GasâLiquid Mass Transfer Characteristics in Two Inline High Shear

Article pubs.acs.org/IECR

Gas−Liquid Mass Transfer Characteristics in Two Inline High Shear Mixers Jintao Shi,† Shuangqing Xu,†,‡ Hongyun Qin,† Wei Li,† and Jinli Zhang*,†,§ †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China General Machinery Research Institute (GMRI), Hefei 230031, P. R. China § College of Chemistry and Chemical Engineering, Shihezi University, Shihezi 832003, P. R. China ‡

S Supporting Information *

ABSTRACT: The mass transfer characteristics of a gas−liquid continuous flow system accompanied by reaction in two commercial inline high shear mixers (HSMs) were evaluated by the sulphite oxidation method. The gas−liquid specific interfacial area, a, and the volumetric mass transfer coefficient, kLa, were measured under different operating conditions involving the rotor speed, the liquid flow rate, the gas flow rate and the surface tension. The results indicate that a and kLa increase with the rotor speed and liquid flow rate due to an increase of turbulence intensity. Both parameters increase slightly first but then decrease with the gas flow rate. For either the dual rows ultrafine-toothed or the single-row blade-screen configuration of HSMs, a increases while kLa decreases with the surfactant concentration, and both of them tend to be changeless at the surfactant concentration higher than 30 mg/L. Correlations for the specific interfacial area and the Sherwood number are obtained to guide the process design and scale-up of both types of inline HSMs.

1. INTRODUCTION High shear mixers (HSMs) have been widely employed in the process industries of chemical, biochemical, pharmaceutical, and food-processing as a reactor or a contactor with their inherent advantages of highly localized energy dissipation rate and high shear rates that they input to the system.1−6 Inline HSMs, with the advantages of continuous operation and short residence time compared with batch units, are most common in high-capacity processing.6,7 Commercial inline HSMs usually adopted the toothed or blade-screen configuration to meet different process requirements. Patented fine chemical productions using inline HSMs have been booming recently in the multiphase systems due to the high interphase heat and mass transfer rates.3,8−15 Despite their popularity, the design and scale-up of HSMs still rely on engineering judgments and trial-and-errors owing to the lack of systematic assessments.2,16 Some attempts have been made, thereby, to predict or assess the device performance. Specifically, the flow regime, the backmixing behavior, the dispersion and mixing of the liquid phase, the pump capacity, and power consumption have been studied to understand the hydrodynamic characteristics of inline HSMs.2,17−21 In terms of the gas−liquid mass transfer, deoxidization of water with nitrogen was adopted to explore the mass transfer coefficients of inline HSMs.22−24 It is found that the volumetric gas−liquid mass transfer coefficient kLa increases with an increase of the rotor speed, the liquid flow rate, and the gas flow rate. The HSM equipped with multiple rows of rotor−stator teeth can promote the gas−liquid mass transfer. However, the data are still scarce considering the narrow scopes of operating variables and conditions. In addition, no literatures have been found so far on the gas− liquid specific interfacial area within an inline HSM, although it is fundamental to the design and scale-up of the inline HSM for the purpose of mass transfer intensification. © 2014 American Chemical Society

The values of gas−liquid specific interfacial areas and volumetric mass transfer coefficients are closely dependent on the geometry of the contactor, the operating conditions, and the chemical and physical properties of the gas−liquid systems. The sulphite oxidation method, based on the oxidation of sodium sulphite aqueous solutions in the presence of Co2+ catalysts, is one of the most popular chemical methods to determine the specific interfacial area.25,26 The specific interfacial area or the volumetric mass transfer coefficient can be calculated from the experimentally measured absorption rates of the oxygen reacting with a dissolved sulphite in such a reaction regime where the absorption rate is proportional to the specific interfacial area or the volumetric mass transfer coefficient. This method has been widely employed in various kinds of gas−liquid contactors such as stirred tanks,27,28 impinging stream reactors,26 bubble columns,25,29 etc. In this article, both gas−liquid interfacial areas and volumetric mass transfer coefficients were studied by the sulphite oxidation method in two commercial inline HSMs adopting the dual rows ultrafine-toothed or the single-row blade-screen configurations. The effects of the operating variables on mass transfer properties were investigated, including the rotor speed, the liquid flow rate, the gas flow rate and the surface tension. Correlations for the specific interfacial area and the Sherwood number are obtained to guide the process design and scale-up of inline HSMs. Received: Revised: Accepted: Published: 4894

June 21, 2013 January 2, 2014 March 3, 2014 March 3, 2014 dx.doi.org/10.1021/ie401957q | Ind. Eng. Chem. Res. 2014, 53, 4894−4901

Industrial & Engineering Chemistry Research

Article

Figure 1. Experimental geometry of the inline high shear mixer: (A) Process flow diagram of the gas−liquid mass transfer rig; (B) geometric details of (a, c) the stator and (b, d) the rotor in (a, b) the toothed and (c, d) the blade-screen inline high shear mixers.

2. EXPERIMENTAL METHODS The mass transfer properties of the inline HSMs were measured by the sulphite oxidation method based on the reaction between sodium sulphite and the dissolved oxygen, with cobalt sulfate as the catalyst due to its more reproducible action.30 The oxidation is considered to occur entirely in the film when the oxygen from air was absorbed into a 0.8 kmol/m3 aqueous sodium sulphite solution with a Co2+ concentration of 10−3 kmol/m3.26,31 In this case, the absorption is accompanied with a fast pseudo-second order reaction and the interfacial area a can be calculated by eq 1.31 R O2a = acO*2

2 DO k 2cO*2 3 2

the transfer of oxygen into the phase containing sulphite and kLa can be calculated by eq 4.31 R O2a = kLacO*2

Therefore, the specific interfacial area a and volumetric mass transfer coefficient kLa can be calculated from the experimentally obtained overall specific oxygen absorption rate with the knowledge of cO*2, DO2, and k2, respectively. 2.1. Experimental Setup and Procedure. The experimental setup is schematically shown in Figure 1 and the inline HSM is a custom-built pilot-scale unit of FDX series provided by FLUKO. As shown in the inset of Figure 1A, the gas−liquid mixtures exiting the HSM pass through a short vertical transparent tube (diameter of Φ25 × 2 mm and length of 100 mm) and then flow into the separator through a horizontal tube (diameter of Φ25 × 2 mm and length of 100 mm). Within the horizontal tube there is a stratified flow involving the separate gas phase and liquid phase, so that at the separator there is almost no liquid entrainment. The rotor and stator of the mixer are designed as interchangeable so that the two main commercial rotor-stator designs can be expediently tested in the same model. The geometric details of the dual rows ultrafine-toothed and the single-row blade-screen configurations can be found in our previous work.18 Basic structure of the toothed and blade-screen inline HSM are shown in Figure 1B. Sulphite solution was prepared with analytic grade sodium sulphite (Tianjin Guangfu Fine Chemical Research Institute, China) and deionized water with and without Tween 80 (Tianjin Guangfu Fine Chemical Research Institute, China). The sulphite solution at 20−22 °C was fed by a centrifugal pump; therefore the flow rate and rotational speed of the inline HSM were controlled separately. The liquid flow rate was varied from 0.1 to 1.0 m3/h. The rotor speed N was varied from 500 to 3000 rpm. The compressed air from a cylinder was introduced to the aqueous line upstream of the HSM via a Tpiece. The air flow rate was controlled from 0.2 m3/h to 0.8 m3/h by a mass flowmeter. The liquid and gas contacted cocurrently in the HSM to complete the mass transfer process with the initial pH of 8.5 by adding sulfuric acid and measured by a pH meter (HANNA Instruments), under the Co2+ concentration of either 10−3 kmol/m3 or 10−6 kmol/m3.

(1)

where a is the interfacial area, c*O2 is the concentration of oxygen at the interface in the solution, DO2 is the diffusivity of oxygen in the solution, k2 is the second-order rate constant and can be ́ 32 and RO2a is calculated by eq 2 according to Linek and Tvrdik, the experimentally measured overall specific oxygen absorption rate and can be calculated by eq 3. ⎧ pH − 7.9 + 0.04(T − 273.15) ⎫2 ⎬ k 2 = 1.44 × 1010c Co2+⎨ ⎩ 0.6 + 0.04(T − 273.15) ⎭ ⎧ ⎛1 1 ⎞⎫ ⎟⎬ exp⎨−8450⎜ − ⎝ ⎩ T 293.15 ⎠⎭ R O2a = (cO2,IN − cO2,OUT)/HRT

(4)

(2) (3)

where cCo2+ is the concentration of cobalt ions in the liquid phase; cO2,IN is the concentration of oxygen in the gas at the inlet of HSM; cO2,OUT is the concentration of oxygen in the gas at the outlet of the gas−liquid separator; HRT is the hydraulic mean residence time of a continuous reactor and calculated by the volume of the reactor Vr and the volumetric flow rate QG, i.e., HRT = Vr/QG. On the other hand, the oxidation can be considered as taken place totally in the liquid bulk when the sulphite solution contains a Co2+ concentration of 10−6 kmol/m3.26,31 In this case, the overall specific oxygen absorption rate is controlled by 4895

dx.doi.org/10.1021/ie401957q | Ind. Eng. Chem. Res. 2014, 53, 4894−4901


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oxygen in the sodium sulphite solutions was estimated from the expression proposed by Ratcliff and Holdcroft:34

Then, the reaction product is discharged from the outlet of the HSM to the gas−liquid separator, where the gas is evacuated from the top and the liquid is collected at the bottom. The gas samples were taken from the gas inlet and outlet, respectively. And the concentration of O2 at the gas inlet and outlet were analyzed by a Beifen-Ruili SP-2100A gas chromatography equipped with a 5A molecular sieve packed column and a thermal conductivity detector (TCD) (Beijing Beifen-Ruili Analytical Instrument (Group) Co., Ltd., China). The absorption rate of oxygen was determined from the depletion of oxygen concentration over the residence time of gas. For each operating condition, the experiment was repeated for at least three times and the averaged results were discussed here. 2.2. Materials and Properties. The liquid densities were measured by the pycnometer method. A viscometer (LVDV-II +Pro, Brookfield) was utilized for measuring the liquid viscosities. The liquid surface tensions were measured using an automatic surface tensiometer (JK99B, Powereach Co., Ltd.). The physical properties of the liquid phases are presented in Table 1.

DO2 = D0(1 −

viscosity

surface tension

(kg/m3)

(mPa·s)

(mN/m)

sodium sulphite sodium sulphite+5 mg/L

1090 1090

1.5 1.5

61.3 50.1

sodium sulphite+30 mg/L

1090

1.5

40.2

sodium sulphite+50 mg/L

1090

1.5

35.3

fluids 3

0.8 kmol/m 0.8 kmol/m3 Tween 80 0.8 kmol/m3 Tween 80 0.8 kmol/m3 Tween 80

(5)

i

where DO2 is the diffusivity of oxygen in the electrolyte solution, D0 is the diffusivity of oxygen in water without glycerin, 2.0 × 10−9 m2/s, Ci is the concentration of the ith electrolyte, and εi is a constant that is practically independent of temperature. The value of εi for Na2SO3 was 2.5 × 10−4. The concentration of oxygen at the interface in mixed solutions of electrolyte i and organic substance j was estimated by eq 6:35 ⎛ c* ⎞ O ,0 log⎜⎜ 2 ⎟⎟ = ⎝ cO*2 ⎠

∑ (hi + hG)ci + ∑ K n,jcn,j i

j

(6)

where c*O2,0 and c*O2 are the concentration of oxygen at the interface in water and the solution, respectively, hi and hG denote the ion-specific and gas-specific parameters, ci is the molar concentration of the ion, Kn, j is the Sechenov constant for organic substances, and cn, j is the mass concentration of organic substances. The values of these parameters for each ion, organic substance and gas can be found in the literature.35,36

Table 1. Physical Properties of the Liquid Phases Investigated at 20 °C density

∑ εiCi)

3. RESULTS AND DISCUSSION 3.1. Effect of Rotor Speed. The gas−liquid specific interfacial area a, the volumetric mass transfer coefficient kLa and liquid side mass transfer coefficient kL, expressed as kL = kLa/a, under different rotor speeds and constant gas and liquid flow rates are shown in Figure 2. In both inline HSMs, the specific interfacial area and the mass transfer coefficients increase with the rotor speed as expected. For instance, with the increase of rotor speed from 500 to 3000 rpm in the toothed HSM, the values of a, kLa and kL increase from 290 m2/m3, 0.08 s−1 and 2.8 × 10−4 m/s to 1307 m2/m3, 0.77 s−1 and 5.9 × 10−4 m/s, respectively. It is easy to understand that the intensified turbulence under higher rotor speed breaks up the gas bubbles into smaller sizes and reduces more the mass transfer resistances by the faster surface renewal. Moreover, it should

In our work the small amount of surfactant (Tween 80) additive causes no change in the viscosity of the sodium sulphite solution, thus the concentration of oxygen at the interface and diffusivity of oxygen in sodium sulphite solutions with Tween 80 are considered as the same as those in sodium sulphite solutions without surfactant.25,33 The diffusivity of

Figure 2. Effect of the rotor speed on (a) specific interfacial area, a. (b) volumetric mass transfer coefficient, kLa and liquid side mass transfer coefficient, kL. 4896



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Figure 3. Effect of the liquid phase flow rate on (a) specific interfacial area, a. (b) volumetric mass transfer coefficient, kLa and liquid side mass transfer coefficient, kL.

Figure 4. Effect of the gas phase flow rate on (a) specific interfacial area, a. (b) volumetric mass transfer coefficient, kLa, and liquid side mass transfer coefficient, kL.

and 6.1 × 10−4 m/s at the liquid flow rate of 1.0 m3/h. It is reported in the literature that the power consumption of an inline HSM has a “flow term” to account for the liquid flow through the mixer.7,18,19,37 Also, the liquid jet emanating from the stator slots (or holes) contributes significantly to the turbulence level and thereby the mixing/dispersing performance.2,6,17 Therefore, the increased turbulence intensity in the HSMs under the higher liquid flow rate tends to generate finer bubbles and to bring different phases into vigorous contact. 3.3. Effect of Gas Phase Flow Rate. Figure 4 presents the influence of gas flow rate on the gas−liquid specific interfacial area, a, the volumetric mass transfer coefficient, kLa and liquid side mass transfer coefficient kL under constant liquid flow rate and rotor speed. In both HSMs, the specific interfacial area and the volumetric mass transfer coefficient increase slightly first and then decrease with the gas flow rate. As for the liquid side mass transfer coefficient, it increases slowly with the gas flow rate to a plateau in the toothed HSM; while it is somewhat insensitive to the gas flow rate in the blade-screen unit. The effect of gas flow rate on mass transfer is not so significant as

be noted that the values of a, kLa and kL in the toothed HSM are higher than those in the blade-screen unit under the same operating conditions. For example, the values of a, kLa and kL under the rotor speed of 3000 rpm are 970 m2/m3, 0.53 s−1 and 5.4 × 10−4 m/s for the blade-screen HSM, whereas for the toothed unit they are 1307 m2/m3, 0.77 s−1, and 5.9 × 10−4 m/s respectively. This can be reasonably ascribed to the superiority of dispersing performance of the dual rows ultrafine toothed HSM with backward inclined stator teeth, considering its capability to deliver higher energy input and to avoid the channeling and/or short circuiting defects.17,18 3.2. Effect of Liquid Phase Flow Rate. The effects of liquid flow rate on the gas−liquid specific interfacial area, a, the volumetric mass transfer coefficient, kLa, and liquid side mass transfer coefficient kL under constant gas flow rate and rotor speed are shown in Figure 3. It is found that the values of a, kLa, and kL increase with the liquid flow rate in both inline HSMs. Quantitatively, for the blade-screen HSM, the values of a, kLa, and kL are 1213 m2/m3, 0.70 s−1, and 5.8 × 10−4 m/s at the liquid flow rate of 0.5 m3/h; while 1480 m2/m3, 0.91 s−1, 4897



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Figure 5. Effect of the surfactant concentration on (a) specific interfacial area, a. (b) volumetric mass transfer coefficient, kLa, and liquid side mass transfer coefficient, kL.

Figure 6. Comparison of the experimental data of (a) aD and (b) ShL from inline HSM with the predicted values.

compared with the liquid flow rate. Quantitatively speaking, the variations of a, kLa, and kL in both HSMs are almost less than 20% with the gas flow rate from 0.2 to 0.8 m3/h. By increasing the gas flow rate, the perturbation of the fluid flow inside the mixer is intensified and the turbulence intensity is increased. However, it is worth noting that, the intensification on turbulence is not so significant as compared with the increased liquid jet. Therefore, the improvement on the reduction of bubble size and mass transfer resistance is slight somewhat. On the other hand, the very large gas flow rates through the HSMs cause the slugging, short circuiting and channeling defects. Some gas bubbles cannot be broken up to finer ones and the big slug bubbles reduce the contact efficiency with the liquid phase, leading to the decrease of specific interfacial area and mass transfer coefficients at higher gas flow rates. 3.4. Effect of Surfactant Concentration. The surface tension is adjusted by adding varied amounts of Tween 80 as surfactant to the sulphite solution. According to Weiss and Clements,38 the CMC of Tween 80 is about 0.0013 wt % (13 mg/L). As shown in Table 1, the surface tension decreases with

increasing surfactant concentration. Figure 5 shows the variations of the gas−liquid specific interfacial area, a, the volumetric mass transfer coefficient, kLa, and liquid side mass transfer coefficient, kL, with the surfactant concentration. From Figure 5a, the specific interfacial area is found to increase with the surfactant concentration and approach a plateau when the concentration is above 30 mg/L. It is well-known that even a small amount of surfactant added to the solution causes significant decrease in liquid surface tension. Since the liquid surface tension is related to the surface energy, the inhibition of coalescing between small bubbles taken place at lower liquid surface tension leads to a decrease in bubble size and therefore an increase in specific interfacial area.39 However, above the surfactant concentration of 30 mg/L, which is above its critical micelle concentration (CMC), the micelle formed in the surfactant solution and the liquid surface tension do not change significantly. Therefore the bubble size and further the specific interfacial area reach a plateau above the surfactant concentration of 30 mg/L. As shown in Figure 5b, the volumetric mass transfer coefficient kLa and liquid side mass transfer coefficient kL 4898



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rates near the mixing head. The reduced reactor volume improves the intrinsic safety of the unit because of the small inplant inventories of hazardous materials.

decrease with the surfactant concentration and level off above the surfactant concentration of 30 mg/L. The presence of surfactant at the gas−liquid interface hinders the mass transfer due to two effects. First, the surfactant accumulating near the bubble surface increases the thickness of liquid film and the resistance in mass transfer.40 Second, the presence of surfactant molecules at the gas−liquid interface causes the damping of turbulence on the liquid film.33,41 However, when above the CMC, the surfactant molecules at the gas−liquid interface have reached dynamic equilibrium, and the effect of surfactant concentration on mass transfer is not so remarkable. 3.5. Dimensional Correlation of Mass Transfer Parameters. In this work, the experimentally measured mass transfer properties have been fitted by the following dimensionless parameters, taking into account both the operating conditions of the HSMs and the physical properties of the fluids. To correlate the specific interfacial area, a, the product of the specific interfacial area and the outer swept rotor diameter of the HSM was used as a dimensionless term. The experimental data of the specific interfacial area in the two HSMs are fitted using eqs 7 and 8 with a regression coefficient R2 = 0.96 and 0.94, respectively. The dimensionless Sherwood number, expressed as ShL = kLD/DO2, is calculated by the experimentally obtained a and kLa. The Sherwood numbers in the toothed and blade-screen inline HSMs are correlated by eqs 9 and 10, with the regression coefficients of R2 = 0.91 and 0.91, respectively. As shown in Figure 6, the calculated values of aD and ShL fit very well with the related experimental data. These equations are valid for the toothed and blade-screen HSMs when evaluating the mass transfer performance with 500 ≤ N ≤ 3000 rpm, 0.1 ≤ QL ≤ 1.0 m3/h, 0.2 ≤ QG ≤ 0.8 m3/h, and 35.3 ≤ σ ≤ 61.3 mN/m. Correlations for the gas−liquid specific interfacial area, a Tooted HSM aD = 6.07We 0.50FlL0.41Fr 0.12

Blade‐screen HSM aD = 3.84we

4. CONCLUSIONS The gas−liquid specific interfacial area, a, and the volumetric mass transfer coefficient, kLa, were determined in the dual rows ultrafine toothed and the single-row blade-screen inline HSMs by the chemical method. Both a and kLa increase with the rotor speed and liquid flow rate. Both parameters increase slightly first but then decrease with the increased gas flow rate in the two mixers. In both HSMs, a increases while kLa decreases with the surfactant concentration, and both parameters approach a plateau above the concentration of 30 mg/L. Comparing with the blade-screen HSM, the toothed HSM has higher values of the specific interfacial area and the volumetric mass transfer coefficient due to its capability to deliver higher energy input and to avoid the possible channeling and/or short circuiting defects. The Sherwood number can be well correlated by the Webber, Flow, and Froude numbers.

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Table containing gas−liquid mass transfer performances of different contactors. This material is available free of charge via the Internet at http://pubs.acs.org.

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FlL0.33Fr 0.20

*Tel: 86-22-27890643. Fax: 86-22-27890643. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by NSFC (21076144), the Special Funds for Major State Basic Research Program of China (2012CB720300), and Program for Changjiang Scholars and Innovative Research Team in University (IRT1161). The authors gratefully acknowledge FLUKO Equipment Shanghai Co., Ltd. for providing the custom-built inline high shear mixer of FDX series and offering technical support.

(8)

Correlations for the Sherwood number, ShL: Tooted HSM ShL = 1.83 × 107We−1.07FlL0.069Fr1.30

(9)

Blade‐screen HSM ShL = 8.83 × 106We−0.98FlL0.078Fr1.30

■

(10)

where We = ρLN D /σ is the Webber number; FlL = QL/ND3 is the liquid Flow number; and Fr = N2D/g is the Froude number. Table S1 (Supporting Information and refs 42−51) lists some mass transfer coefficients in conventional gas−liquid contactors in previous literatures, as well as the data of HSMs obtained in this work. It is clear that the value of kLa in the HSM is 0.03−1.5 s−1 and that in the spray column and the two impinging streams reactor are 0.015−0.022 and 0.09−0.41 s−1 in the similar working fluids. It is difficult to compare the performance of the HSM with previous literature data in other contacting devices, owing to lack of consistent parameters. The aim of the present paper is to provide the information of different contactors for the convenient choice of a potentially suitable reactor according to the process requirements. For example, comparing with the stirred-tank reactors, HSM have more potential applications to intensify typical energy intensive operation and chemical reactions with fast inherent reaction rates but relatively slow mass transfer due to high rotor tip speeds, high shear rates, and highly localized energy dissipation 2

AUTHOR INFORMATION

Corresponding Author

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0.46

ASSOCIATED CONTENT

S Supporting Information *

3

4899

NOMENCLATURE a specific interfacial area, m2/m3 cO*2 concentration of oxygen at the interface in the solution, kmol/m3 c*O2,0 concentration of oxygen at the interface in the water, kmol/m3 cO2,IN concentration of oxygen in the gas at the inlet of HSM, kmol/m3 cO2,OUT concentration of oxygen in the gas at the outlet of gas−liquid separator, kmol/m3 cn,j mass concentration of organic substances, kg/m3 ci the molar concentration of the i ion, kmol/m3 Ci the concentration of the i electrolyte, kmol/m3 D the outer rotor diameter, m D0 the molecular diffusivity of oxygen in water, m2/s DO2 the diffusivity of oxygen in the electrolyte solution, m2/s g gravitational acceleration, m/s2 hi ion-specific parameters hG gas-specific parameters dx.doi.org/10.1021/ie401957q | Ind. Eng. Chem. Res. 2014, 53, 4894−4901


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k2 second-order rate constant, m3/(kmol s) kL liquid-side mass transfer coefficient, m/s kLa volumetric mass transfer coefficient, s−1 Knj Sechenov constant for organic substances QG gas flow rate, m3/s QL liquid flow rate, m3/s R2 regression coefficient RO2a absorption rate per unit volume of reactor, kmol/(m3 s) Vr volume of the reactor, m3

(15) Hassan, A.; Bagherzadeh, E.; Anthony, R. G.; Borsinger, G. High shear system and method for the production of acids. US20100324308A1, 2010. (16) Calabrese, R. V.; Francis, M. K.; Kevala, K. R.; Mishra, V. P.; Padron, G. A.; Phongikaroon, S. Fluid dynamics and emulsification in high shear mixers, in: In: Proc. 3rd World Congr. Emuls., Lyon, France, 2002. (17) Xu, S. Q.; Shi, J. T.; Cheng, Q.; Li, W.; Zhang, J. L. Residence time distributions of in-line high shear mixers with ultrafine teeth. Chem. Eng. Sci. 2013, 87, 111. (18) Cheng, Q.; Xu, S. Q.; Shi, J. T.; Li, W.; Zhang, J. L. Pump capacity and power consumption of two commercial In-line high shear mixers. Ind. Eng. Chem. Res. 2013, 52, 525. (19) Cooke, M.; Rodgers, T. L.; Kowalski, A. J. Power consumption characteristics of an in-line silverson high shear mixer. AIChE J. 2012, 58, 1683. (20) Hall, S.; Cooke, M.; El-Hamouz, A.; Kowalski, A. J. Droplet break-up by in-line Silverson rotor−stator mixer. Chem. Eng. Sci. 2011, 66, 2068. (21) Thapar, N. Liquid-liquid dispersions from in-line rotor-stator mixers. Ph.D. Dissertation; The Cranfield University: Cranfield Bedfordshire, U.K., 2004. (22) Lin, H. Studies on gas-liquid mass transfer and pressure drop characteristics of rotor-stator reactor. M.E. Dissertation; Beijing University of Chemical Technology: Beijing, China, 2007. (23) Lin, H.; Song, Y.; Chu, G.; Chen, J. Experimental investigation on gas-liquid mass transfer characteristics of rotor-stator reactor. J. Chem. Eng. Chin. Univ. 2007, 21, 882. (24) Niu, X.; Song, Y.; Chen, J.; Chu, G.; Zhao, X. Gas-liquid mass transfer characteristics of rotor-stator reactor with different inner structures. J. Chem. Eng. Chin. Univ. 2009, 23, 381. (25) Vazquez, G.; Cancela, M. A.; Riverol, C.; Alvarez, E.; Navaza, J. M. Determination of interfacial areas in a bubble column by different chemical methods. Ind. Eng. Chem. Res. 2000, 39, 2541. (26) Dehkordi, A. M.; Savari, C. Determination of interfacial area and overall volumetric mass-transfer coefficient in a novel type of two impinging streams reactor by chemical method. Ind. Eng. Chem. Res. 2011, 50, 6426. (27) Linek, V.; Moucha, T.; Kordač, M. Mechanism of mass transfer from bubbles in dispersions Part I .Danckwerts’ plot method with sulphite solutions in the presence of viscosity and surface tension changing agents. Chem. Eng. Pocess 2005, 44, 353. (28) Linek, V.; Mayrhoferova, J. The chemical method for the determination of the interfacial area The influence of absorption rate on the hold-up and on the interfacial area in a heterogeneous gasliquid system. Chem. Eng. Sci. 1969, 24, 481. (29) Miller, D. N. Interfacial area, bubble coalescence and mass tranfer in bubble column reactors. AIChE J. 1983, 29, 312. (30) Linek, V.; Vacek, V. Chemical engineering use of catalyzed sulfite oxidation kinetics for the determination of mass transfer characteristics of gas-liquid contactors. Chem. Eng. Sci. 1981, 36, 1747. (31) Doraiswamy, L. K.; Sharma, M. M. Heterogeneous Reactions: Analysis, Examples, and Reactor design. In Fluid-Fluid-Solid Reactions; John Wiley & Sons: New York, 1984. (32) Linek, V.; Tvrdík, J. A generalization of kinetic data on sulphite oxidation systems. Biotechnol. Bioeng. 1971, 13, 353. (33) Vazquez, G.; Antorrena, G.; Navaza, J. M. Influence of surfactant concentration and chain length on the absorption of CO2 by aqueous surfactant solutions in the presence and absence of induced marangoni effect. Ind. Eng. Chem. Res. 2000, 39, 1088. (34) Ratcliff, G. A.; Holdcroft, J. G. Diffusivities of gases in aqueous electrolyte solutions. Trans. Inst. Chem. Eng. 1963, 41, 315. (35) Rischbieter, E.; Schumpe, A. Gas solubilities in aqueous solutions of organic substances. J. Chem. Eng. Data 1996, 41, 809. (36) Hermann, C.; Dewes, I.; Schumpe, A. The estimation of gas solubilities in salt solutions. Chem. Eng. Sci. 1995, 50, 1673. (37) Kowalski, A. J. An expression for the power consumption of inline rotor-stator devices. Chem. Eng. Pocess 2009, 48, 581.

Greek Symbols

εi constant μ0 viscosity of water, Pa·s ρL liquid phase density, kg/m3 σ surface tension, N/m Dimensional Groups

FlL = QL/ND3 liquid Flow number Fr = N2D/g Froude number ShL = kLD/DO2 Sherwood number for liquid phase We = ρLN2D3/σ Weber number

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REFERENCES

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GasâLiquid Mass Transfer Characteristics in Two Inline High Shear

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