Abdelgadir Bashir Banaga, Yan-Bin Li,3, Zhi-Hao Li, Bao-Chang Sun,*, Guang-Wen Chu,*

1 State Key Laboratory of Organic-Inorganic Composite, Beijing University of Chemical Technology, Beijing 100029, China

2 Research Center of the Ministry of Education for High Gravity Engineering and Technology, Beijing University of Chemical Technology, Beijing 100029, China

3 Department of Chemical Engineering, Tiangong University, Tianjin 300387, China

Keywords:

ABSTRACT

1. Introduction

Mixing is portrayed as reducing non-homogeneity to get the requested process,which plays a principal role in several industrial operations[1,2].The mixing efficiency in the reactors has a definite influence on fast and complex reactions[3],and it is found to have a deep consequence on the overall performance, thus affecting both production cost and quality of final products [4]. The level of the non-homogeneity between the regions within mixing vessels is usually demonstrated by the intensity of segregation [2,5],which depends on deciding the concentration field[6].To estimate the mixing efficiency, the scale and the intensity of segregation were proposed by Danckwerts in 1952 [7], which is a factor that reflects the extension of fluid elements with constant concentration [8]. The intensity of segregation (Is) is an important property of a mixture that is affected by molecular diffusion. It is usually determined by examining how the composition at each point differs from the average composition of the mixture and can be considered as a statistical quantity to measure the mixing efficiency[9]. All of the definitions which give access to Isare described as the mean square deviation of the concentration of composition from the mean for a specific time(t)compared to its value at time zero [10]. In addition, the value of Isvaries from unity for a completely segregated system to zero for an ideal homogeneous system [11,12].

A rotating bar reactor(RBR)consists of the inner rotating cylinder and the outer static cylinder. The RBR is designed with an improved feeding system that consists of radial and tangential feeding modes [13]. The type of reactor inlet affects the performance of the reactor. The axial velocity distribution was more homogeneous when the reactor operated with the tangential inlet than the other inlets [14]. Banaga et al. [13] reported that the RBR with tangential feeding mode had high micromixing performance with a micromixing time of ～10-5s. The RBR offered the advantages of a rich cascade of different flow states that provided a range of hydrodynamic conditions, both laminar and turbulent[15]. The Reynolds number (Re) of the RBR [16] was varied with the alteration of rotational speed. Nemri et al. [17] experimentally investigated the flow regimes based on the Re. The flow regimes were categorized into Taylor vortex, wavy vortex, modulated wavy vortex, and turbulent flows. The turbulent flow regime was observed at Re higher than 2500. In fact, RBR has been widely applied in many processes, including homogeneous transition metal catalysis, photocatalytic and enzymatic reactions, polymer synthesis,crystallization, aggregation-flocculation processes, separation and mixing processes[18,19].Aiming to enhance the mixing efficiency of RBR,the flow regime can consequently be tailor-made mainly to the requirements for the process of blending and dispersing because of excessive shear forces to excessive flow segregation leading to a plug-flow nature [20]. Under these circumstances, an extra-axial liquid flow from bottom to top balance the flow regimes. Hence, increased axial flow causes the spreading of the vortices in the axial direction. Significantly the turbulence RBR flow combines the advantages of intense mixing with small axial dispersion [21].

The accurate, non-intrusive techniques used for assessing Isinclude the planar laser-induced fluorescence (PLIF) [6,22] and electrical resistance tomography (ERT) [23]. PLIF technique was used for liquid flows in different mixing devices, which is more suitable for the instantaneous measurement of concentration in a laminar flow [24–26]. In contrast, ERT has been successfully adopted to characterize changes in conductivity/resistivity that can be operated in an opaque system [27,28]. These nonintrusive techniques had the ability to measure the intensity of segregation in the reactors, but the techniques are expensive and complicated due to the need for data processing algorithms and many operation devices [24–28]. Further, the conductivity technique proposed as an intrusive technique can determine the concentration of components at multiple levels along the reactor. It has been used to identify the mean residence time distribution to characterize the macromixing [29,30],by which the concentration distributions can be estimated with high resolutions.It will be presented in this work as a method for evaluating the intensity of segregation. Conductivity is an estimate of the ability of a solution to bring an electric current.It is affected by the temperature,concentration,mobility,the valence state of the ionized species in a liquid[31]. The conductivity strategy can be applied conveniently since the materials required are available, few devices are utilized, and the cost could be reduced, which could be a promising alternative for evaluating the intensity of segregation.

There are several publications on measuring the mixing efficiency in Taylor Couette (TC) reactors similar to the rotating bar reactor. Different strategies have been experimentally used to determine mixing properties inside the TC reactor. For example,Desmet et al.[32,33]implemented a color tracer technique to estimate local and global dispersion. Akonur and Lueptow [34] estimated a mixing characteristic of particles seeded within Taylor Couette flows by implementing particle image velocimetry (PIV).Nemri et al. [35] studied the mixing properties of different Taylor-Couette flow regimes and their consequence on axial dispersion of a passive tracer by applying both PIV and PLIF. Richter et al. [36] discussed the process of mixing in a continuous flow Taylor-vortex reactor, and the characterization was performed through tracer experiments. The characterization was performed through tracer experiments. As a significant measuring factor, a segregation index has been used to analyze mixing efficiency in particle-laden TC flows, summarized by Zeinab et al. [37]. Liu et al.[38]found that a rotating bar reactor with different internals,including gas distributor and liquid disturbing pin, successfully enhanced the mass transfer. From the above previous literature,hitherto exist no reports on study the intensity of segregation distribution along the axial direction of RBR.

This article aims to investigate the mixing efficiency distribution along the RBR. For the first time, the investigation on the intensity of segregation at multiple levels in the axial direction of RBR was obtained using the conductivity technique to acquire the concentration field directly. Effects of rotational speed, flow rate, length of the reactor, and tracer concentration on the intensity of segregation were investigated. In addition, to study the impact of the concentration distribution on the mixing efficiency.In the case of an RBR, this work is also performed to investigate the conductivity technique’s suitability for rotating reactors.

2. Experimental

An RBR was selected as a working reactor. As illustrated in Fig.1,the RBR consists of inner and outer cylinders.Table 1 shows the details of geometric dimensions. The feeding mode is defined as a tangential feeding mode, which means that solution A (high flow rate) enters through the big tangential tube while solution B(low flow rate) enters through the small radial tube. Our previous work has proved that the tangential feeding method effectively enhanced the micromixing efficiency [13]. Thus the experiments were carried out by using a tangential feeding inlet.

The sampling points were fixed at four levels along the reactor(at heights of 62,87,112,and 330 mm).The bottom of the RBR was defined as the base level where the axial height was 0 mm. The sampling sections were arranged not uniformly since the mixing efficiency changes drastically near the inlets. A neutralization experiment was preliminarily developed to judge the mixing height of the RBR by the de-colorization method, which was performed by using two solutions A & B. The aqueous sulfuric acid was introduced as a solution B (1.0005 mol H2SO4dilated in 5 L DI water). The solution A consisted of 200 ml of NaOH solution(1.005 mol?L-1),120 ml phenolphthalein solution(5 mg phenolphthalein per liter ethanol), and 100 L DI water.

Each section had six points for sampling in the same crosssection area. The bottom section is located at 62 mm and the top section at 330 mm. The sampling tubes pull the samples at different distances from the wall of RBR(1,2,and 3 mm from the wall).Hence, it almost covered the total area of the cross-section between the two cylinders.

2.1. Measurement method of the intensity of segregation

A direct method for determining mixing efficiency is developed by measuring concentrations of samples obtained within the RBR.Fig. 1 illustrates the schematic diagram of the experimental setup of the conductometry. The most important factor for efficacious conductometry implementation is the probes have a very fast response time [39]. Conductivity is an estimate of the ability of a solution to bring an electric current.Inorganic compound solutions have appropriate conductivity, while solutions of organic mixture which no longer dissociate in water have poor conductivity. As a consequence, the conductivity method with a strong electrolyte was judged to be more convenient for this method[31],and a solution of NaCl served as a tracer.As shown in Fig.1,the NaCl solution of 100 g?L-1and the deionized water were prepared as solutions B and A in storage tanks,respectively.Then,the solutions were fed to the RBR through two peristaltic pumps. Solution B was injected into the reactor from the radial tube (1.6 mm in diameter) with a flow rate of VB,and solution A entered the RBR from the tangential tube (6.4 mm in diameter) with a flow rate of VA. The flow rates were measured by flow meters and controlled by the frequency of the pumps. In most experiments, the ratio of VAand VB(VA:VB)was kept at a constant of 10:1, except for investigating the influences of VAand VBon the Is. The solutions flowed upward in the RBR to a drain tank through the outlet tube. The rotational speed of the inner cylinder of the RBR was controlled by a motor, which promoted the mixing of components in the bulk solutions. After 5 minutes from the beginning of the experiment, the samples were collected from four sections, with six samples for each section simultaneously. The sample conductivity was measured by a conductivity device (Mettler Toledo) with an accuracy of 99.5%,which is accessible for the conductivity range of 0.01 to 200.00 mS?cm-1. The conductivity values are then converted into concentration data using the calibration equation based on the linear relationship between concentrations of the NaCl solution and conductivity, which is displayed in Fig. 2. The mixing efficiency is represented by the concentration field inside the reactor.It is possible to measure the local intensity of segregation at a multitude of points inside the reactor.The experimental conditions are summarized in Table 2.

Fig. 1. Schematic diagram of experimental setup: 1—tank, 2—pump, 3—flow meter, 4—inlet section, 5—outer cylinder, 6—inner rotating cylinder, 7—motor, 8—outlet, 9-1—sampling level 1 (bottom section), 9-2—sampling level 2, 9-3 —sampling level 3, 9-4—sampling level 4 (top section), 10—drain tank.

Table 1 Parameters of the used RBR

2.2. Evaluation of mixing efficiency

Mixing efficiency can be measured by the intensity of segregation which depends on the concentration of species A and B, and defined as [40,41]:

Fig. 2. Calibration equation and curve based on the linear relationship between concentrations of the NaCl solution and conductivity.

The average concentration of NaCl (Cav) is calculated according to the concentrations and flow rates of solutions A and B, which conformed to the following formulas:

Table 2 Specifications of the experimental conditions

3. Results and Discussion

3.1. De-colorization phenomena

Fig.3 optically shows the color change of the pink solution.The colorless zone in the RBR indicates a good mixing performance,which can roughly determine the mixing height of RBR. It could be seen from the figure that with the rotational speed increasing from 100 to 500 r?min-1, the mixing height of RBR was approximately reduced from 160 to 60 mm. Based on the qualitative results, it could be concluded that the mixing was mostly progressed near the inlet plane. The RBR was thus divided into three parts along the axial direction. In the first part (0–148 mm, inlet tubes are at Z = 30 mm), three layers of sampling points were arranged (62, 87, 112 mm), and the last sampling layer(330 mm) was designed in the third part (300–445, outlet tube is at Z = 390 mm).

3.2. Effects of rotational speed on the axial distribution of Is

Fig.4 shows the axial distribution of Isat four measuring levels along the RBR under different rotational speeds.It can be seen that before reaching the reactor outlet, the Isat the height of 330 mm was close to zero. In contrast, the Isat the locations between 62 mm to 112 mm near the RBR bottom were always greater than that at 330 mm, indicating a large concentration gradient at the bottom of the reactor. The phenomenon was also reflected by the discrepant concentration distribution at the bottom and top sections of the RBR,as shown in Fig.5.It is indicated that the inhomogeneity of concentrations appeared at the bottom, while the top generated homogeneity. At the experimental condition of N = 500 r?min-1, VA= 60 L?h-1, VB= 6 L?h-1, and CNaCl,0= 10 g?L-1,the Isat the bottom section was two orders of magnitude higher than that at top section, which decreased from 6.53 × 10-5to 1.57 × 10-7. The large aspect ratio of the RBR generated enough time for the different shear forces to uniform the concentrations gradually with the influence of the axial flow. In addition, numerous Taylor vortices collapsed along the reactor due to the buoyancy and centrifugal force,significantly promoting the mixing efficiency[20].

Fig. 3. Estimation of mixing height of RBR by the de-colorization method and neutralization experiments (VA = 60 L?h-1, VB = 6 L?h-1).

Fig. 4. Effect of rotational speed on the axial distribution of Is along RBR.

Fig. 5. Concentration distribution of NaCl at the bottom and top sections of RBR.

Fig.4 also presents the effect of the rotational speed of the inner cylinder on Is.It is clear from the curve at zero rotational speed that the Isvalues increased between 87 mm to 112 mm and then decreased again at 330 mm. It was derived from the absence of rotational speed to enhance mixing efficiency.When the rotational speed increased from 100 to 700 r?min-1, the mixing performance was improved. With increasing N from 0 to 700 r?min-1, the Isat the bottom and top sections decreased from 4.27 × 10-3to 7.10 × 10-5and from 1.93 × 10-3to 7.29 × 10-7, respectively.The rotating shaft generated different shear forces through different rotation speeds, which could strengthen the process of mixing and mass transfer in RBR [45]. The striation thickness decreased due to the reinforced centrifugal field and the axial or radial velocity at the injection position [46]. As mentioned above, the turbulent flow regime was achieved at Re higher than 2500 in the RBR.For this experiment at 500 r?min-1, the Re was equal to 2595. It could be argued that the flow regime was turbulent flow. Therefore, increasing the rotational speed above 500 r?min-1slightly improved the mixing efficiency [47]. In addition, fluid mixing depends on the complicated vortex motion at different rotational speeds [48].

3.3. Effect of the flow rate of solution A on the axial distribution of Is

The influence of the flow rate of solution A(VA)on the values of Isis shown in Fig.6.The Isdecreased with increasing VAalong RBR,showing that the mixing performance between the two fluids is improved. The increase in the liquid flow rate provides a higher velocity of solutions, which is useful to enhance the interaction between fluid elements.An increase in the feed flow rate enhances the turbulence,energy lavished in the solution,and thus the shear stress wielded on the liquid contents,which is anticipated to ameliorate the mixing efficiency. Furthermore, as the inlet flow rate increases, the moving velocity of the vortex in the axial direction linearly increases [49]. The axial movement carriages the vortices in which the toroidal movement of fluid items causes effective mixing along the RBR [17].

3.4. Effect of the flow rate of solution B on the axial distribution of Is

Fig.6. Effect of the flow rate of solution A on the axial distribution of Is along RBR.

The influence of the flow rate of solution B(VB)on the intensity of segregation at four measuring levels along the RBR (from 62 to 330 mm) is illustrated in Fig. 7. Results show that the increment of VBcaused an enlargement of Isand a worse mixing efficiency.It can be seen that Isat the four measuring levels under the flow rates of 5 and 6 L?h-1is always smaller than that under a flow rate of 7.5 L?h-1. The intensity of segregation decreases sharply between heights 62 mm to 87 mm, then decrease slightly up to 330 mm.Since the flow rate of the main solution VAwas not changed, the liquid velocity caused by variation of VBcan be neglected in the RBR, resulting in a negligible change in the flow field. However,the increase of VBproduced more components to be dispersed in the main solution, which aggravated the agglomeration of micro-elements in the reactor. As a consequence, the mixing efficiency declined.

3.5.Effect of sodium chloride concentration on the axial distribution of Is

Fig.7. Effect of the flow rate of solution B on the axial distribution of Is along RBR.

Fig. 8. Effect of sodium chloride concentration on the axial distribution of Is along RBR.

The effect of sodium chloride concentration on the mixing efficiency is displayed in Fig. 8. The values of Iswere measured with different concentrations of NaCl (10, 100, 200 and 300 g?L-1,respectively).The results showed that Isincreased with an increase in sodium chloride concentration. It is dependent on the presence of ions in the solution. Ions are derived from ionic compounds(NaCl) dissolved in water. In general, the increase of NaCl concentration increases the ion concentration in the solution,resulting in an increase in the solution conductivity.Mixing can be considered as the permeation of fluid clumps with different components of a certain concentration[42]. In RBR,the performance of mixing was supposed to be affected by two aspects. On one hand, it was the interaction between fluid clumps (namely macro mixing), which was determined by the flow conditions, such as the intensity of turbulence,the stength of shear force,etc.The smaller fluid clumps were favorable for better macro mixing performance.On the other hand, the concentration of components in the clumps affects the result of micro mixing, that is molecular scale mixing. The large concentration gradient of components in different fluid clumps would affect the mixing speed. As a result, changing the component concentration at the inlet affected the mixing efficiency through changing the molecular diffusion. More components needed to be transferred, which meant that the ‘‘load” for reactor mixing became larger, and thus the value of Iswas varied. It is essential to discover the concentration distribution of the RBR with inside the liquid–liquid system with a higher concentration,which is useful to manual the design and optimization of RBR implemented to the higher concentration running conditions.

4. Conclusions

This work studied the intensity of segregation along the RBR using the experimental conductivity method. The conductivity technique was carried out by measuring the conductivity of samples pulled from four axial levels along RBR, which was converted to the intensity of segregation based on Danckwerts law. The effects of rotational speed, flow rate, and concentration of NaCl were experimentally analyzed on the axial distribution of Is. The mian conclusions were listed as follows:

(1) The mixing efficiency was improved along the axial direction from the bottom to the top in the RBR.The inhomogeneity of concentrations appeared at the bottom, while homogeneity was generated at the top. At the experimental condition of N = 500 r?min-1, VA= 60 L?h-1, VB= 6 L?h-1, and CNaCl,0=10 g?L-1, the Isat the bottom section was two orders of magnitude higher than that at top section, which decreased from 6.53 × 10-5to 1.57 × 10-7.

(2) The rotation of inner cylinder of RBR greatly reduced the Isand improve the mixing efficiency.With the increase of rotational speed from 0 to 700 r?min-1, Isat the bottom and top sections decreased from 4.27×10-3to 7.10×10-5and from 1.93×10-3to 7.29×10-7,respectively.The additional neutralization experiments based on the de-colorization method demonstrated that mixing was mostly progressed near the inlet of RBR. With the rotational speed increasing from 100 to 500 r?min-1, the mixing height of RBR was approximately reduced from 160 to 60 mm.

(3) The increases in flow rate of solution A,and the decreases in the concentration of NaCl and flow rate of solution B gave rise to the reduction of Is, signifying an improved mixing efficiency. These findings demonstrated that RBR can consider successful in controlling the uniformity of concentrations. The current study successfully presented a feasible approach for calculating the intensity of segregation,characterized by simplicity and low cost.

Data Availability

Data will be made available on request.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (21725601).

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