Influences of Axial Mixing of Continuous Phase and Polydispersity of

Sep 18, 2015 - In order to evaluate the degree of the axial mixing and the polydispersity, the important variables affecting axial dispersion coeffici...
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Influences of Axial Mixing of Continuous Phase and Polydispersity of Emulsion Drops on Mass Transfer Performance in a Modified Rotating Disc Contactor for an Emulsion Liquid Membrane System Lelin Zeng, Li Yang, Qi Liu, Wensong Li, and Yunquan Yang* School of Chemical Engineering, Xiangtan University, Xiangtan City, Hunan 411105, P. R. China ABSTRACT: A mathematical model considering the effects of axial mixing of continuous phase and polydispersity of dispersed emulsion drops was developed to describe the mass transfer mechanism of an emulsion liquid membrane (ELM) in a modified rotating disc contactor (MRDC). The calculated results indicate that the axial mixing lowered the concentration gradient along the column, and the polydispersity caused the maldistribution of the interfacial area and the volume for the different sized drops, which also reduced the mass transfer performance. In order to evaluate the degree of the axial mixing and the polydispersity, the important variables affecting axial dispersion coefficient (EM), emulsion phase holdup (Φ), and drop size distribution (α and β) including rotating speed, flow ratio, total flow, surfactant concentration, and stirring paddle width were also studied. It was found that the standard deviation of the drop size (β) had same variation trend as the mean drop size (α). The increase in the rotating speed and the paddle width enhanced the turbulence which increased the EM and the Φ and simultaneously decreased the α and the β. The increase in the flow ratio markedly increased the Φ, the α, and the β, whereas the increase in the total flow signally increased the EM. The increase in the surfactant concentration primarily decreased the α and the β; meanwhile, the membrane leakage was obviously inhibited. Finally, the dimensionless correlations were established to predict these hydrodynamic parameters (EM, Φ, α, and β) with the AAREs of 5.2%, 7.5%, 2.7%, and 4.4%, respectively.

1. INTRODUCTION The emulsion liquid membrane (ELM) technique has been widely studied in many fields such as wastewater treatment,1−3 hydrometallurgy,4,5 biochemistry,6,7 etc. However, there are few studies working on the continuous operation of the ELM process.8 The column apparatuses used in liquid−liquid extraction were also generally considered to be suitable continuous equipment for the ELM system. Bhowal et al.9 investigated the continuous removal of chromium using a modified spray column by the ELM. Nevertheless, the contact time of continuous and dispersed phases in the spray column is usually short, and the axial mixing is more serious than other columns with baffles. Lee et al.10 used an Oldshue-Rushton type column to separate acetic acid from succinic acid by the ELM. Even though the mixing ability in the Oldshue-Rushton column is strong, this strong mixing ability would easily cause the reemulsification between the emulsion phase and the continuous phase. Thus, rotating disc contactor (RDC) seems to be a suitable choice for the ELM system. The stator rings in the RDC can reduce the axial mixing of the continuous phase. Unfortunately, the shearing force of the disc is not enough for the ELM system, because the viscous stress of the emulsion is relatively large. In this paper, the disc in the RDC was modified by adding two flat paddles onto its upper and under planes, respectively. Due to this modification, the degree of mixing in the modified rotating disc contactor (MRDC) was appropriately increased. It is vital to estimate the effects of the hydrodynamic properties including the axial mixing of the continuous phase and the polydispersity of the dispersed drops on the mass transfer performance.11,12 Due to the axial mixing, the flow pattern in the RDC column deviates from ideal plug flow and the concentration © 2015 American Chemical Society

gradient at the axial direction of the column declines. Usually, the degree of the axial mixing can be quantitatively described by the axial dispersion coefficient (EM).13,14 To date, the axial mixing analysis for the continuous operation of the ELM is extremely scanty. Moreover, the polydispersity of the emulsion drops can also affect the mass transfer efficiency of the ELM. The smaller drops have larger specific interfacial area and shorter mass transfer distance than the bigger drops. The drop size, together with emulsion phase holdup, determines the specific interfacial area which markedly affects the mass transfer rate. Several studies have been reported with the aim of obtaining empirical or semiempirical correlations for the dispersed phase holdup, the mean drop size, and its distribution in the liquid−liquid extraction columns.15−17 However, these correlations could not accurately apply to the ELM system. Moreover, population balance modeling could accurately predict the drop size distribution if the kernel functions (models) for drops breakup and coalescence were correct.18 Even though a number of breakup and coalescence models were reported,19,20 these models could not apply to the ELM system due to their limiting conditions (i.e., their main application range: gas−liquid system or liquid−liquid system). In comparison with the above simple two-phase system, the ELM system is much more complex due to the surfactant and the third phase (internal aqueous droplets) in the ELM. To sum up, it is necessary to further investigate the influences of these hydrodynamic properties on the mass transfer analysis in the MRDC for the ELM system. Received: Revised: Accepted: Published: 9832

July 29, 2015 September 18, 2015 September 18, 2015 September 18, 2015 DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

Article

Industrial & Engineering Chemistry Research

Figure 1. Model of the ELM in the MRDC: (1) inflow of continuous phase; (2) variation of cM, c due to axial mixing; (3) variation of cM, c due to continuous phase flow ; (4) mass transfer at external interface; (5) outflow of continuous phase; (6) inflow of emulsion phase; (7) variation of cM, o due to emulsion phase flow; (8) variation of cM, s due to emulsion phase flow; (9) stripping reaction; (10) outflow of emulsion phase; (11) mass transfer in thin water layer; (12) extraction equilibrium; (13) mass transfer in thin oil layer; (14) diffusion in membrane phase; (15) stripping equilibrium.

2. MATHEMATICAL MODELING As shown in Figure 1, considering the axial mixing of the continuous phase and the polydispersity of the emulsion drops, the mass balance in the continuous phase was calculated by

So far, only few mathematical models considering the effects of the axial mixing and the polydispersity on the mass transfer behaviors have been reported. Kinugasa et al.21 proposed a model taking into account the axial mixing of the continuous phase for the ELM system. Bhowal et al.9 also considered the effect of the axial mixing in the mass transfer description of chromium removal by the ELM. In the above two studies, the parameter estimations of the axial dispersion coefficient were both calculated using a correlation proposed by Baird and Rice.22 Nevertheless, this correlation is only applicable to the columns without baffle. For the dispersed phase, few studies were presented on the polydispersity of the emulsion drops in the ELM system. Chakraborty et al.23 investigated the effect of drop size distribution on the mass transfer analysis in a batch ELM operation. Lorbach and Hatton11 systematically studied the polydispersity of the drops in column-type contactors, batch operation vessel and mixer-settler, respectively. In the above two papers, the advancing front model was used to describe the mass transfer in the different sized emulsion drops. Generally, the stripping reaction was assumed to be irreversible in the advancing front model. This model has been well applied to explain the mechanism of phenols removal by the ELM.21 However, the ELM systems with reversible stripping reaction are also universal. For example, the stripping reactions of the metal ions in the ELM could be described by the reaction kinetics or equilibrium equations.24,25 Hence, it is indispensable to establish more accurate mathematical models for the ELM system. In this study, a mathematical model considering the axial mixing of the continuous phase and the polydispersity of the emulsion drops was developed to analyze the mass transfer behavior in the MRDC for the ELM system. The extraction and stripping reactions were both assumed to be in equilibrium and could be described by the partition coefficients (m and n).26,27 In order to evaluate the degree of the axial mixing and the polydispersity, the effects of rotating speed, flow ratio, total flow, surfactant concentration, and stirring paddle width on the axial dispersion coefficient (EM), the emulsion phase holdup (Φ), and the drop size distribution parameters (α and β) were also, respectively, studied. Finally, empirical correlations were established to predict the above hydrodynamic parameters (EM, Φ, α, and β), respectively.

EM

d 2cM,c dz 2

+ Uc

dcM,c dz

N

−

∑ Koca(i)(mcM,c − cM,o(i)|r= R f(i)) = 0 i=1

(1)

where a(i) = 6Φ(i)/d(i), Φ(i) = Φ·PV(i), i = 1, 2, 3, ..., N. N is the number of the drop size classes. Koc was defined by the following equation: * i)) Koc(mc M,c − c M,o(i)|r = R f(i)) = kM(c M,c − c M,c( * i) − c M,o(i)|r = R ) = kE(c M,o( f(i)

(2)

where cM, o = mcM, c. The mass balance in the organic phase of the emulsion drops was given by (1 − φ(′i))UE(c M,o(i) − (c M,o(i) + dc M,o(i)))SPV(i) + Sdz Φ(i) DE,eff

1 ∂ ⎛ 2 ∂c M,o(i) ⎞ ⎟ − a′rs(i) = 0 ⎜r ∂r ⎠ r 2 ∂r ⎝

(3)

where φ′(i) = φ/(1 − ε(i)) , φ = vs/(vs + vo), ε(i) = 1 − Rf(i)/R(i), R(i) = d(i)/2, Rf(i) = R(i) − δ. Herein, the superficial velocities of the different sized drops (UE) were assumed to be uniform.28 The following equation was the mass balance in the internal aqueous phase: 3

φ(′i)UE(c M,s(i) − (c M,s(i) + dc M,s(i)))SPV(i) + a′rs(i) = 0

(4)

At the internal interface, the stripping reaction equilibrium was represented by c M,s = nc M,o (5) According to the eqs 3−5, the eq 6 was obtained and expressed as ((1 − φ(′i))UE + nφ(′i)UE)

∂cM,o(i) ∂z

= ΦDE,eff

1 ∂ ⎛ 2 ∂cM,o(i) ⎞ ⎜r ⎟ ∂r ⎠ r 2 ∂r ⎝ (6)

Following are the boundary conditions: z = 0, 9833

∂c M,o(i) ∂z

= 0,

c M,o(i) = 0,

0 c M,c = c M,c

(7)

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

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Industrial & Engineering Chemistry Research

Figure 2. Experimental apparatus (Dimensions of the paddle were: 16 mm in length; 4 mm in thickness; 4, 5, 6, 8, or 10 mm in width.).

z = L, r = 0,

r = R,

EM

dc M,c dz

∂c M,o(i) ∂r

= Uc(c M,f − c M,c)

(8)

=0

Koc(mc M,c − c M,o(i)|r = R f(i)) = DE,eff

spindle (8 mm diameter) equipped with 17 discs (40 mm diameter) is powered by a geared motor. The disc is located in the central of each compartment. Unlike the traditional RDC, each disc in the MRDC was improved by affixing two paddles on its upper and under planes, respectively. The injection inlet of S0 and the sampling opening of S1 and S2 for the axial mixing experiment were, respectively, located at the wall of the column. The distance between S1 and S2 was 300 mm. 3.2. Materials and Methods. The feed solution was prepared by dissolving 3CdSO4·8H2O (Sinopharm Chemical Reagent Co., Ltd. (Shanghai, China)) in distilled water and adding 0.1 mol/L citric acid−sodium citrate buffer solution (Fengchuan Chemical Reagent Co., Ltd. (Tianjin, China)) to obtain a constant pH value of 4.0. The internal stripping solution was 0.5 M sulfuric acid (Kaixin chemical Co., Ltd. (Hengyang, China)). The organic phase was composed of a solvent of kerosene (Sinopec), an extractant of di(2-ethylhexyl)phosphoric acid (P204, Zhongda Chemical Co.,Ltd. (Luoyang, China)), a stabilizer of polyisobutylene (PIB, Mw ≈ 100 000, Luzhongshanhe Trade Co., Ltd. (Jinan, China)), and a surfactant of T154 (polyisobutylenesuccinimide, Kangtai Lubricant Additives Co., Ltd. (Jinzhou, China)). The LiCl solution with an initial concentration of 3000 mg/L and a dosage of 20 mL was used as a tracer to measure residence time distribution (RTD) in the MRDC. In order to evaluate membrane breakage ratio, another trace of KCl (3000 mg/L) was added into the internal phase. The emulsion was prepared by mixing the internal stripping solution and the organic phase with a volume ratio of 1:3. A homogenizer (Specimen and Model Factory (Shanghai, China)) was used in the emulsification process at the speed of 7500 rpm for 30 min (2 L emulsion solution for each time). The emulsion and the continuous aqueous phase formed a countercurrent flow in the column owing to the density difference. When the concentration of Cd2+ in the continuous phase at the exit of the column no longer changed, the steady state was reached, and then, the samples at the different positions of the column were taken for Cd2+ concentration profile analysis. The analysis of the

(9)

∂c M,o(i) ∂r

r = R f(i)

(10)

The above partial differential equations system was discretized into an ordinary differential equations system which was solved by calling an internal function called ODE23S in the MATLAB. Besides, the parameter of the emulsion phase holdup was calculated by vE Φ= vE + vc (11) By combining the assumptions of this paper, the effective diffusivity (DE,eff) and the thickness of the thin oil layer (δ) were, respectively, computed according to a study proposed by Teramoto and Matsuyama:29 DE,eff = DE(1 − φ1/3 + DEφ1/3(nφ2/3DM + (1 − φ2/3)DE)−1)−1 (12)

δ=

1/3 1⎛4 ⎞ ⎜ π⎟ dμ(φ−1/3 − 1) 2⎝3 ⎠

(13)

3. EXPERIMENTAL SECTION 3.1. Experimental Apparatus. As shown in Figure 2, the experimental apparatus is composed of a MRDC (80 mm internal diameter, 850 mm effective height) and auxiliary equipment. The MRDC was separated into 17 stages by the stator rings (45 mm opening diameter). There are eight sampling ports uniformly distributed in the flank of the column. A rotor 9834

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

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Industrial & Engineering Chemistry Research ⎛ EM ⎞ Δσ 2 = 2 ⎜ ⎟ Δt ̅2 ⎝ UcL1 ⎠

concentration of Cd2+, K+, and Li+ was done using an atomic absorption spectrophotometer (AA6300C, Shimadzu, (Kyoto, Japan)). The pH value was determined by a pH meter (PHS-3D, Precision & Scientific Instrument CO., Ltd. (Shanghai, China)). The measurement of the interfacial tension was done by an interface tensiometer (Hengping Instrument and meter Factory (Shanghai, China)). A viscometer (SNB-1, Precision & Scientific Instrument CO., Ltd.) was used to measure the viscosity of the membrane phase. The partition coefficients (m and n) were estimated by extraction and stripping equilibrium experiments. The extraction experiments were carried out in a closed vessel with magnetic stirring for 24 h at different values of cadmium concentration in the range of 10 to 100 ppm. Then, the loaded organic phase was stripped by 0.5 M sulfuric acid solution. The emulsion phase holdup was measured by the volume displacement method. The diameter of the internal aqueous droplets was determined by the laser particle analyzer (Mastersizer2000, Malvern Instruments Ltd. (Malvern, UK)).The experimental conditions of the ELM were shown in Table 1.

rotating speed (rpm) flow ratio (Vc/Vd) total flow (Vc + Vd, L/h)

2

Δσ 2 = σ2 2 − σ12 ,

Δ t ̅ 2 = ( t 2̅ − t1̅ )2

(15)

Following are the equations to define t ̅ and σ : 2

∞

t̅ =

∫0 tC dt

=

∞

∫0 C dt

∑ t jCjΔt j ∑ CjΔt j

∞

2

σ =

≅

∫0 (t − t ̅ )2 C dt ∞

∫0 C dt ∑ t j 2CjΔt j ∑ CjΔt j

(16) ∞

=

∫0 t 2C dt ∞

∫0 C dt

− t ̅2

− t ̅2 (17)

3.4. Determination of Drop Size Distribution. The emulsion drops photographs were taken from the MRDC using a Canon camera (60D; Canon (Tokyo, Japan)) with a zoom lens and a close-up filter. In order to take into account the effect of the mass transfer on the drop size,30 the experiments of the drop size determination were carried out during the mass transfer process. An image processing program was developed to measure and analyze the drop size using the function of REGIONPROPS in the MATLAB. As an example, Figure 4a shows an emulsion drops photograph. The frequency of volume fraction of the drops was calculated by

Table 1. Experimental Conditions variables

(14)

where Δσ and Δt ̅ were, respectively, calculated by 2

conditions 200, 250, 300, 350, and 400 1.25/8.75, 1.67/8.33, 2/8, 2.5/7.5, and 3.33/6.67 1.25 + 5, 1.67 + 6.67, 2 + 8, 2.5 + 10, and 3.33 + 13.33 3, 4, 5, 6, and 7

T154 concentration (%, v/v) stirring paddle width (mm) 4, 5, 6, 8, and 10

3.3. Determination of Axial Dispersion Coefficient (EM). The axial dispersion coefficient could be obtained from the residence time distribution (RTD) experiment. As shown in Figure 2, a pulse of tracer (LiCl) was rapidly injected at the position of S0. Two sampling openings of S1 and S2 were used to measure the tracer concentration curves. The samples for RTD measurement were periodically taken once the tracer was injected. Because the squirt of tracer was not an ideal pulse, to overcome this disadvantage, the tracer curve of S2 was considered as the response from the nonideal pulse stimulus of S1. As an example, Figure 3 shows the tracer concentration distribution curves. The flow in the MRDC was regarded as open−open boundary condition, so the axial dispersion coefficient was calculated by the following equation:14

1

fV(i) =

k(i) 6 πd(i)3 1

∑ k(i) 6 πd(i)3

(Δd(i))−1 (18)

As a result, the drop size distribution based on the volume of the drops was shown in Figure 4b. It was found that the drop size distribution fitted well with normal distribution which was defined by following probability density function: fV(i) =

2 2 1 e−(d(i)− α) /(2β ) 2π β

(19)

During the fitting process, the probability density function was integrated and converted into a cumulative probability distribution function. Because the experimental data were discrete, the intersectional length of the drop size was equally divided into ten sections. Then, the parameters of α and β were calculated by optimization in the MATLAB using the function of FMINCON. An average absolute relative error (AARE) was used as an objective function in the optimization process. The AARE was calculated by AARE =

1 n

n

∑ i=1

|cexp − ccalc| cexp

(20)

The parameter estimation method of the FMINCON was aimed to minimize the AARE. As an example, the fitted result was presented in Figure 5a. The comparison between the calculated normal distribution curve and the experimental data was also illustrated in Figure 5b. As mentioned above, the drop size was divided into ten equidistant sections. For the purpose of further simplification, the drop size of each section (d(i)) was simplified by a mean drop size (d̅(i)) which was defined as

Figure 3. Tracer concentration distribution curves (Experimental conditions were: N = 300 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm). 9835

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Figure 4. (a) Emulsion drops photograph; (b) drop size distribution based on the volume of the drops (Experimental conditions were: N = 350 rpm, Vc/ Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm).

Figure 5. (a) Fitted results of the cumulative probability distribution; (b) comparison between the calculated normal distribution curve and the experimental data of the drop size distribution (Experimental conditions were: N = 350 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm).

Figure 6. (a) Calculated results of the concentration profile of Cd2+ along the column for different models; (b) concentration profiles of Cd(II) in the different sized emulsion drops (0 ≤ r ≤ Rf(i)) (Experimental conditions were: N = 350 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm.).

d(̅ i) =

d(i),min + d(i),max 2

4. RESULTS AND DISCUSSION (21)

4.1. Calculated Results of the Model. As shown in Figure 6a, the experimental data of the concentration profile of Cd2+ along the column were fitted with the present model based on the axial mixing and the polydispersity. The overall mass transfer coefficient (Koc) was obtained by optimization using the function of the FMINCON in the MATLAB. For comparison purposes, the Koc was tested in the calculation of the concentration profile

Then, the percentage of the drops volume for each section was, respectively, calculated by 1

PV(i) =

k(i) 6 πd(i)3 1

∑ k(i) 6 πd(i)3

(22) 9836

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

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Figure 7. Calculated concentration distribution of Cd(II) in the different sized emulsion drops (0 ≤ r ≤ Rf(i); (a) Rf(1), (b) Rf(3), (c) Rf(6), (d) Rf(10)) along the column (Experimental conditions were: N = 350 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm.).

external phase, while the emulsion drops breakup means that a maternal drop breaks into several daughter drops. Conversely, the small drops can also coalesce into a big drop. Stroeve and Varanasi32 observed the above two breakup behaviors using a cinemicrophotography technique and proved that the membrane breakage is almost independent of the drops breakup. However, the drops breakup could increase the specific interfacial area of the emulsion drops which would expose more internal water droplets at the emulsion drops surface and then intensify the membrane breakage. The membrane breakage ratio (η) could be calculated by

using other two models (i.e., Model (I): the model without considering the axial mixing; Model (II): the model with a mean diameter). The Model (I) is usually known as a plug flow model (PFM)31 in which the continuous phase is assumed to form an ideal plug flow (i.e., EM = 0), whereas the Model (II)9,21 is another type of simplified model which assumed that all dispersed drops have the same diameter (e.g., Sauter mean diameter (d32)). In this study, except for the above different assumptions (i.e., for the Model (I): EM = 0; for the Model(II): d(i) = d32), the above two models were the same as the presented model. Comparing the calculated results of the above models, it was found that the axial mixing lowered the concentration gradient along the column which led to the decrease in the mass transfer impetus. The polydispersity of the emulsion drops also showed a negative effect on the mass transfer performance. Figure 6b illustrates that the concentration of Cd2+ in the smaller drops was relatively higher than that in the bigger drops. Figure 7 further demonstrates the variation of the concentration profile along the column. With the increase in the column height, the concentration profile in the big drops significantly increased, while in the small drops, it just increased slightly. This is mainly because the smaller drops have larger specific interfacial area and shorter mass transfer distance than the bigger drops. In summary, the influences of the hydrodynamic properties of the axial mixing and the polydispersity played very important roles on the mass transfer behaviors of the ELM in the MRDC. Hence, it is necessary to further study the effects of different variables on the hydrodynamic parameters (EM, Φ, α, and β). 4.2. Membrane Breakage. Note that membrane breakage and emulsion drops breakup are two different behaviors. The membrane breakage denotes that the internal water droplets located at the edge of the emulsion drop surface leak into the

η=

Vdc K′ + Vc Φc K0+

× 100% (23)

As shown in Table 2, decreasing the surfactant concentration from 5% to 3% led to the evident increase in the membrane leakage ratio, whereas with the increase of the rotating speed, the increasing trend of the membrane breakage was not significant even though the drops breakup was obviously intensified. Hence, the surfactant concentration showed greater effect on the Table 2. Membrane Leakage Ratio (η) N (rpm)a

η (%)

T154 (%, v/v)b

η (%)

200 250 300 350 400

0.84 1.02 1.81 2.46 3.73

3 4 5 6 7

9.86 4.78 1.81 1.17 0.75

a Experimental conditions were: Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v, Hr = 6 mm. bExperimental conditions were: N = 300 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), Hr = 6 mm.

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Figure 8. (a) Effect of rotating speed on the EM and the Φ. (b) Effect of rotating speed on the drop size distribution (N = 400 rpm, α = 5.21 × 10−4 m, β = 1.65 × 10−4 m; N = 350 rpm, α = 6.28 × 10−4 m, β = 2.15 × 10−4 m; N = 300 rpm, α = 7.86 × 10−4 m, β = 2.80 × 10−4 m; N = 250 rpm, α = 9.94 × 10−4 m, β = 4.57 × 10−4 m; N = 200 rpm, α = 13.4 × 10−4 m, β = 5.71 × 10−4 m) (Experimental conditions were: Vc/Vd = 2/8, Vc+Vd = 2 + 8 (L/h), T154:5%, v/ v, Hr = 6 mm.).

Figure 9. (a) Effect of flow ratio on the EM and the Φ. (b) Effect of flow ratio on the drop size distribution (Vc/Vd = 1.25/8.75, α = 7.08 × 10−4 m, β = 2.35 × 10−4 m; Vc/Vd = 1.67/8.33, α = 7.37 × 10−4 m, β = 2.49 × 10−4 m; Vc/Vd = 2/8, α = 7.86 × 10−4 m, β = 2.80 × 10−4 m; Vc/Vd = 2.5/7.5, α = 8.70 × 10−4 m, β = 2.91 × 10−4 m; Vc/Vd = 3.33/6.67, α = 9.92 × 10−4 m, β = 3.32 × 10−4 m) (Experimental conditions were: N = 300 rpm, Vc + Vd = 2 + 8 (L/ h), T154: 5%, v/v, Hr = 6 mm.).

Figure 10. (a) Effect of total flow on the EM and the Φ. (b)Effect of total flow on the drop size distribution (Vc + Vd = 1.25 + 5 (L/h), α = 7.12 × 10−4 m, β = 2.68 × 10−4 m; Vc + Vd = 1.67 + 6.67 (L/h), α = 7.62 × 10−4 m, β = 2.74 × 10−4 m; Vc + Vd = 2 + 8 (L/h), α = 7.86 × 10−4 m, β = 2.80 × 10−4 m; Vc + Vd = 2.5 + 10 (L/h), α = 8.25 × 10−4 m, β = 3.01 × 10−4 m; Vc + Vd = 3.33 + 13.33 (L/h), α = 9.38 × 10−4 m, β = 3.17 × 10−4 m) (Experimental conditions were: N = 300 rpm, Vc/Vd = 2/8, T154: 5%, v/v, Hr = 6 mm.).

4.3. Effect of Rotating Speed. The effect of the rotating speed on the hydrodynamic parameters (EM, Φ, α, and β) was, respectively, shown in Figure 8. The drop size distribution was

membrane breakage. Owing to the right amount of the surfactant, the membrane breakage was negligible in the above mathematical modeling process. 9838

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Figure 11. (a) Effect of surfactant concentration on the EM and the Φ. (b)Effect of surfactant concentration on the drop size distribution (T154: 7%, v/v, α = 6.79 × 10−4 m, β = 2.64 × 10−4 m; T154: 6%, v/v, α = 7.66 × 10−4 m, β = 2.71 × 10−4 m; T154: 5%, v/v, α = 7.86 × 10−4 m, β = 2.80 × 10−4 m; T154: 4%, v/v, α = 8.64 × 10−4 m, β = 3.29 × 10−4 m; T154: 7%, v/v, α = 9.69 × 10−4 m, β = 3.43 × 10−4 m) (Experimental conditions were: N = 300 rpm, Vc/ Vd = 2/8, Vc + Vd = 2 + 8 (L/h), Hr = 6 mm.).

Figure 12. (a) Effect of stirring paddle width on the EM and the Φ. (b)Effect of stirring paddle width on the drop size distribution (Hr = 10 mm, α = 7.33 × 10−4 m, β = 2.58 × 10−4 m; Hr = 8 mm, α = 7.44 × 10−4 m, β = 2.70 × 10−4 m; Hr = 6 mm, α = 7.86 × 10−4 m, β = 2.80 × 10−4 m; Hr = 5 mm, α = 8.85 × 10−4 m, β = 3.36 × 10−4 m; Hr = 4 mm, α = 9.13 × 10−4 m, β = 3.58 × 10−4 m) (Experimental conditions were: N = 300 rpm, Vc/Vd = 2/8, Vc + Vd = 2 + 8 (L/h), T154: 5%, v/v.).

the average specific interfacial area (6Φ/α) from 145.8 to 213.5 m2/m3. However, when the treatment capacity of the ELM was considered, the superfluous increase in the dispersed phase flow was not advisable. Furthermore, the standard deviation of the drop size (β) also increased with the flow ratio. That is, the drop size became more dispersive when the flow ratio increased. 4.5. Effect of Total Flow. The effect of the total flow on the hydrodynamic parameters (EM, Φ, α, and β) was also investigated as shown in Figure 10. The increase in the total flow significantly intensified the turbulence which caused the obvious increase in the axial dispersion coefficient (EM). Even though the mean drop size (α) slightly increased with the total flow in the range of 6.25 to 16.66 L/h, the holdup (Φ) significantly increased, which led to the increase of the average specific interfacial area (6Φ/α) from 122.1 to 354.4 m2/m3. Figure 10 demonstrates that the variation of the drop size distribution was unremarkable. In addition, the total flow indirectly indicates the flux of the MRDC column. Comprehensive consideration, in order to achieve favorable mass transfer efficiency, to appropriately increase the total flow is desirable. 4.6. Effect of Surfactant Concentration. As presented in Figure 11, with the increase in the surfactant concentration, the interfacial tension was reduced and the mean drop size (α) and

illustrated by comparing the normal distribution curve with the experimental data calculated by eq 18. When the rotating speed increased from 200 to 400 rpm, the holdup (Φ) increased significantly from 0.72% to 6.57% and the mean drop size (α) decreased markedly from 13.4 × 10−4 to 5.21 × 10−4 m, which finally led to the increase of average specific interfacial area (6Φ/ α) with 23.5 times (from 32.2 to 756.6 m2/m3). In this study, it was also found that the standard deviation of the drop size (β), which indicates the dispersivity of the drop size, had the same variation trend as the α. Moreover, the axial dispersion coefficient (EM) increased from 1.98 × 10−5 to 5.93 × 10−5 m2/s with the increase of the rotating speed. As mentioned above, the membrane breakage increased gradually with the increment of stirring intensity, which was harmful to the mass transfer process. 4.4. Effect of Flow Ratio. As illustrated in Figure 9, the effect of the flow ratio of the emulsion phase to the continuous phase on the EM, the Φ, the α, and the β was studied under a constant total flow. As shown, the axial dispersion coefficient (EM) slightly declined with the increase in the flow ratio. With the increase of the flow ratio from 1.25/8.75 to 3.33/6.67, the mean drop size (α) increased from 7.08 × 10−4 to 9.92 × 10−4 m, while the holdup (Φ) increased from 1.72% to 3.53%. The increasing trend of the Φ exceeded that of the α, which resulted in the increase of 9839

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

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Industrial & Engineering Chemistry Research

Figure 13. Comparison between calculated values and experimental data for the Pe, the Φ, the α0, and the β0.

4.8. Correlations for EM, Φ, α, and β. In order to predict the variation of the hydrodynamic parameters (EM, Φ, α, and β) with different operating conditions, structure sizes, and physicochemical properties of the ELM fluids, the dimensionless correlations were established by Buckingham’s π-Theorem as shown in the following equations:

the standard deviation of the drop size (β) also obviously decreased. Meanwhile, the axial dispersion coefficient (EM) and the holdup (Φ) only increased marginally with the surfactant concentration. As presented in Table 2, the membrane breakage ratio increased observably when the surfactant concentration decreased from 5% to 3%. It seems that increasing the surfactant concentration could not only augment the stability of the emulsion but also obtain a larger specific interfacial area. However, the mass transfer rate would decrease with the increase in the surfactant concentration.1,24 At the external interface, the adsorbed surfactant molecules could reduce the local concentration of ions (Cd2+), which would lower the mass transfer rate of the Cd2+. When the surfactant concentration increased from 5% to 7%, the adsorbing capacity of the surfactant molecules at the interface gradually reached a critical micelle concentration (CMC), and then, the influence of the surfactant concentration almost no longer changed. 4.7. Effect of Stirring Paddle Width. In this study, the disc was modified by adding four flat paddles to appropriately strengthen the mixing degree as illustrated in Figure 2. The increase in the paddle width, like the increase in the rotating speed, resulted in the increase of the turbulent eddy kinetic energy which undoubtedly led to the increase in the axial dispersion coefficient (EM) and the holdup (Φ) and the decrease in the mean drop size (α) and the standard deviation of the drop size (β). As a result, the increment of the average specific interfacial area (6Φ/α) was from 101.9 to 253.9 m2/m3. As shown in Figure 12, with the increase of the paddle width from 4 to 6 mm, a remarkable decrease of the drop size was obtained, while the further increase from 6 to 10 mm could not drastically reduce the drop size. Therefore, the paddle width of 6 mm was considered to be an appropriate size in this study.

Pe = f (Re , γ , τ , ρc0 , μc0 , Dr0 , D h0 , Hr0 , HC0 , Φ)

(24)

Φ = f (Re , γ , τ , ρc0 , μc0 , Dr0 , D h0 , Hr0 , HC0 , We)

(25)

α 0 = f (Re , γ , τ , ρc0 , μc0 , Dr0 , D h0 , Hr0 , HC0 , Φ, We)

(26)

β 0 = f (Re , γ , τ , ρc0 , μc0 , Dr0 , D h0 , Hr0 , HC0 , Φ, We)

(27)

where Pe =

UcL , EM

τ=

α 0 = α / DH ,

πNHCDH 2 , 4(Vc + Vd)

Dh0 =

Dh , DH

Hr0 =

ρc0 = Hr , DH

β 0 = β / DH , ρc ρd

,

μc0 =

HC0 =

μc μd

HC , DH

Re = ,

NDr 2ρc μc

Dr0 = and

,

γ=

Vc , Vd

Dr , DH

We =

N2Dr 3ρc σ

The dimensionless variables of ρ0c , μ0c , D0r , H0C, and D0h were constants in this work. Then, the following correlations were obtained by fitting the experimental data using the function of the FMINCON in the MATLAB. 9840

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

Article

Industrial & Engineering Chemistry Research ⎛ ND 2ρ ⎞−0.829⎛ V ⎞0.567 ⎛ πNH D 2 ⎞1.06 r c C H ⎟⎟ ⎜ ⎟ Pe = 0.448⎜⎜ ⎜ c⎟ μ + V V Vd) ⎠ 4( ⎝ d⎠ ⎝ ⎝ c ⎠ c ⎛ Hr ⎞−0.447 −0.572 Φ ⎜ ⎟ ⎝ DH ⎠

(3) As shown in the eqs 28−31, the dimensionless empirical correlations considering the above influential factors were established to predict the hydrodynamic parameters (EM, Φ, α, and β) over the range of the variables considered in this study (200 < N < 400 rpm, 1.25/8.75 < Vc/Vd < 3.33/ 6.67, 6.25 < Vc + Vd < 16.67 L/h, 7.5 < σ < 13.4 mN/m, 4 < Hr< 12 mm). The comparisons between the calculated values and the experimental data of the Pe, the Φ,the α0, and the β0 indicate that the correlations could satisfactorily predict these hydrodynamic parameters with the AAREs of 5.2%, 7.5%, 2.7%, and 4.4%, respectively.

(28)

⎛ ND 2ρ ⎞3.39⎛ V ⎞0.593⎛ πNH D 2 ⎞−1.48 r c C H ⎟⎟ ⎜ c ⎟ ⎜ ⎟ Φ = 8.66 × 10 ⎜ ⎝ μc ⎠ ⎝ Vd ⎠ ⎝ 4(Vc + Vd) ⎠ −9 ⎜

⎛ Hr ⎞0.716 0.558 We ⎟ ⎜ ⎝ DH ⎠

■

(29)

Corresponding Author

⎛ Vc ⎞0.326⎛ πNHCDH 2 ⎞−0.368⎛ Hr ⎞−0.201 −0.0793 ⎜ ⎟ Φ α = 0.406⎜ ⎟ ⎟ ⎜ ⎝ DH ⎠ ⎝ Vd ⎠ ⎝ 4(Vc + Vd) ⎠

*Tel.: +86 731 58298809. Fax: +86 731 58293801. E-mail: [email protected] (Y. Yang).

0

We−0.376

Notes

(30)

⎛ ND 2ρ ⎞ r c ⎟⎟ β 0 = 0.641⎜⎜ ⎝ μc ⎠

−0.282

⎛ Vc ⎞ ⎜ ⎟ ⎝ Vd ⎠

⎛ Hr ⎞−0.219 −0.198 −0.253 Φ We ⎟ ⎜ ⎝ DH ⎠

0.357

AUTHOR INFORMATION

The authors declare no competing financial interest.

■

⎛ πNH D 2 ⎞ C H ⎜ ⎟ ⎝ 4(Vc + Vd) ⎠

−0.456

ACKNOWLEDGMENTS This research was supported by the Project of Hunan Provincial Natural Science Foundation of China (No. 14JJ5027) and the National Science and Technology Major Project of China on the Water Pollution Control and Treatment (No. 2010ZX07212008).

(31)

■

Figure 13 shows the comparisons between the calculated values and the experimental data of the Pe, the Φ, the α0, and the β0, respectively. The values of the AAREs for the Pe, the Φ, the α0, and the β0 were, respectively, about 5.2%, 7.5%, 2.7%, and 4.4% over the range of the variables considered in this study (200 < N < 400 rpm, 1.25/8.75 < Vc/Vd < 3.33/6.67, 6.25 < Vc + Vd < 16.67 L/h, 7.5 < σ < 13.4 mN/m, 4 < Hr< 12 mm).

NOMENCLATURE specific interfacial area of the drops with a diameter of d(i) (m2/m3) a′ specific interfacial area at internal interface (m2/m3) AARE average absolute relative error c concentration (mol/m3) c* concentration at the external interface (mol/m3) 0 c concentration for z = 0 (mol/m3) c′ concentration in the external phase at the exit of the column (mg/L) C tracer concentration (mg/L) d(i) emulsion drops diameter (m) d(i),max maximum in the ith section of drop size (m) d(i),min minimum in the ith section of drop size (m) d̅(i) mean diameter defined by eq 21 (m) d32 Sauter mean diameter of emulsion drops (m) dμ Sauter mean diameter of internal aqueous droplets (m) D diffusivity (m2/s) DE,eff effective diffusivity in emulsion phase (m2/s) Dh stator ring opening diameter (mm) D0h dimensionless stator ring opening diameter DH column diameter (mm) Dr disc diameter (mm) D0r dimensionless disc diameter EM axial dispersion coefficient (m2/s) f V(i) frequency of volume fraction of the drops (10−5 m)−1 HC compartment height (m) H0C dimensionless compartment height Hr propeller width (mm) H0r dimensionless propeller width number of the drops with a diameter of d(i) k(i) kM metal ion mass transfer coefficient in the thin water layer (m/s) kE metal ion mass transfer coefficient in the thin oil layer (m/s) Koc overall mass transfer coefficient (m/s) a(i)

5. CONCLUSIONS (1) A mathematical model considering the axial mixing of the continuous phase and the polydispersity of the emulsion drops was developed to describe the mass transfer mechanism of the ELM system in the MRDC. The axial mixing markedly lowered the concentration gradient of Cd2+ in the continuous phase along the column. Due to the polydispersity of the different sized drops, the smaller drops have larger specific interfacial area and shorter mass transfer distance than the bigger drops. Comparing the presented model with the other two previous models (i.e., the Model (I) and the Model (II)), it was found that the mass transfer performance was obviously declined due to the effects of the axial mixing and the polydispersity. (2) In order to evaluate the degree of the axial mixing and the polydispersity, the effects of different variables on the axial dispersion coefficient (EM), the emulsion phase holdup (Φ), and the drop size distribution (α and β) were, respectively, studied. The results indicate that the increase in the rotating speed and the paddle width led to the increase in the EM and the Φ and the decrease in the mean drop size (α) and the standard deviation of the drop size (β). The increase in the flow ratio markedly increased the Φ, the α, and the β, whereas the increase in the total flow obviously increased the EM. The increase in the surfactant concentration could obviously decrease the α and the β. Overall, the rotating speed showed greater influence on the above hydrodynamic parameters (EM, Φ, α, and β) in comparison with the other influential factors. 9841

DOI: 10.1021/acs.iecr.5b02788 Ind. Eng. Chem. Res. 2015, 54, 9832−9843

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Industrial & Engineering Chemistry Research L L1 m MRDC n N Pe PV(i) r rs R(i) Re Rf(i) S t t̅ U v V We z

Aqueous Solutions by Emulsion Liquid Membranes. J. Hazard. Mater. 2011, 192, 986. (4) Talekar, M. S.; Mahajani, V. V. E-Waste Management via Liquid Emulsion Membrane (LEM) Process: Enrichment of Cd(II) from Lean Solution. Ind. Eng. Chem. Res. 2008, 47, 5568. (5) Sengupta, B.; Bhakhar, M. S.; Sengupta, R. Extraction of Zinc and Copper-Zinc Mixtures from Ammoniacal Solutions into Emulsion Liquid Membranes using LIX 84I®. Hydrometallurgy 2009, 99, 25. (6) Chakrabarty, K.; Saha, P.; Ghoshal, A. K. Separation of Lignosulfonate from its Aqueous Solution using Emulsion Liquid Membrane. J. Membr. Sci. 2010, 360, 34. (7) Berrios, J.; Pyle, D. L.; Aroca, G. Gibberellic Acid Extraction from Aqueous Solutions and Fermentation Broths by using Emulsion Liquid Membranes. J. Membr. Sci. 2010, 348, 91. (8) Mok, Y. S.; Lee, W. K.; Lee, Y. K. Modeling of Liquid Emulsion Membranes Facilitated by two Carriers. Chem. Eng. J. 1997, 66, 11. (9) Bhowal, A.; Bhattacharyya, G.; Inturu, B.; Datta, S. Continuous Removal of Hexavalent Chromium by Emulsion Liquid Membrane in a Modified Spray Column. Sep. Purif. Technol. 2012, 99, 69. (10) Lee, S. C.; Kim, H. C. Batch and Continuous Separation of Acetic Acid from Succinic Acid in a Feed Solution with High Concentrations of Carboxylic Acids by Emulsion Liquid Membranes. J. Membr. Sci. 2011, 367, 190. (11) Lorbach, D. M.; Hatton, T. A. Polydispersity and Backmixing Effects in Diffusion Controlled Mass Transfer with Irreversible Chemical Reaction: An Analysis of Liquid Emulsion Membrane Processes. Chem. Eng. Sci. 1988, 43, 405. (12) Kadam, B. D.; Joshi, J. B.; Patil, R. N. Hydrodynamic and Mass Transfer Characteristics of Asymmetric Rotating Disc Extractors. Chem. Eng. Res. Des. 2009, 87, 756. (13) Roetzel, W.; Balzereit, F. Determination of Axial Dispersion Coefficients in Plate Heat Exchangers using Residence Time Measurements. Rev. Gen. Therm. 1997, 36, 635. (14) Levenspiel, O. Chemical Reaction Engineering, 3rd ed.; John Wiley and Sons: New York, 1998. (15) Kadam, B. D.; Joshi, J. B.; Koganti, S. B.; Patil, R. N. Dispersed Phase Hold-up, Effective Interfacial Area and Sauter Mean Drop Diameter in Annular Centrifugal Extractors. Chem. Eng. Res. Des. 2009, 87, 1379. (16) Gholam Samani, M.; Haghighi Asl, A.; Safdari, J.; TorabMostaedi, M. Drop Size Distribution and Mean Drop Size in a Pulsed Packed Extraction Column. Chem. Eng. Res. Des. 2012, 90, 2148. (17) Khajenoori, M.; Haghighi-Asl, A.; Safdari, J.; Mallah, M. H. Prediction of Drop Size Distribution in a Horizontal Pulsed Plate Extraction Column. Chem. Eng. Process. 2015, 92, 25. (18) Drumm, C.; Attarakih, M. M.; Bart, H.-J. Coupling of CFD with DPBM for an RDC Extractor. Chem. Eng. Sci. 2009, 64, 721. (19) Luo, H.; Svendsen, H. F. Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions. AIChE J. 1996, 42, 1225. (20) Prince, M. J.; Blanch, H. W. Bubble Coalescence and Break-up in Air-Sparged Bubble Columns. AIChE J. 1990, 36, 1485. (21) Kinugasa, T.; Watanabe, K.; Utunomiya, T.; Takeuchi, H. Modeling and Simulation of Counterflow (W/O) Emulsion Spray Columns for Removal of Phenol from Dilute Aqueous Solutions. J. Membr. Sci. 1995, 102, 177. (22) Baird, M. H. I.; Rice, R. G. Axial Dispersion in Large Unbaffled Columns. Chemical Engineering Journal 1975, 9, 171. (23) Chakraborty, M.; Bhattacharya, C.; Datta, S. Effect of Drop Size Distribution on Mass Transfer Analysis of the Extraction of Nickel(II) by Emulsion Liquid Membrane. Colloids Surf., A 2003, 224, 65. (24) Reis, M. T. A.; Carvalho, J. M. R. Modelling of Zinc Extraction from Sulphate Solutions with Bis(2-ethylhexyl)thiophosphoric Acid by Emulsion Liquid Membranes. J. Membr. Sci. 2004, 237, 97. (25) Gameiro, M. L. F.; Bento, P.; Ismael, M. R. C.; Reis, M. T. A.; Carvalho, J. M. R. Extraction of Copper from Ammoniacal Medium by Emulsion Liquid Membranes using LIX 54. J. Membr. Sci. 2007, 293, 151.

column height (m) distance between sampling openings of S1 and S2 (m) distribution coefficient at external interface modified rotating disc contactor distribution coefficient at internal interface rotating speed (rpm) Peclet number percentage of volume of the drops with a diameter of d(i) radial coordinate (m) stripping reaction rate per unit of the internal interface (mol/m2s) radius of the emulsion drops (m) Reynolds number radius of emulsion drops inner core (0 ≤ r ≤ Rf(i), m) total interfacial area at the external interface (m2) time (s) average time distribution of tracer (s) superficial velocity (m/s) volume (m3) flow(L/h) Weber number axial coordinate (m)

Greek Letters

α α0 β β0 γ δ μ μ0 ρ ρ0 ε η σ2 τ φ φ′ Φ Φ(i)

mean emulsion drop size (expected value of drop size, m) dimensionless expected value standard deviation of emulsion drop size (m) dimensionless standard deviation flow ratio (γ = Vc/Vd) thickness of the thin oil layer (m) viscosity (Pa s) dimensionless viscosity density (kg/m3) dimensionless density parameter for the definition of φ′ membrane leakage ratio (%) standard deviation of tracer concentration curve (s2) dimensionless residence time volume ratio of internal aqueous phase to emulsion phase φ/(1 − ε)3 dispersed emulsion phase mean holdup holdup of the emulsion drops with a diameter of d(i)

Subscripts

c calc d E exp f M o s

■

continuous phase calculated value dispersed emulsion phase emulsion experimental value inflow metal ion organic phase (membrane phase) internal aqueous phase

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