, Effects of surface-active agents on mass transfer of a solute into single buoyancy driven drops in solvent extraction systems, Chem. Eng. Sci. 58 (2003) 3793–3806. [40] M. Wegener, M. Fevre, A.R. Paschedag, M. Kraume, Impact of Marangoni instabilities on the fluid dynamic behaviour of organic droplets, Int. J. Heat Mass Transf. 52 (11–12) (2009) 2543–2551. [41] M. Torab Mostaedi, P. Khadiv Parsi, M. Moosavian, Experimental investigation of phase inversion of liquid-liquid systems in a spray extraction column, Iran. J. Chem. Chem. Eng 27 (2) (2008) 135–140. [42] A. Kumar, S. Hartland, Correlation for prediction of masstransfer coefficients in single drop system and liquid–liquid extraction columns, Chem. Eng. Res. Des. 77 (Part A) (1999) 372–384. [43] J. Saien, M. Mozafarvandi, S. Daliri, M. Norouzi, (Liquid + liquid) equilibria for the ternary (water+acetic acid+toluene) system at different temperatures: experimental data and correlation, J. Chem. Thermodynam. 57 (2013) 76–81. [44] J.C. Godfrey, M.J. Slater, Liquid-Liquid Extraction Equipment, Wiley, Chichester, UK/New York, 1994. [45] J. Temos, H. Pratt, G. Stevens, Mass transfer to freely-moving drops, Chem. Eng. Sci. 51 (1996) 27. [46] A. Rahbar, Z. Azizi, H. Bahmanyar, M.A. Moosavian, Prediction of enhancement factor for mass transfer coefficient in regular packed liquid–liquid extraction columns, Can. J. Chem. Eng. 89 (2011) 508–519. [47] Z. Azizi, M. Rezaeimanesh, H. Abolghasemi, H. Bahmanyar, Effective diffusivity in a structured packed column: experimental and Sherwood number correlating study, Chem. Eng. Res. Des. 92 (2014) 43–53. [48] Z. Azizi, M. Rezaeimanesh, Packing effect on mass transfer and hydrodynamics of rising toluene drops in stagnant liquid, Chem. Eng. Res. Des. 115 (2016) 44– 52. [49] A.E. Handlos, T. Baron, Mass and heat transfer from drops in liquid –liquid extraction, AIChE J. 3 (1957) 127–136. [50] R. Higbie, The rate of absorption of a pure gas into still liquid during short periods of exposure, Tram. Am. InPt. Chem. Eng. 31 (1935) 365.
A. Hatami et al. / Separation and Purification Technology 176 (2017) 107–119 [51] E. Nagy, T. Feczkó, B. Koroknai, Enhancement of oxygen mass transfer rate in the presence of nano sized particles, Chem. Eng. Sci. 62 (2007) 7391–7398. [52] S.W. Park, B.S. Choi, J.W. Lee, Effect of elasticity of aqueous colloidal silica solution on chemical absorption of carbon dioxide with 2-amino-2-methyl-1propanol, KoreaeAust. Rheol. J. 18 (2006) 133–141. [53] P.M. Rose, R.C. Kintner, Mass transfer from large oscillating drops, A.1.Ch.E. J. 12 (3) (1966) 530–534. [54] C. Gerardi, D. Cory, J. Buongiorno, L.W. Hu, T. McKrell, Nuclear magnetic resonance-based study of ordered layering on the surface of alumina nanoparticles in water, Appl. Phys. Lett. 95 (25) (2009) 253104. [55] A.B. Newamn, The drying of porous solids. Diffusion and surface emission effects, Trans. Am. Inst. Chem. Eng. 27 (1931) 203–220.
119
[56] R. Kronig, J.C. Brink, On the theory of extraction from falling drops, Appl. Sci. Res. 2 (1) (1951) 142–154. [57] M.J. Slater, A combined model of mass transfer coefficients for contaminated drop liquid-liquid systems, Can. J. Chem. Eng. 73 (1997) 462. [58] A.M. Dehkordi, S. Ghasemian, D. Bastani, Model for excess mass-transfer resistance of contaminated liquidliquid systems, Ind. Eng. Chem. Res. 46 (5) (2007) 1563–1571. [59] L. Steiner, Mass transfer rates from single drops and drop swarms, Chem. Eng. Sci. 41 (8) (1986) 1979–1986.