Intensification of viscous fluid mixing in eccentric stirred tank systems

Intensification of viscous fluid mixing in eccentric stirred tank systems

Chemical Engineering and Processing 66 (2013) 36–43 Contents lists available at SciVerse ScienceDirect Chemical Engineering and Processing: Process ...

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Chemical Engineering and Processing 66 (2013) 36–43

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Intensification of viscous fluid mixing in eccentric stirred tank systems Mengxue Zhang, Yinyu Hu, Wentan Wang, Ting Shao, Yi Cheng ∗ Department of Chemical Engineering, Tsinghua University, Beijing 100084, PR China

a r t i c l e

i n f o

Article history: Received 10 September 2012 Received in revised form 22 November 2012 Accepted 18 January 2013 Available online 26 January 2013 Keywords: Mixing Stirred tank Fluid mechanics Visualization Highly viscous fluid Laminar flow

a b s t r a c t The mixing process of highly viscous liquids in a small stirred tank for High Throughput Experimentation (HTE) apparatus was investigated using a visualization approach, i.e., the Planar Laser-Induced Fluorescence (PLIF) technique. Segregated regions were detected despite a long period of agitation, indicating that the mixing homogeneity can be hardly attained for the mixing of highly viscous liquid. Based on the image analysis of PLIF results, we defined a desegregating time to quantify the mixing process of viscous liquids and to compare the mixing performances under different operating conditions. Eccentric agitation proved to be an efficient way to intensify the mixing of viscous liquid for the fact of significantly reduced desegregating time under the same stirring rate. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Mixing is a central operation of many processes in the food, pharmaceutical, cosmetic, paper, plastics, ceramic and rubber industries [1]. A lot of work has been done to increase the efficiency of mixing, which involves reducing not only the time, but also the expenses of a mixing process. Since mixing operations are carried out on a large scale in many industrial sectors, studies have been made and empirical correlations have been deduced for the scale-up of mixing processes, whereas the fundamentals of mixing processes remain unclear, especially for the mixing of highly viscous liquids. Improving the mixing performance of viscous liquids has always been an important issue in chemical engineering because of its complicity and its increasing industrial relevance. Mixing occurs at two levels: macromixing and micromixing (Danckwerts [2]). Macromixing occurs because of different circulation loops caused by convective flows in the fluid; the latter refers to the intermixing of molecules due to the diffusion between small cells. For high viscosity liquids, a poor macromixing is usually the rate-determining step of mixing. Most researches about the intensification of viscous materials mixing have been done with close clearance impeller systems (Coyle et al. [3]; Dieulot et al. [4]). Nevertheless, the dimension of impellers is quite near to that of the reactor in the case of close clearance impellers, which leads to significant energy cost. The smaller

∗ Corresponding author. Tel.: +86 10 62794468; fax: +86 10 62772051. E-mail address: [email protected] (Y. Cheng). 0255-2701/$ – see front matter © 2013 Elsevier B.V. All rights reserved.

dimension adopted by the open impeller design is less energydemanding, but meanwhile less efficient as for the mixing of very viscous fluids. Concerning the open impeller design, a common strategy of mixing is to introduce complicated impeller geometries in the system to disorder the liquid. Other approaches were also mentioned such as using variable speed protocols to create chaos in the laminar regime [5–7], installing asymmetric arrays of baffles [8], and employing an eccentric impeller location to achieve a widespread chaos [9–14], etc. However, few studies have been carried out with axial flow impeller design for fluids of high viscosity. For decades, chemical engineers have been working on the scale-up of agitated tanks while the knowledge about the scaledown of stirred vessels is still limited for the small reactors of High Throughput Experimentation (HTE) equipments. It is still unclear a priori whether the same rules remain valid for scale-down as in scale-up. With the rapid development of High Throughput Experimentation reactors (Hall et al. [15]), more attention has been drawn to the scale-down of mixing processes in a small stirred vessel so as to determine if classical approaches for solving the problem are applicable for small scale systems. To quantify the ‘goodness’ of mixing, a number of visualization techniques have been developed in recent years. Cabaret et al. [16] used colorimetric methods and image analysis to investigate the mixing time of various processes. Different from some other traditional methods, a laser-induced fluorescence technique (LIF) proved to be an accurate and versatile way to quantify mixing performances of miscible liquids, e.g., the studies of Arcoumanis et al. [17], Alvarez et al. [18], Hu et al. [19], Unger and Muzzio [20], and Ventresca et al. [21]. Fountain et al. [22] reshaped the

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Nomenclature C Ce Cmax

Cmeas d D e GV H N Re t S tb T V VT wb x, y, z

bottom clearance (m) the average Rhodamine-B concentration when thoroughly mixed (␮g dm−3 ) the maximal tracer concentration (␮g dm−3 ) for a linear relationship between tracer concentration and fluorescence intensity measured concentration of Rhodamine-B (␮g dm−3 ) shaft diameter (m) impeller diameter (m) eccentricity gray value liquid height (m) impeller speed (rpm) Reynolds number time (min) area of segregated region thickness of impeller blade (m) tank diameter (m) volume of liquid in the tank (m3 ) volume of the injected tracer (m3 ) width of impeller blade (m) coordinate position (m)

Greek symbols area covered by the tracer (1–segregated area)  a largest area that the tracer can cover (%) b ability of the tracer to spread thoroughly (min−1 ) liquid density (kg m−3 )   liquid viscosity (Pa s)

understanding of mixing by introducing a 3-D visualization technique based on LIF technique. In this paper, we use the Planar Laser Induced Fluorescence (PLIF) technique to visualize and to quantify the mixing performance of viscous Newtonian fluids in a small stirred tank. We demonstrate that introducing eccentricity to the system is an efficient way to intensify the mixing process in small stirred vessels, especially for the mixing of viscous liquids.

Fig. 1. Mixing vessel configuration.

diameter of the impeller D = 0.05 m, and the diameter of the impeller shaft d = 0.006 m. The bottom clearance of the impeller is fixed at C = 0.33 T by a high-speed torque blender (WB-2000D, Wiggens, Germany). The eccentricity is defined as the ratio of the distance between the middle of the shaft and the centerline of the tank to the radius of the tank. In order to minimize the optical distortion due to the curvature of the tank, the cylindrical vessel is placed in a second rectangular liquid-filled glass chamber during the observation. 2.3. Operating conditions Experiments are conducted under impeller speeds of 100, 200, 300, 500, and 600 rpm, where the corresponding Reynolds numbers are 4, 8, 12, 20 and 24, respectively. Here the Reynolds number in the stirred tank is defined as: Re =

D2 N 


where  is the liquid density,  is the liquid viscosity, D is the impeller diameter and N is the stirring rate. The whole system is maintained at 25 ◦ C so that the viscosity remains at 1.3 Pa s. The tracer dye, i.e., 2.0 cm3 of Rhodamine-B solution (15 g m−3 ), is introduced in the system with an injection pump within 1 s. 2.4. PLIF technique

2. Materials and methods 2.1. Materials A Newtonian fluid glycerin (AR, Beijing Modern Oriental Fine Chemistry Co. Ltd, China) is used as the working fluid in our systems so as to study the mixing behavior of viscous liquid. The temperature of experiments is kept at 25 ◦ C so that the viscosity remains 1 Pa s for glycerin liquid. The density of glycerin at this temperature is maintained at 1260 kg m−3 . 2.2. Mixing vessel configuration To better visualize the mixing process, flat-bottom transparent acrylic cylindrical vessels with a diameter (T) of 0.10 m are employed, as shown in Fig. 1. The liquid height (H) is also 0.10 m. 0.79 × 10−3 m3 glycerin is initially introduced in the vessel as working fluid. The impeller is a 30◦ four-blade pitch downpumping impeller made of stainless steel. A homogeneous layer of black matt paint (Zhongshan Datian Industries Inc., China) covers the impeller thoroughly to reduce possible laser reflection. The width of the blade wb = 0.008 m, the thickness tb = 0.001 m, the

In this work, Planar Laser-Introduced Fluorescence (PLIF) is used as the main measuring technique as it is a quantitative, precise and non-intrusive method to evaluate concentration fields. A typical PLIF visualization system consists of a laser source, a CMOS camera, a computer, and the mixing vessel, as shown in Fig. 2. A 1.5 W pumped solid-state continuum laser produces a laser sheet with a wavelength of 532 nm to illuminate the medium in the vessel. A small amount of tracer solution containing Rhodamine-B (tracer) is injected in the pure glycerin system to study the mixing behavior. The Rhodamine-B molecules absorb the laser light energy and re-emits light at a wavelength of 553 nm. The fluorescence emitted by the tracer is captured by a CMOS camera (MotionPro X3, IDTTM ) equipped with a narrow-band filter, so that only the fluorescent light is recorded on the computer. The computer then translates the fluorescence intensity to different gray values on the images. The sampling frequency of the camera is 50 fps, and the smallest pixel size is 160 ␮m. The laser plan is slightly shifted from the impeller shaft plan so that the whole transaction plane can be illuminated. The distance between the laser plan and the shaft plan is 5 mm. The injection point of the fluorescent dye is situated on the laser plan, and the coordinate is (72 mm, 5 mm, 150 mm).


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Fig. 2. Schematic of the PLIF setup.

Previous studies [23–25] show that the intensity of re-emitted fluorescence is proportional to the concentration of fluorescent tracer in the liquid system for a fixed laser light intensity at a certain tracer concentration range (0 ∼ Cmax ). Cmax varies depending on the experimental condition (laser intensity, relative position camera/laser source, etc.) With a calibration procedure which will be described in the next part, we can deduce the concentration field of the tracer based on the fluorescence intensity obtained. 3. PLIF calibration theory and calculation 3.1. Concentration range of calibration In order to avoid the influence of tracer fluid on the bulk fluid dynamics, we limit the volume of Rhodamine-B solution to 2.0 cm3 , inferior to 10−2 of the total volume of the glycerin liquid, which gives rise to a huge gap between the initial Rhodamine-B concentration in the tracer solution (C0 = 15 mg dm−3 ) and the average Rhodamine-B concentration in the stirred tank when thoroughly mixed (Ce = 38.2 ␮g dm−3 ). If C0 is chosen as Cmax , a better description about the behavior of tracer solution at the moment of release can be given [15]. Nevertheless, we focus on the overall mixing performance in this study rather than the initial mixing state; in other words, the range of interests is in the vicinity of Ce rather than C0 . Therefore, the experiments are conducted in a way that Cmax has the same order of magnitude as Ce (Cmax chosen to be 150 ␮g dm−3 in this work). This manipulation omits the information of concentration fields when the tracer concentration C is between Cmax and C0 , but gives more details when the tracer concentration C is between 0 and Cmax . Eq. (2) describes the relationship between the actual tracer concentration C and the measured concentration Cmeas .

Cmeas =


(C ≤ Cmax )


(C ≥ Cmax)

uniformly mixed), the fluorescence intensity is linearly related to the tracer concentration. Once the tracer concentration exceeds Cmax , it is considered Cmax accordingly (Eq. (2)). Homogeneous Rhodamine-B solutions of 0, 20, 40, 60, 80, 100, 120, 130, 140, 150, 200 ␮g dm−3 are respectively prepared so that reference images of the tank containing are recorded while the laser illumination and the set-up remain unchanged. These images are then averaged for each concentration and Fig. 3 shows the relationship between the fluorescence intensity and the concentration of RhodamineB. In spite of the error that this calibration may bring to the local tracer concentration during the initial mixing phase, this treatment ameliorates the resolution when measuring the distribution of concentration of Rhodamine-B and these reference images help to eliminate image noises of mixing experiments. 4. Results and discussion To better present the concentration distribution in the tank, we use pseudo-color images to replace gray-level images of PLIF


3.2. Calibration experiments Prior to the PLIF experiments, a set of experiments are conducted for the in situ calibration. When the tracer concentration is between 0 and Cmax (150 ␮g dm−3 , the concentration of tracer when

Fig. 3. Relationship between the fluorescence intensity and the concentration of Rhodamine-B.

M. Zhang et al. / Chemical Engineering and Processing 66 (2013) 36–43


Fig. 4. Pseudo-color images of the tracer distribution (N = 100 rpm). I-Segregated region above the impeller; II-Segregated region below the impeller; III-Segregated region in the vicinity of the vessel bottom.

measurement. The pure red denotes tracer of Cmax (or above) while the pure blue denotes 0 ␮g dm−3 . 4.1. Characterization of high viscosity mixing It is important to well identify a mixing process before any efforts to intensify it. Mixing time and the intensity of segregation (IOS) are two parameters frequently used for the characterization of the mixing performance in agitated tanks. The parameter IOS, proposed by Danckwerts [2] in 1952, measures the difference in concentration between the pure liquid with tracer and that of the pure liquid without tracer. But in the case of viscous fluid mixing, chances are that uniformity cannot be attained despite a very long agitation time, and the IOS value may not rightly reflect the local mixing performance because of a poor macromixing. Therefore we use another parameter, the desegregating time, to quantify the macro-mixing performance of viscous fluids. Fig. 4 shows the evolution of the 2-D mixing pattern at different moments for the impeller speed of 100 rpm. The sequence shows a

compartmentalization in the stirred tank. In the meantime, the transport of the tracer exhibits a certain pattern: The tracer goes down from the surface till the end of the shaft, and then it is thrown away to the tank wall, forming symmetric ‘paths’. Then the tracer distribution gradually stabilizes. Since there is practically no turbulence in the tank, molecular diffusion is the main regime of Rhodamine-B transport once the stable path is established. This sequence demonstrates the presence of segregated toroidal regions where the tracer cannot reach even after a long period of mixing. To quantify these zones, we define a segregated region as the region where the concentration of Rhodamine-B is inferior to 5% of the mean tracer concentration in the fluid. As shown in Fig. 5, Region II plays a key role in controlling the mixing performance. As we increase the rotation speed to 300 rpm (Re = 12), the mixing performance in the vessel is similar to that of 100 rpm, as shown in Figs. 6 and 7. What is particular in this case is that Region II breaks into several small sub-regions at t = 15 min. In this part of our experiments, the formation of stable segregated areas during the mixing of viscous fluid is detected. The

Fig. 5. Segregated region of viscous fluid at N = 100 rpm. I-Segregated region above the impeller; II-Segregated region below the impeller; III-Segregated region in the vicinity of the vessel bottom. At the instant t = 6 min, the area of Region I is the biggest, whereas that of Region III is the smallest; SI :SII :SIII = 1:0.65:0.14. At t = 20 min, Region II becomes the largest region, which demonstrates that diffusion undergoes faster in Region I than in Region II. At t = 60 min, SI :SII :SIII = 1:21.3:0.20, there is no significant change of Region II.


M. Zhang et al. / Chemical Engineering and Processing 66 (2013) 36–43

Fig. 6. Pseudo-color images of the tracer distribution (N = 300 rpm). The tracer spreads around the shaft at the liquid surface in the first place, and then it descends to the other end of the shaft. Afterwards it follows the ‘path’ to reach the interior wall of the tank and stabilizes.

intensity of segregation is no longer a good mixing criterion when the mixing is inefficient and segregated zones appear. We will further discuss about the concept of mixing time in the following part of this work, aiming to better characterize the mixing performance of high viscosity liquid. To improve the mixing performance of viscous systems, a reduction of segregated areas is primarily necessary. In this article, we will mainly discuss how eccentricity can diminish the area of segregated regions so as to enhance the macromixing and thereby intensify the mixing process of highly viscous fluids.

it propagates initially in the vicinity of the impeller shaft at liquid level, then descends and diffuses to the vessel wall following a certain trajectory before spreading out completely. But the path of tracer in eccentric stirred tank is not symmetric and disorder is thus introduced into the system. A better mixing is more quickly attained with eccentric mixing in both Figs. 8 and 9. Since there are segregated regions in viscous systems and homogeneity is often unattainable, we use the desegregating time rather than the IOS value as the key parameter to quantify the degree of mixing.  is the area covered by the tracer (1–segregated area).

4.2. Effect of shaft eccentricity on mixing

 = a [1 − exp(b t)]

Alvarez et al. [9] have pointed out that introducing eccentricity can enhance the mixing performance in a Rushton impeller stirred tank. In this work, we mainly focus on the advantages of eccentric mixing for viscous fluids mixing. To compare segregated regions in the case of eccentric stirred tanks with that of concentric systems, Figs. 8 and 9 show the instant distribution of Rhodamine-B at 200 rpm and 500 rpm. The tracer in eccentric systems follows similar paths as in concentric ones:

In the work of Cabaret et al. [16], the author also describes the existence of segregated regions. Fig. 10 shows the evolution of tracer coverage, which is in accordance with the mixing curve of Cabaret et al. [16]. We use Eq. (3) to express the area covered by the tracer . a signifies the largest area that the tracer can spread. b shows the ability of the tracer to thoroughly spread, the greater this value is, the easier it is for the tracer to spread in a very short time. Table 1 lists different parameters under various operating

Fig. 7. Segregated regions of viscous liquid at N = 300 rpm. Compared with N = 100 rpm, Region III almost disappears. At t = 6 min, SI :SII = 1:3.9; at t = 15 min, SI :SII = 1:4.5.


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Fig. 8. Pseudo-color images of the tracer distribution (N = 200 rpm) in concentric systems and in eccentric systems. The eccentricity breaks the symmetry of segregated regions.

Fig. 9. Pseudo-color images of the tracer distribution (N = 500 rpm) in concentric systems and in eccentric systems. At t = 1 min, the ratio of area of segregated region in eccentric stirred tank versus that in concentric stirred tank is 1: 2.4, which shows that eccentricity can remarkably decrease segregated area and intensify the mixing of fluids.

Fig. 10. The evolution of tracer coverage at different rotation speeds. (a) 100, 200, 300 rpm; (b) 500 rpm.


M. Zhang et al. / Chemical Engineering and Processing 66 (2013) 36–43

Table 1 Estimated parameters (a and b ) under different operating conditions. Rate (rpm)

Eccentricity (e)

a (%)

b (min−1 )

100 200 200 300 500 500

0 0 0.30 0 0 0.30

92.8 94.8 100 100 100 100

0.048 0.076 0.20 0.12 2.2 2.8

twice as much as the desegregating time of an eccentric mixing of e = 0.15, and five times longer than the desegregating time of the eccentric mixing of e = 3. As we increase the stirring rate, this advantage of eccentric mixing is however less obvious. At 500 rpm, the desegregating time of e = 0.3 is 78% of the desegregating time of a concentric mixing at the same condition. As a matter of fact, the Reynolds number of the system is 8 at 200 rpm. The flow regime in the stirred tank stays strictly laminar. As the stirring rate increases, the Reynolds number becomes 24 at 600 rpm. Cabaret et al. [10] has established dimensionless mixing curves between the Reynolds number, mixing times and the eccentricity for laminar flows. It is believed that a small shaft eccentricity has a low impact on the tracer coverage  at low Reynolds number, whereas the shaft eccentricity has a larger impact with the increase of the Reynolds number. Our work gives a conclusion from a different point of view: the desegregating time is largely reduced by a small eccentricity at low Reynolds number, while this advantage of shaft eccentricity is less obvious for a larger Reynolds number. 5. Conclusions

Fig. 11. Desegregating time under different mixing conditions.

conditions. At low rotation rate, the tracer coverage cannot attain 100% in 3 h because of the low velocity of fluid in the vessel. Based on Eq. (3), the desegregating time is easily defined: the minimum time it takes for  to be equal or greater than 70% is defined as  70 ; accordingly, the minimum time it takes for  to get to 80%, 90% or 95% are  80 ,  90 or  95 . Fig. 11 shows the desegregating time under different configurations. We can see that for a certain degree of uniformity, the desegregating time decreases while the stirring rate augments, probably because of the enhancement of disturbance in the tank. In the meantime, we can also get to the conclusion that the eccentricity favors the decrease of desegregating time. We can see from Fig. 12 that a greater eccentricity leads to a shorter desegregating time  95 , especially at low stirring rate: at 200 rpm, the desegregating time of a concentric mixing is

In this article, we used the Planar Laser Induced Fluorescence (PLIF) technique to visualize the mixing process of high viscosity fluids in a small stirred tank with the help of a high speed camera. Segregated areas were detected because of the low regional fluid velocity. The concept of segregated regions was brought up for viscous fluids mixing, and so was the concept of desegregating time as the essential criterion for the mixing of viscous liquids. The contour and the area of these segregated regions could be quantitatively determined by the PLIF technique. We pointed out that the notion of segregated region outshined other mixing criterions like the intensity of segregation (IOS) to characterize the mixing behavior of highly viscous fluids. The intensification of viscous liquid mixing by converting concentric stirring to eccentric stirring was discussed in this work. The symmetric geometry of the flow field was broken up by the eccentricity, which accordingly diminished segregated areas, therefore accelerated the rate-determining step of mixing for viscous fluids. Acknowledgements Financial supports from National 973 Project of PR China (No. 2013CB733600), National Natural Science Foundation of China (No. 21036003 & No. 20776074) and Specialized Research Fund for the Doctoral Program of Higher Education (No. 20090002110069) are acknowledged. This work is also under the support of Key Lab for Industrial Biocatalysis, Ministry of Education, China. References

Fig. 12. The influence of eccentricity value on desegregating time ( 95 ) at different stirring rate.

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