Effect of Stator Geometry on the Emulsification and Extraction in

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Effect of Stator Geometry on the Emulsification and Extraction in the Inline Single-Row Blade-Screen High Shear Mixer Hongyun Qin, Qin Xu, Wei Li, Xiuhu Dang, You Han, Kailiang Lei, Litao Zhou, and Jinli Zhang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b01362 • Publication Date (Web): 26 Jul 2017 Downloaded from http://pubs.acs.org on August 2, 2017

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Industrial & Engineering Chemistry Research

Effect of Stator Geometry on the Emulsification and Extraction in the Inline Single-Row Blade-Screen High Shear Mixer Hongyun Qin, † Qin Xu, † Wei Li, † Xiuhu Dang, † You Han, † Kailiang Lei, § Litao Zhou, § and Jinli Zhang *, †, ‡

†

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072,

P. R. China. ‡

School of Chemistry and Chemical Engineering, Shihezi University, Shihezi 832003,

P. R. China. §

FLUKO Co., Ltd., Shanghai 201802, P. R. China.

*Corresponding Author E-mail address: [email protected] (J. Zhang) Tel: 86-22-22704495. Fax: 86-22-22704495.

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ABSTRACT: A series of stators were designed with the same opening area but different opening shape and number for the inline single-row blade-screen high shear mixers (HSMs), to study the emulsification and extraction respectively. The opening number has a significant influence on the emulsification and extraction, comparing with the opening shape. The computational fluid dynamics (CFD) analysis was used to disclose the intensifying rules of HSMs with desirable stator geometry. In the rotor and screen region both energy dissipation rate and shear stress increase first but then decrease as the opening number rises, whereas in the jet region both of them decrease with the opening number. The opening number can affect the flux through screen and shear gap, as well as the reentrainment and jet behaviors in the screen region. These results provide important guidance on the design and optimization of HSMs structures to intensify the emulsification and extraction. Key Words: high shear mixer, stator geometry, opening shape, opening number, emulsification, extraction

1. INTRODUCTION High shear mixers (HSMs) have been considered as a new kind of efficient device for process intensification, owing to the feature of highly localized energy dissipation rates and high shear rates near the mixing head1-4. Hence, HSMs have been widely 2


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used in some energy intensive processes, involving emulsification, dispersion, chemical reactions, cell disruption, deagglomeration, etc.5-8 Based on the operation mode, HSMs can be commercially classified into the inline units and batch units. The batch HSMs are operated in the batch mode, while the inline units are continuously operated with the advantages of high throughput9. The inline HSMs have attracted more recent attention in the continuous industrial automatic production processes.2,10 As one of the most important components of HSMs, the mixing heads play an important role in enhancing the droplet break-up and mass transfer, which are generally classified into two basic types: the rotor-stator teethed and the blade-screen configuration. For the blade-screen configuration, the rotor consists of several similar blades and can generate larger impetus on the fluids than the teethed one, which has the advantage over teethed one in self-priming capacity, pump capacity, etc.1,11 On the other hand, the stator can be designed as various types according to the hole/slot shape and number, such as the general purpose disintegrating screen (GPDH), the emulsor screen (ES), the square hole high shear screen (SQHHSS), the slotted disintegrating screen (SH), etc.12 Some literature has shown the intensification effects of HSMs associated with the unique structural type of the accessories. For example, Rodgers et al.13 studied the role of the ES for the inline HSMs, and indicated that the ES stator could reduce the bypass around the agitator in the single pass process compared with the detached stator. Hall et al.14-16 studied the emulsification of silicone oil in water using the inline HSM equipped with ES, achieving the droplet size about 2 ~ 4 µm under the conditions of 1.1×104 rpm and the dispersed phase viscosity of 9.4 mPa·s. Rueger et al.17-18 investigated the emulsification of crystal oil and water using a batch HSM equipped with SH stator, obtaining the equilibrium Sauter mean diameter about 10 µm

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under 9×103 rpm and the dispersed phase viscosity of 93.2 mPa·s. Shi et al.19 studied the emulsification of silicone oil in water using an inline HSM with square holes, which has different opening shape and number compared with SQHHSS, generating the equilibrium Sauter mean diameter of 5 µm under 3.5×103 rpm and the dispersed phase viscosity of 1.2 mPa·s. In addition, Thapar12 compared the emulsification property of four kinds of stators (GPDH, ES, SQHHSS, SH) for the inline HSMs, and concluded that adopting SQHHSS and ES could achieve the smallest mean droplet size. Utomo et al.20 studied the effect of the stator geometry (GPDH, SH, SQHHSS) on the energy dissipation rate and the flow pattern in the batch HSMs, and showed that jets emerging from GPDH extended up to the chamber wall whereas the fluids emerging from SH and SQHHSS dissipated near the mixing head; suggesting that the screen with narrow slots could create more uniform energy dissipation rate in the holes region and result in the narrow drop size distributions. Mortensen et al.21 studied the effect of stators with different opening number and constant opening area on the velocity fields and flowrate in the batch HSM; suggesting that the flowrate decreases with the increase of slot width and the narrower slots can promote dispersion. All these results reflect the fact that the droplet break-up in HSMs is greatly associated with manifold structural parameters including the hole/slot form, the hole/slot number as well as the opening area, although no report has been found so far on the effect of the structural parameters with the same opening area in the inline HSM. The principle of adjusting the droplet break-up is essential to understand deeply the mass transfer properties in HSMs, which is fundamental to explore the intensification applications of HSMs in emulsification and extraction processes. Herein we designed a series of stators with the same opening area but different opening shape and number for the inline single-row blade-screen HSMs, and studied

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the droplet size distribution and the volumetric mass transfer coefficients during the emulsification and the extraction respectively. The computational fluid dynamics (CFD) aided analysis was used to disclose the intensifying rules of HSMs with desirable stator geometry. These results provide important guidance on the design and optimization of HSMs structures to intensify the emulsification and extraction processes.

2. EXPERIMENTAL METHODS 2.1 Experimental Apparatus The experimental flow diagrams of the emulsification and the extraction were similar to our previous work.19,22 The experiments were all conducted on a custom-built pilot scale inline HSM manufactured by FLUKO. A series of mixing heads with different opening shape (circular, rhombus, “s” hole, teethed, crisscross) and opening number (circular holes, 30, 60, 120, 480) were designed to study the effect of different structural parameters on the emulsification and the extraction in such HSM. Figure 1 shows the detailed structures of the rotor and the stators with different opening shape. Opening shape represents the holes shape on the stator screen. The rotor in Figure 1(a) has a single row of 6 blades with the outer diameter of 59.5 mm; the blade is 15° backward inclined and the blade height is 8 mm. The stator is a single row screen with the inner diameter of 60.5 mm and the outer diameter of 70 mm. The shear gap (the annular space between the rotor and the stator) width is 0.5 mm. The base to tip (the axial space from the stator base to the rotor tip) clearance is 1 mm. All the stators have an opening number of 30, except that the “S” stator has an opening

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number of 16. These stators maintain the same opening area of 22.3% that is calculated based on the outer circular face of screen.

Figure 1. The rotor and the stators with different opening shape. (a) rotor; (b) circular screen; (c) rhombus screen; (d) “s” hole screen; (e) teethed screen; (f) crisscross screen

Figure 2 shows the detailed structures of the stators with different opening number. Opening number represents the holes number on the stator screen. To make the discussion clear, the stator is denoted in terms of both the diameter and number of holes, i.e., 4.8 mm×30 indicates the stator with the hole diameter of 4.8 mm and the hole number of 30, while 1.2 mm×480 denotes that with the hole diameter of 1.2 mm and the holes number of 480. The stator 4.8mm×30 has the same structure as shown in Figure 1(b).

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Figure 2. The stators with different opening number of circular hole. (a) 4.8mm×30; (b) 3.4mm×60; (c) 2.4mm×120; (d) 1.2mm×480

2.2 Experimental Materials and Measurement Techniques The deionized water was used as the continuous phase in the emulsification and the extraction, while kerosene (Tianjin Jiangtian Chemical Technology Co., Ltd, China) was used as the disperse phase in the emulsification. For the extraction, the kerosene containing 0.2 wt% benzoic acid (AR, Tianjin Guangfu Fine Chemical Research Institute, China) was used as the disperse phase. The viscosity of the deionized water and kerosene is respectively 1.18 mPa·s and 1.43 mPa·s; the density is respectively 998 kg/m3 and 783 kg/m3 for the deionized water and kerosene. The sodium dodecyl sulfate (SDS) surfactant (Aladdin Bio-Chem Technology, China) was used as an emulsifier to avoid the coalescence of the dispersed droplets in the emulsification process. The concentration of SDS was 1 wt% in the continuous phase, much higher than its critical micelle concentration of 0.18 wt%23. Adding this 1 wt% SDS had no effect on the viscosities and densities of the aqueous phase and the organic phase, while it decreased the interfacial tension from 23.1 to 4.5 mN/m. Using this surfactant, 7



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the emulsions could maintain the stable drop size distribution in 4 h and the results of ten parallel measurements were shown in Figure S1 in the Appendix I.1 of the Supporting Information. The viscosities were determined by a viscometer (LVDV-II+Pro, Brookfield); the densities were determined through the pycnometer method; the interfacial tensions between the oil and water phase were measured using an automatic surface tensiometer (JK99B, Powereach Co. Ltd.). The drop size distributions and the Sauter mean drop sizes (d32) were measured by the Malvern laser particle size analyzer 3000 (Malvern Instruments, Malvern, UK). The measurement range is 0.01~3500 µm with an accuracy of 0.5%. The Lorenz-Mie theory was employed in the measurement. The relative refractive indices (RI) of the water phase and kerosene phase are 1.33 and 1.43, respectively. The imaginary component of kerosene absorption index is 0.001.12 The drop size distributions were presented by volume frequency, which was useful to compare the effect of different stators on the drop size. The general purpose mode was employed in the process of the data analysis. The rotor speed and the shaft torque were determined by using an AKC-215 transducer (China Academy of Aerospace Aerodynamics) connected with the drive shaft and collected through the data-logging system. The bearing losses were estimated by the power consumption measured in pure water under the conditions of rotating the shaft at zero flow rates with the rotor detached. And the power consumption generated by the fluid drag acted on the shaft was assumed to be negligible.

2.3 Experimental Procedure 8


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All the experiments were performed at 15±2℃. The rotor speed was controlled by a frequency converter varying from 2000 rpm to 3500 rpm. In the emulsification, the flow rate of deionized water was 200 L/h and the dispersed phase volume fraction was 0.01. In the extraction, the flow rate of deionized water was 100 L/h and the organic phase volume fraction was 0.5. The kerosene and deionized water were mutually saturated before the extraction experiment. All measured samples were taken from the outlet of the HSM after a period of stable operation (about 20 times of the hydraulic mean residence time). The emulsification samples were analyzed immediately; the extraction samples were put into a centrifuge immediately to obtain a rapid separation and analyzed immediately.

2.4 Analytical Method The extraction performance was characterized by the extraction efficiency (E) and the volumetric mass transfer coefficients (KLa). The calculation formulas are expressed as follows (eqs 1, 2 and 3).24-29 E=

TOT C TOT ,i − CORG Amount transferred ,o = ORG TOT TOT * Maximum transferable CORG ,i − CORG , o

TOT TOT QORG (CORG ,i − CORG ,o ) = K L aV ∆Cm

∆Cln =

(1)

(2)

TOT TOT * TOT TOT * (CORG ,i − CORG ,i ) − (CORG ,o − CORG ,o ) TOT TOT * TOT TOT * ln[(CORG ,i − CORG ,i ) / (CORG ,o − CORG , o )]

(3)

TOT where CORG is the concentration of benzoic acid in the organic phase; i and o represent TOT * the inlet and outlet of the HSM respectively; CORG is the benzoic acid quasi

equilibrium concentration in the organic phase corresponding to its concentration in TOT aqueous phase CAQ ; V is the reactor volume; QORG is the flow rate of the organic

phase; ∆Cm is the mean concentration driving force, which can be calculated by 9



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∆Cln . The concentration of benzoic acid in both phases was measured by acid base titration with 0.01 mol/L NaOH standard solution. In particular, 2 ~ 4 droplets surfactant Tween 80 was added into the organic phase before titration. The maximal error per titration is less than ± 3%. The detailed calculating strategy of KLa can be found in the Appendix I.2 of the Supporting Information. The power delivered to the fluid by the rotor can be calculated by eq 4.

Pfluid = 2π NM − 2π NM n

(4)

where Pfluid is the net power (W); N is the rotor speed (rpm); M is the torque (N·m) at the working condition and Mn (N·m) is the torque measured with water and the rotors detached.

2.5 CFD Modeling Methods In order to observe the detailed flow pattern of HSMs with several different stators, the Ansys Fluent14.0 was employed to simulate the flow field. The detailed simulation procedure is described as follows. 2.5.1 Computational Mesh Figure S2 in the Appendix II.1 of the Supporting Information shows the computational domain and geometric structure of HSM. The simulated model was the same as the experimental model. It should be noted that the XY plane of Z = 0 mm is located in the base of stator head and the direction of Z is shown in Figure S2. The original unstructured tetrahedral elements were gained by Gambit mesh generator. The original computational grids were refined based on the converged velocity gradient, which were calculated by the standard k-ε model with first-order accuracy and the enhanced near wall function. The refined grids had 2.6 million cells

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with over 70% cells in the stator-rotor area, as shown in Table S1 in the Appendix II.2 of the Supporting Information. Figure 3 shows the refined grid based on the velocity gradient.

Figure 3. Refined grid according to the calculated velocity gradient.

(a) YZ plane X = 0; (b) XY plane Z = 5.5

2.5.2 Simulation Method The LES model had been proved to be effective in predicting the complicated flow pattern for the HSMs in our previous work30-32. Thus, the LES model was also adopted to analyze the flow characteristics. The multiple reference frames (MRF) technique was employed to simulate transient motion of stator and rotor. The velocity inlet, pressure outlet, no slip wall were separately setup. The discretized equations were solved by the SIMPLE segregated algorithm with default model constants. The momentum equations were calculated by the bounded central differencing scheme with the standard Smagorinsky-Lilly subgrid-scale model and the second-order implicit transient formulation. The Courant number can compare the time step to the characteristic time of transit of a fluid element across a control volume. The large time 11



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step can cause numerical instability and convergence difficulty. In this paper, the period of revolution Tr was separated into 600 time steps and the time step was

Tr/600.30-32 The global maximum Courant numbers was in the range of 7.4 ~ 9.9. The property of pure water was used in our simulations. The mesh independence was checked in the Appendix II.3 of the Supporting Information.

3. RESULTS AND DISCUSSION 3.1 Effect of Opening Shape on the Emulsification Property The effect of opening shape on the emulsification property of the inline HSMs was studied under different rotor speeds. Figure 4(a~e) shows the drop size distributions of the emulsions using five stators with different opening shape. With the increase of rotor speed, the curves of drop size distributions (DSDs) from all different stators shift left obviously. It is indicated that the higher rotor speed increases the volume fraction of small drop size, while reduces the volume fraction of large drop size. Since the increase of rotor speed can significantly enhance the shear rate and the turbulence energy dissipation rate, which results in the better droplet breakage effect. In addition, it can be observed that the peak value of the DSDs decreases with the rising of rotor speed, indicating that a large span of the DSDs is generated. This phenomenon can be explained by the following reasons: 1) the higher rotor speed improves the shear rate and the turbulence in the mixing chamber, which can break the droplets into the smaller size; 2) the higher rotor speed can cause serious back-mixing, which can makes the droplet size reduced; 3) the higher rotor speed improves the drainage capacity of blades and more fluids can overflow from the shear gap between the rotor and stator. The overflowed fluids from the shear gap suffer smaller velocity gradient and smaller energy dissipation rate. Thus, their drop sizes are larger than those of the

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fluids draining from the holes/slots of the screens.

Figure 4. Effect of the opening shape on the drop size distributions.

(a) circular screen; (b) rhombus screen; (c) teethed screen; (d) “s” hole screen; (e) crisscross screen; (f) the drop size distributions at 3000 rpm

Figure 4(f) shows the DSDs at 3000 rpm for different kinds of stators. It can be observed that the DSDs for these stators with different opening shape show no

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significant variations. The same trend can also be seen for the Sauter mean drop sizes (d32) in Figure 5. Figure 5(a) shows the effect of the opening shape on the value of d32, in particular, below each group of data markers there is the value of mean d32 as well as the standard deviation. For example, the value of 26.0 ± 0.93 at 2000 rpm represents the mean value d32 of 26.0 µm and the standard deviation of 0.93 µm. In addition, it can be seen that the stators with circular and rhombus generate the smallest d32, while the crisscross holes stator form the largest d32, with the teethed and “s” holes stators as the intermediates. For example, with the rotor speed rising from 2000 to 3500 rpm, the values of d32 for the circular hole and rhombus hole stators decrease from 24.9 µm and 25.6 µm to 11.9 µm and 11.7 µm, respectively; for the teethed and “s” hole stators, the values of d32 decrease from 26.6 µm and 25.6 µm to 12.0 µm and 12.2 µm, respectively; for the crisscross hole stator, the value decreases from 27.2 µm to 12.2 µm. Although the value of d32 for different stators is inconsistent at the same rotor speed, but the standard deviation is rather small. It is indicated that the effect of opening shape on the mean drop size is not obvious.

Figure 5. (a) Effect of the opening shape on the d32; (b) Effect of the opening shape on the

net power consumptions.

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Figure 5(b) shows the effect of the opening shape on the fluid net power consumption (Pfluid). For all stators with different opening shape, Pfluid increases with the increase of rotor speeds. For example, Pfluid of the circular stator increases from 11.6 to 46.9 W when the rotor speed rises in the range of 2000 ~ 3500 rpm. In addition, the rhombus holes and circular holes stators have the larger values of Pfluid, the stator with crisscross holes has the smallest Pfluid, with the teethed and “s” holes stators as the intermediates. The Kolmogorov length scale ( η K ) of stators with different opening shape is in the order of 10.6 ~ 16.1 µm at the rotor speed of 2000~ 3500 rpm. The drop sizes are larger than the η K , indicating that the droplet breakage mechanism in the inline HSMs at high rotor speed is due to the turbulent inertial stresses when the disperse phase has a low viscosity.14,19 In the inertial subrange, the relationship between dmax and ε max can be described by eq 5.33-36

d max ∝ (

σ 3/5 −2/5 ) ε max ρc

(5)

In geometrically similar turbulent systems, ε max is proportional to the average energy dissipation rate. The average energy dissipation rate in rotor swept volume ( ε N Q ) can be estimated by eq 6.

ε NQ =

Pfluid

(6)

ρVH

where VH is the volume of swept rotor, Pfluid is the net power, which can be measured by the torque method. In the inline HSM, the power draw can be expressed by eq 7.9,14-16,37,38 P = N PN ρ N 3 D 5 + N PQ ρ N 2 D 2Q

(7)

where NPN is ‘zero flow’ power constant; NPQ is the ‘flow’ power constant. From eqs 5

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and 6, it is clear that the drop size is inversely proportional to the fluid power consumption. The stators with circular holes and rhombus holes have relatively large Pfluid, which can produce relatively small drop size.

Figure 6. The turbulent dissipation rates of the HSMs with different opening shape on the XY

plane of Z = 5.5 mm under the condition of N = 2000 rpm and Q = 200 L/h. (a) teethed screen (b) “s” hole screen (c) rhombus screen (d) circular screen; (e) crisscross screen

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Comparing with other configurations, as shown in Figure 6, the stators with circular and rhombus holes can generate relatively large turbulent dissipation rates, which can result in a relatively small drop size. It can be confirmed by Figure 5(a) showing that the circular and rhombus generate a relatively small value of d32. The method of calculating the turbulent dissipation rate in LES is shown in Appendix III (eqs S11, S12, S13 and S14) of the Supporting Information.

3.2 Effect of Opening Shape on the Extraction Property

Figure 7. (a) Effect of the opening shape on the extraction efficiency; (b) Effect of the

opening shape on the volumetric mass transfer coefficient.

Figure 7 shows the effect of the opening shape on the extraction efficiency E and the volumetric mass transfer coefficient KLa. It is indicated that E and KLa increase with the increase of rotor speed, reaching to a plateau as the rotor speed is higher than 3000 rpm, suggesting the existence of the serious back-mixing at high rotor speed22. This behavior is also observed in the above emulsification experiment. At this moment, the rotor speed is not the leading factor, which can determine the mass transfer performance. In addition, it can also be seen that the standard deviation of E 17



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and KLa is rather small, indicating that the different opening shape does not show obvious effect on E and KLa, this is consisted with the result of the effect of the opening shape on the emulsification property.

Figure 8. (a) Effect of the average energy dissipation rate on the d32; (b) Effect of the average

energy dissipation rate on the KLa.

Figure 8 also exhibits the effect of ε N Q on the d32 and KLa. It shows that d32 decreases while KLa increases with the increase of ε N Q for different stators, both d32 and KLa display a little variation at higher ε N Q . In particular, Figure 8(a) shows that the stators with different opening shape have similar d32 at different ε N Q , especially for 3500 rpm. This phenomenon can be explained by the following reasons. As shown in eq 7 the power consumption in the inline HSM is related to the flow characteristics, which depends on the rotor-stator geometric configurations. The stators with different opening shape can exhibit different power consumption. However, in the HSMs the drop size mainly depends on the high turbulent dissipation rate in the rotor-stator region.39 Thus part power from flow may contribute a little role for drop breakup. Thus it can exhibit a similar d32 at different average energy dissipation rate for five stators with different opening shape. 18


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It should be noted that all stators in this section have low opening number (less than or equal to 30), the slight difference of each stator in term of emulsification and mass transfer performance may not be displayed effectively. The apparent difference may be observed when employing the high opening number. Taking into account the stators with complicated holes/slots geometries would be very hard to manufacture as well as the circular hole screen has a relative good emulsification and mass transfer performance, the circular hole is considered to be the optimal for the investigation of the effect of the opening number. Thus, another three circular stators with different opening number were employed in our research.

3.3 Effect of Opening Number on the Emulsification Property

Figure 9. Effect of the opening number on the drop size distributions.

(a) 4.8mm×30; (b) 3.4mm×60; (c) 2.4mm×120; (d) 1.2mm×480 19



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Figure 9 shows the effect of the opening number on the drop size distributions of the emulsification. The curves of drop size distributions shift obviously toward smaller values and the spans of the distribution curves increase with the rise of the rotor speeds. However, the differences of various stators cannot be effectively observed. Further, the drop size distributions at 3000 rpm and the d32 with corresponding standard deviation from all stators were shown in Figure 10. Figure 10(a) shows that the curves of DSDs shift left when the opening number increases from 30 to 120, but then shift right as the opening number increases further to 480. All the curves are log-normal with the similar variance at about 1.2 µm2. However, the median drop sizes are different. The stator with 120 holes has the smallest median drop size of 14.6 µm; the stator with 480 holes has the largest median drop size of 16.6 µm; the stator with 30 holes and 60 holes are due to 16.5 µm and 15.8 µm, respectively. Such behavior can also be seen for the changes in d32. For example, with the rotor speed increasing from 2000 to 3500 rpm, d32 of the stator with 30 holes decreases from 24.1 to 11.8 µm; for the stators of 60 and 120 holes, d32 decreases from 23.5 and 22.9 µm to 11.3 and 10.5 µm, respectively, while for the 480 holes’ stator, d32 decreases from 24.3 to 12.1 µm. It is obvious that the stator with 120 holes has the smallest d32, while the stator with 480 holes has the largest d32. The results indicate that the stator with 120 holes generates a relatively small particle size distribution. In addition, the open number shows a relatively large standard deviation comparing with the effect of open shape on d32.

20


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Figure 10. (a) Drop size distributions from stators with different opening number at 3000

rpm; (b) Effect of the opening number on the d32.

In the single-row blade-screen HSMs systems, the entered fluid can flow out through different pathways, as shown in Figure 11. The fluid can be partially jetted from the screen holes, or partially overflowed from the shear gap between rotor and stator. In the inertial subrange the maximum stable drop size is determined by the maximum local energy dissipation rate. In the HSMs, the maximum energy dissipation rates mainly concentrate in the mixing head.39 Comparing with the fluid emerging from shear gap, the fluid jetted from the holes can collide with the leading edge to generate a large velocity gradient, which can result in a smaller mean drop size. Therefore, the amount of fluid colliding with the leading edge and jetting from holes will have an important influence on the overall drop size distributions. As the opening number increases from 30 to 480, the wetted perimeter of the holes will become larger; consequently more collision frequency and flow resistance occur. The enhanced collision frequency can effectively increase the energy dissipation rate in the stator screen region; the enlarged flow resistance can obviously reduce the amount of fluid jetting from the holes, which can reduce the energy dissipation rate. Thus, the stators with different opening number will have different energy dissipation rates that

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can result in different drop size distributions.

Figure 11. The sketch of the volume flow flowing out through different pathways.

3.4 Effect of Opening Number on the Energy Dissipation Rate and Strain Rate Figure 12 further shows the energy dissipation rates of the HSMs with different opening number. Figure 13 shows the strain rates of the HSMs with different opening number. The shear stress plays a dominate role in enhancing the emulsion and mass transfer.32,35,36,40 In the Newtonian fluids, the shear stress is related to the strain rate and dynamic viscosity and is linearly proportional to the strain rate. Thus, the strain rate can be used to reflect the shear stress. It is indicated that in the rotor and screen region both the energy dissipation rate and the shear stress increase first but then decrease as the opening number rises, whereas in the jet region both of them decrease with the opening number.

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Figure 12. The energy dissipation rates of the HSMs with different opening number on the XY

plane under the condition of N = 2000 rpm and Q = 200 L/h. (a) 4.8 mm×30, z = 5.5mm; (b) 3.4 mm×60, z = 3mm; (c) 2.4 mm×120, z = 2.5mm; (d) 1.2 mm×480, z = 1.75mm

Figure 13. Contours of strain rates under the condition of N = 2000 rpm and Q = 200 L/h.

(a) 4.8 mm×30; (b) 3.4 mm×60; (c) 2.4 mm×120; (d) 1.2 mm×480

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3.5 Effect of Opening Number on the Flow Characteristic

Figure 14. Contours of velocity vectors on the YZ plane of X = 0 for the case of N = 2000

rpm and Q = 200 L/h. (a) 4.8 mm×30; (b) 3.4 mm×60; (c) 2.4 mm×120; (d) 1.2 mm×480

In order to further investigate the effect of opening number on the emulsification, the flow characteristics were simulated. Figure 14 shows the velocity vectors on the YZ plane of X = 0 under the condition of Q = 200 L/h and N = 2000 rpm. As expected, the fluid can enter into the chamber through two different pathways, including screen holes and shear gap. The stators with different opening number result in different flow characteristics. With the opening number of 30, more back-flow can be observed in the holes region. As the opening number increases, the back-flow becomes weaker. In 24


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particular, the back-flow can hardly be observed when the opening number equals 480. On the other hand, the jet flow through the shear gap can also be observed. The stronger jet occurs for the stator with 30 holes. With the opening number increasing from 30 to 120, the jets become much weaker. However, for the case with 480 holes, the jet flow becomes relatively stronger again.

Table 1. The volume flow through two different pathways under the condition of Vt = 200 L/h Vh (L/h) a

Vt1 Vs

No.

Vs/Vt

Vt2 Vs/Vt1

Vh2

Vh1+ Vh2

(L/h)

(L/h)

(L/h)

(a)

613

-632

-19

219

110

1464

15.0

832

26.3

(b)

576

-427

149

51

26

1054

4.8

627

8.1

(c)

593

-408

185

15

8

1016

1.5

608

2.5

(d)

187

-40

147

53

27

280

18.9

240

22.1

a

(L/h)

(%)

Vh1- Vh2+ Vs

Vs /Vt2

Vh1

(%)

(L/h)

Vh1 + Vs

(%)

(L/h)

(a) 4.8 mm×30; (b) 3.4 mm×60; (c)2.4 mm×120; (d)1.2 mm×480

Table 1 lists the volume flow through the shear gap (Vs) and the holes (Vh) respectively. When the opening number is 30, the ratio of Vs/Vt (Vt represents the total volume flow) is about 110%, such high value of the ratio is due to the back-flow that can partially outflow from the shear gap. As displayed in Figure S4 in the Appendix IV of the Supporting Information, the fluids can partially return back to the rotor region just in front of the blade position, while more fluids can return back to the rotor region behind the blade position, resulting in the high value of Vs/Vt ratio. Previously, some literature21,40 has shown that the wider holes on the screen can result in more back-flow, which may give rise to lower net flow pass the screen. The fluid emerging 25



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from the shear gap has smaller velocity gradient, thus the large ratio of Vs/Vt can result in a large drop size. The value of Vs/Vt ratio decreases first but then increases as the opening number rises, and the stator with 120 holes generates the smallest value of Vs/Vt. It is indicated that the stator with 120 holes is the optimal choice for the emulsification, in combination with the drop size distributions shown in Figure 10. In addition, according to the value of Vs/Vt, it is indicated that the emulsification performance of 480 holes should be better than 30 holes. However, the experimental results show that the stator with 30 holes has the better emulsification performance comparing with 480 holes. In order to explain this phenomenon, the whole net flow through the screen holes was divided into the forward volume flow (Vh1) and the backward back-flow (Vh2) based on the converged CFD simulation results of 2 times Tr, as listed in Table 1. Both the forward volume flow and the backward back-flow suffer from the velocity gradient and the shear force. The ratio of Vs/Vt1 (Vt1 = Vh1 Vh2 + Vs) is more useful to reflect the impact of opening number on the breakage process. As listed in Table 1, the ratio of Vs/Vt1 for the stator with 30 holes is lower than that for the stator with 480 holes, it is indicated that the stator with 30 holes exhibits better emulsification performance. Moreover, it can also be seen from Figures 12 and 13 that the stator with 30 holes has a relatively large energy dissipation rate and strain rate in the jet region, which can further break droplets of the back -flow into smaller sizes. Figure 15 shows the effect of the opening number on the fluid power consumption. It is clear that Pfluid increases firstly and then decreases with the opening number. The

26


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result is consistent with the emulsification performance in Figure 10.

Figure 15. Effect of the opening number on the fluid net power consumptions.

3.6 Effect of Opening Number on the Extraction Property

Figure 16. (a) Effect of the opening number on the extraction efficiency; (b) Effect of the opening number on the volumetric mass transfer coefficient.

The effect of the opening number on the extraction was also studied under different rotor speeds. Figure 16 displays a significant difference of E and KLa among the stators with different opening number. Both E and KLa increase with the opening

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number rising from 30 to 120, whereas they exhibit a decreasing trend when the opening number increases further to 480. For example, the values of KLa are 4.6 and 4.8 min-1 for the stator 30 holes and the stator 60 holes at 3500 rpm, while the values are 5.8 min-1 and 4.7 min-1 for 120 holes and 480 holes. The volumetric mass transfer coefficient has an increase of 26% with the opening number increasing from 30 to 120. This phenomenon is consistent with the result of the emulsification. However, the mass transfer property of the stator 480 holes is better than the stator 30 holes. In the emulsification the back-flow can further reduce the drop size distributions. In the extraction the back-flow can reduce the driving force of mass transfer, which may result in the second extraction caused by the reentrainment behavior only can contribute a little to the mass transfer performance. Thus different from emulsification, the ratio of Vs/Vt2 (Vt2 = Vh1 + Vs) will have a more direct impact on the mass transfer. As listed in Table 1, the Vs/Vt2 of the stator with 480 holes is lower than that of the stator with 30 holes, it is indicated that the mass transfer of the stator with 480 holes is better than that of 30 holes. Figure 17 also exhibits the effect of the ε N Q on the d32 and KLa of stators with different opening number. It shows that the d32 decreases and KLa increases with the increase of ε N Q .

Figure 17. (a) Effect of the average energy dissipation rate in rotor swept volume on the d32; 28


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(b) Effect of the average energy dissipation rate in rotor swept volume on the KLa.

The above results indicate that the opening number on the stator screens has an obvious influence on the emulsification and extraction in the inline HSM, and there exists the optimal opening number for the two operations. In our experiment, the stator with 120 holes has the optimal performance for both processes. Moreover, according to the above analysis, it is indicated that improving the opening area at the same holes size is hopeful to enhance the emulsification and extraction performance, because it could not only increase the leading edge but also increase the flux through the holes. These all can effectively increase the collision frequency between the fluid and the stator screen and improve the energy dissipation rates. In addition, reducing the thickness of the stator can also be adopted to improve the emulsification performance of the HSMs. Because reducing the thickness of the stator with large number of holes could effective increase the flux through the screen, which can lead to decrease the amount of fluid jetting from the shear gap and further increase the energy dissipation rates. These results provide important guidance on intensifying the emulsification and extraction in the inline high shear mixers.

4. CONCLUSION The effects of stator geometry on the emulsification and extraction were studied in this paper. The mean drop size (d32), extraction efficient (E) and volumetric mass transfer coefficient (KLa) of the HSMs with different stators, which have different opening shape and opening number, are determined. Under the same opening area 22.3%, the opening shape has little effect on d32, E and KLa; whereas the opening number has significant influence on these parameters. d32 decreases firstly and then

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increases with the increase of opening number, E and KLa have an opposite trend with the opening number increasing. The opening number can affect the reentrainment and jet behaviors of the screen region and has an important influence on the flux through the screen and shear gap. The energy dissipation rate, shear stress and the flux through the screen can all affect the emulsification and extraction performance. In addition, it further indicated that the flux ratio of jetting from shear gap/( jetting from screen and shear gap) has an important impact on the mass transfer, while the flux ratio of jetting from shear gap/(jetting from screen, shear gap and back-flow of holes region) has a direct impact on the breakage process. The results obtained here are important to intensify the emulsification and extraction in the inline blade-screen high shear mixers.

ASSOCIATED CONTENT Supporting Information Experimental methods (Appendix I), including the selection of emulsifier (Appendix I, section 1) and the analytical method (Appendix I, section 2); CFD modeling methods (Appendix II), including the geometric details and computational domain of HSM (Appendix II, section 1), the refined grids of different HSMs (Appendix II, section 2) and mesh independence (Appendix II, section 3); The method of calculating the turbulent dissipation rate in LES (Appendix III); The velocity vector of stator with 30 holes (Appendix IV).

AUTHOR INFORMATION Corresponding Author †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, 30


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P. R. China.

‡

School of Chemistry and Chemical Engineering, Shihezi University,

Shihezi 832003, P. R. China. E-mail address: [email protected] (J. Zhang). Tel/Fax: 86-22-22704495.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by National Key R&D Program (2016YFC1201503), the NSFC (21476158, 21621004), and the Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_15R46).

NOMENCLATURE DSDs = drop size distributions d32 = Sauter mean drop sizes, µm dmax = maximum stable diameter, µm E (a) = extraction efficiency KLa = volumetric mass transfer coefficient, min-1 M = torque, N·m Mn = torque measured of no rotor attached, N·m N = rotor speed, rpm Pfluid = fluid net power consumption, W QORG = flow rate of the organic phase, L/h Q = flow rate in simulation, L/h 31



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Tr = period of revolution, s Vs = volume flow emerging from the shear gap, L/h Vh = net volume flow flowing from the hole, L/h Vh1 = volume flow jetting from the hole, L/h Vh2 = volume of back-flow in the holes region, L/h Vt = the total volume flow, L/h V = the reactor volume, m3 VH = the volume of swept rotor, m3 Z = axial coordinate, mm

Greek Symbols

ε max = maximum energy dissipation rate, m2/s3 ε NQ = average energy dissipation rate in rotor swept volume, W/kg ε = turbulent energy dissipation rate, m2/s3

η K = Kolmogorov length scale, m

σ = interfacial tension, N/m ρ = fluid density, kg/m3

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Effect of Stator Geometry on the Emulsification and Extraction in

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