Experimental Investigation on Drawdown of Floating Particles in

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Cite This: Ind. Eng. Chem. Res. 2019, 58, 11060−11071

Experimental Investigation on Drawdown of Floating Particles in Viscous Systems Driven by Coaxial Mixers Baoqing Liu,†,‡ Pengfei Gao,† Zilong Xu,† Bengt Sunden,*,‡ and Yijun Zheng† †

Institute of Process Equipment, Zhejiang University, Hangzhou 310027, China Department of Energy Sciences, Lund University, Lund SE-22100, Sweden

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‡

ABSTRACT: In view of the current situation of single form and low efficiency, a coaxial mixer with wide adaptability was combined with the drawdown of floating particles in viscous systems, and the effects of operation mode, impeller type, impeller diameter, impeller submergence, system viscosity, solid concentration and particle size were investigated experimentally. It is found that the coaxial mixer under corotation mode can achieve the critical drawdown of floating particles with lower speed and power than the corresponding single-shaft mixer, and the advantage becomes more obvious with increasing system viscosity and solid volume fraction. Under the same conditions, compared with the axial and radial flow impellers, the mixed flow impeller with downpumping mode can effectively draw the floating particles down with the lowest critical speed and power. Moreover, a larger impeller diameter and smaller impeller submergence are recommended for the drawdown of floating particles, but the impeller diameter should not exceed half of the vessel diameter. suspension state proposed by Zwietering6 for depositing particles. Ozcan-Taskin et al.7 proposed two mechanisms for the drawdown and dispersion of floating particles by the downpumping impeller: when the impeller submergence is large, the particles are mainly transported into the liquid phase by the main circulation flow; when the impeller submergence is small, the surface vortex plays a dominant role. Gong et al.8 researched the drawdown of floating particles in a laminar squared stirred tank by experiments and simulations and found that tangential velocity and particle collision triggered the drawdown of floating particles. Tagawa et al.9 studied the performance of double-layer four-straight-blade disk turbine, double-layer four-pitched-blade turbine, and Maxblend (MB) impeller and Fullzone (FZ) impeller for the drawdown and dispersion of floating particles, respectively. It was found that Maxblend (MB) impeller had the lowest critical drawdown speed and power. Bao et al.10 analyzed the influence of surface state of floating particles on their drawdown and dispersion, and found that the residual hydrophobic solvent will lead to a significant increase in the critical drawdown speed and power. Kuzmanic et al.2,11,12 studied the influence of impeller diameter and particle size on critical drawdown speed, mixing time and concentration distribution of floating particles. It can be found that the existing experimental investigations on the mixing of

1. INTRODUCTION Mixing operations are used widely in process industries, and common processes such as heating, cooling, fermentation, dissolution, and crystallization generally rely on agitation to achieve a better mass-heat transfer effect. According to the type of the mixed materials, the mixing operation can be classified as liquid−liquid, gas−liquid, solid−liquid, and gas−liquid−solid mixing,1 among which solid−liquid mixing can be further divided into the suspension and dispersion of depositing particles as well as the drawdown and dispersion of floating particles. At present, more research works have been focused on the mixing of depositing particles and few on the floating particles.2 However, the operation for the drawdown and dispersion of low-density floating particles is also common in the chemical industry (e.g., process to produce formic acid with phosphoric acid acidification of sodium formate), food fermentation, mineral flotation, sewage treatment, polymerization reaction, and other applications.3 Moreover, the mixing of floating particles is very complex because of the fluctuation of the free liquid surface and the existence of surface vortices.4 Thus, it is necessary to design a rational mixing system to achieve effective drawdown and dispersion of the floating particles by combining the practical problems in industrial production with the investigated contents of this paper. Joosten et al.5 investigated the drawdown and dispersion of floating colloidal particles and cork chips in water for the first time. They then defined the critical drawdown state as the residence time of the floating particles at the liquid surface within 1−2 s based on the criterion of critical off-bottom © 2019 American Chemical Society

Received: Revised: Accepted: Published: 11060

April 4, 2019 May 29, 2019 June 3, 2019 June 3, 2019 DOI: 10.1021/acs.iecr.9b01867 Ind. Eng. Chem. Res. 2019, 58, 11060−11071

Article

Industrial & Engineering Chemistry Research floating particles mostly chose water as the liquid phase. However, practical industrial mixing processes are mostly carried out in viscous systems, and the system viscosity may change during the mixing process, such as the tank coacervation reaction of butadiene rubber and the process system of recovering yellow phosphorus tail gas to produce formic acid,13,14 in which the system viscosities are high and variable. Hence, it is necessary to study the drawdown and dispersion of floating particles in viscous systems and choose a novel mixer suitable for viscous systems.15,16 A coaxial mixer is composed of an inner and an outer impeller driven by two independent motors. The outer impeller is conducive to eliminate the inert zone around the wall, bottom, and liquid surface of the stirring vessel. The coaxial mixer has four operation modes, namely, single rotation of either inner or outer impeller, corotation, or counterrotation of the two impellers. In addition, the mixer has the advantages of flexible operation and wide adaptability and is especially suitable for the mixing of systems with high and variable viscosity, making it recognized quickly by the process industry. Previous studies on coaxial mixers mainly focused on single-phase systems and gas−liquid two-phase systems.17−21 Although there are a few studies on solid−liquid systems, most of them focused on the suspension and dispersion of depositing particles.22 So far, there are no research reports found that have studied the drawdown and dispersion of floating particles in viscous systems driven by a coaxial mixer. In this paper, the coaxial mixer was combined with the drawdown and dispersion of floating particles in viscous systems, and the comparison with single-shaft mixers was carried out. The influencing law and mechanism of the operation mode, inner impeller type, outer impeller speed and other specific factors on critical drawdown of floating particles were also investigated. Furthermore, on the basis of the optimized operation mode and inner impeller type, the influences of impeller diameter, impeller submergence, and other structural parameters of the mixer as well as the system viscosity, particle concentration, particle size and other operation parameters on the drawdown and dispersion of floating particles were also discussed. By combining the technique of coaxial mixing with the drawdown and dispersion of floating particles, it is expected to provide a new method and choice for the drawdown and dispersion of floating particles. The related results are beneficial to promote the application of coaxial mixers.

main sizes are listed in Table 1. The liquid height is identical to the vessel diameter, e.g., 380 mm.

Figure 1. Structure of stirred vessel.

2.2. Experimental Material. Food-grade malt syrup, which is colorless, tasteless, and transparent, was selected as the viscous medium in the experiments. As a typical Newtonian fluid, different viscosity can be obtained by adjusting the concentration of malt syrup. The density and viscosity of the malt syrup solution at different concentrations are shown in Table 2, where the viscosity was measured by a digital rotor viscometer with a spindle, and the density was measured according to the definition of density ρ = m/V. Polyethylene particles with a density of 831.34 kg m−3 were selected as the solid phase, which is a kind of floating particles relative to malt syrup solution. The density was also measured according to the definition of density ρ = m/V, and a smaller density of alcohol solution was selected to measure a certain amount of the floating particle volume by the liquid draining method. Particles of three size grades were obtained by the sieving of standard mesh, and the histograms shown in Figure 3 were obtained by analyzing the distribution of the particle size after photographing with a microscope. The average particle size d32 of the three kinds of particles were calculated by eq 1, which is 0.69, 1.15, and 2.16 mm, respectively.

2. EXPERIMENTAL SECTION 2.1. Experimental Setup. For the convenience of observation and measurement, the experiments were carried out in a transparent organic glass stirred vessel with an inner diameter of 380 mm and a standard ellipsoidal bottom. The stirred vessel was fixed on a hydraulic lifting platform, and the impeller submergence of the mixer can be changed by adjusting the height of the lifting platform. The coaxial mixer is composed of an outer and an inner impeller, which are concentric but driven by two independent motors. In the experiments, the propeller, the six flat-blade disc turbine (Rushton), and the six 45°pitched-blade turbine (PBT6) were adopted as the inner impeller. They represent the axial flow impeller, the radial flow impeller and the mixed flow impeller, respectively, whereas the frame paddle was adopted as the outer impeller. The structures of the vessel and the inner impellers are shown in Figures 1 and 2, respectively, and their

n

d32 =

∑i = 1 di3 n

∑i = 1 di2

(1)

To improve the measuring accuracy of the experiments and reduce the difference between reality and measured value, it is imperative to conduct an error analysis of the experimental data. Even if all the systematic errors have been eliminated, some irregular fluctuations in the measurement results still exist, which come from the precision and stability of the measuring instruments, the subjective judgment of operators, and the variation in environmental factors. Therefore, all the experimental data were measured at least three times to reduce the errors. The specific information on measuring instruments can be found in Table 3. 11061

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Figure 2. Structure of inner impellers.

is within 1−2 s. Record the rotation speed and load torque on inner and outer impellers at this time. Increase the speed of the inner impeller continuously to make the working condition beyond the critical state. Reduce the speed to reach the critical state again. Record the rotation speed and load torque at this time again. Average the critical rotation speed and torque of the inner impeller obtained in the rising speed stage and the falling speed stage, respectively, to act as the critical drawdown speed and critical load torque of current working condition. Repeat the above steps for three times at least. Calculate the critical drawdown speed of inner impeller at different outer impeller speeds. 2.3.3. Calculation of Overall Reynolds Number Re. The classical calculation formula of Reynolds number Re is mainly used in the single-shaft mixing system. In order to apply the classical calculation formula to a coaxial mixing system, the characteristic diameter can be replaced by the inner impeller diameter Di, and the characteristic rotation speed N can be calculated by the following formula:23

Table 1. Main Size Parameters of Vessel and Impeller parameter

CG

Da

H

HG

t

T

Wa

Wb

Wc

value (mm)

50

25

380

120

5

380

338

38

80

Table 2. Concentration, Density, and Viscosity of Malt Syrup Solution (30°C) Cl(L L−1) ρl(kg m−3) μl (Pa s)

0.788 1306 0.1

0.840 1327 0.2

0.867 1338 0.3

0.885 1345 0.4

0.899 1350 0.5

2.3. Experimental Method and Procedures. 2.3.1. Measurement and Calculation of Stirring Power P. The mixing power is calculated by the torque method, wherein the shaft torque is measured by the TQ-660 torque sensor. To eliminate the influence of friction and other factors, the torque is measured under load and without load, respectively. The mixing power can be calculated according to the following equations. P = Po + Pi (2)

N = Ni ±

No RN

(7)

Po = 2πNoMo

(3)

Pi = 2πNM i i

(4)

Mo = Mo,1 − Mo,0

(5)

Therefore, the overall Reynolds number is defined as

M i = M i,1 − M i,0

(6)

2

RN =

Ni No

N yz D 2ρ ij R e = i jjjNi ± o zzz μ jk RN z{

To eliminate the influence of size effect and make the mixing power more valuable for reference, the unit volume power PV(PV = P/V) is generally used to characterize the power performance of the mixer. Therefore, the sum of unit volume power of inner and outer impellers at the critical drawdown state means PVjdo 2.3.2. Measurement of Critical Drawdown Speed of Inner Impeller Nijd. First, turn on the outer impeller and fix its speed at 40 rpm. Increase the speed of the inner impeller slowly until the residence time of the floating particles at the liquid surface

(8)

(9)

where ρ is the density of the stirred material and can be calculated as ρ = ρl (1 − C0) + ρs C0

(10)

Table 4 shows the ranges of overall Reynolds numbers and the critical speeds in every experiment. The structure and physical parameters in every experiment have been listed in Table 5. In this paper, the study was mainly 11062

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Figure 3. Size distribution of polyethylene particles.

Table 3. Technical Parameters of Measuring Instruments name torque sensor electronic balance digital rotor viscometer graduated cylinder

type TQ660 JM NDJ5S

manufacturer Beijing Shitong Kechuang Technology Co., Ltd. Ruian Yingheng Electric Appliance Co., Ltd. Shanghai Jingtian Electronic Instruments Co., Ltd. Kimble Bomex (Beijing) Glass Co., Ltd.

measuring range

Table 4. Ranges of Critical Drawdown Speed and Overall Reynolds Number

accuracy

±100 N m

0.1%

0−3000 g

0.1 g

0.001−100 P s

1%

0−500 mL

5 mL

figure number

critical drawdown speed(s−1)

overall Reynolds number

4 6 7 8 9 10 11

3.13−3.29 3.30−5.04 3.30−10.21 2.88−4.96 3.13−5.04 3.04−3.96 2.88−3.88

788.1−1076.0 821.6−1312.6 821.6−1193.7 708.5−1291.8 389−1774.7 1485.4−2001.1 1374.6−2001.1

and dispersion of the floating particles were discussed and chosen. On the basis of this, the influences of inner impeller diameter, impeller submergence, viscosity of liquid phase, particle concentration, and particle size on the drawdown and dispersion of floating particles were further studied. 3.1. Effect of Operation Mode. Taking six 45° pitchedblade turbines (PBT-6) as an example and considering its uppumping (PBTU) and down-pumping (PBTD) modes, the influences of three operation modes, including the corotation and counter-rotation between the inner impeller and the outer

focused on the difficulty and power consumption of the drawdown of floating particles at critical state, and the distribution of particles in the stirred tank was not concerned. The particles can be well-dispersed throughout the whole vessel in all investigated conditions.

3. RESULTS AND DISCUSSION To investigate the critical drawdown state of the floating particles driven by the coaxial mixer, first, the suitable operation mode and inner impeller type for the drawdown 11063

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Industrial & Engineering Chemistry Research Table 5. Structure and Physical Parameters of Each Experiment number

impeller type

1

PBTU+anchorPBTD+anchor

2

propeller+anchor, PBTD +anchor,TXL+anchor PBTD+anchor

3

rotation mode co-rotationcounter-rotation, stalling-anchor co-rotation

Di/T 0.53

μl(Pa s)

Ds/T 0.33

0.2

dp(mm) 2.16

C0 (L/L) 0.03, 0.05 0.05

4

0.35, 0.42, 0.53 0.53

5

0.53

6 7

0.25, 0.33, 0.41, 0.49 0.33 0.1, 0.2, 0.3, 0.4, 0.5 0.1 0.69, 1.15, 2.16

0.01, 0.03, 0.05, 0.07, 0.09 0.01, 0.05, 0.09

Figure 4. Critical drawdown speed and power under different operation modes (Di = 200 mm, Ds = 125 mm, μl = 0.2 Pa s, dp = 2.16 mm).

Figure 5. Flow patterns under different operation modes (PBTD, Di = 200 mm, Ds = 125 mm, μl = 0.2 Pa s, C0 = 0.05 L L−1, dp = 2.16 mm, No = 20 rpm, Ni = 180 rpm).

by the structure of the stirred vessel and the physical properties of the stirred material but also varies with the outer impeller speed No. Figure 4 shows the critical drawdown speed Nijd and power PVjd of PBT-6 under different operation modes and outer impeller speeds. As can be seen from Figure 4: (1) When the coaxial mixer is operated under corotation mode, both the critical drawdown speed and power are lower than under the single-shaft mode. Meanwhile, Nijd and PVjd decline further with increasing outer impeller speed, which

one and single rotation of inner impeller, on the critical drawdown of floating particles were investigated. In this case, the rotation direction of inner impeller was regarded as positive. Accordingly, the rotation direction of the outer impeller was positive in the corotation mode and negative in the counter-rotation mode. The symbol Njd is usually used to represent the critical drawdown suspension speed in a singleshaft mixer as the critical drawdown suspension speed. Based on this, the critical drawdown suspension speed Nijd of the inner impeller is proposed in this paper. It is not only affected 11064

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the power consumption of the inner impeller, the power consumption of the outer impeller is negligible. However, this does not mean the influence of the outer impeller on the drawdown is negligible. The outer impeller can help to enhance the main circulation flow and the surface vortex, which are beneficial to the drawdown of floating particles. In general, the inner impeller is more critical for the drawdown from the viewpoint of power consumption, and the outer impeller plays an auxiliary role. 3.2. Effect of Inner Impeller Type. The influence of the inner impeller type on the drawdown of floating particles was further investigated under the optimal corotation mode. The propeller, Rushton, and PBT impeller were selected as the representatives of the axial flow impeller, radial flow impeller and mixed flow impeller, respectively, among which both the propeller and PBT adopted the down-pumping mode, namely, the TXL impeller and PBTD turbine, respectively. Figure 6 shows the Nijd and PVjd of different inner impellers and it can be found that (1) Among the three inner impellers, the PBTD impeller has the lowest Nijd and PVjd under the same speed of the outer impeller and is recommended. Compared with the Rushton and TXL impeller, the mixed-flow type of the PBTD impeller can produce not only a strong axial flow but also a radial flow. Both of those play an important role in the drawdown of floating particles accumulating in and around the center of liquid surface and are conducive to the overall drawdown and dispersion of floating particles. (2) The Nijd of the TXL impeller is the largest, but its PVjd is much lower than that of the Rushton turbine. The normal of the smooth surface of the TXL impeller has the largest angle with the rotation direction of the blade, and the axial flow velocity generated at the same rotational speed is the lowest. This results in weak surface turbulence, which is adverse to the drawdown of floating particles accumulating in and around the center of the liquid surface. Therefore, a larger mixing speed is required to make the particles to reach the critical drawdown state. In addition, because of the small resistance on the smooth curved-surface blade, the PVjd of the TXL impeller is still lower than that of the Rushton turbine, even if its Nijd is the largest. 3.3. Effect of Inner Impeller Diameter. The effect of the inner impeller diameter on the drawdown of the floating particles was investigated by using the PBTD as the inner impeller under the corotation mode. Figure 7 shows the Nijd and PVjd under different inner impeller diameters. As can be seen from Figure 7, the Nijd and PVjd of floating particles decrease significantly with increasing inner impeller diameter. This is because at the same rotation speed, the larger the inner impeller diameter, the greater is the linear velocity at the blade tip. Hence, according to the Kolmogorov’s turbulence theory about turbulent length scales and turbulent energy transfer process,28,29 stronger surface turbulence and larger central vortex would be produced, which draw the floating particles into the liquid phase easier, and the corresponding Nijd becomes smaller. In addition, a relatively large decline of Nijd is caused by a relatively small increase in the diameter of inner impeller, so the PVjd would still decrease significantly even if the diameter of the inner impeller increases. Figure 7 also indicates that when the outer impeller speed N0 is high, it is very difficult for the inner impeller with a small diameter to achieve the critical drawdown of floating particles. This is because to reach the critical state, the rotation speed of

makes the competitive advantages of the coaxial mixer more obvious. However, when the inner and outer impellers are under counter-rotation mode, Nijd and PVjd change little, and the influence of the outer impeller speed is not obvious. In fact, the drawdown of floating particles mainly depends on the drag of the main circulation flow and the entrainment of the surface vortex.4 Because the experiments were carried out at a low solid concentration, which is lower than 8%, then the particles had a small effect on the flow field.24,25 Therefore, the results can be explained by the discovery of Bonnot et al.26 in the study of coaxial mixing in single-phase flow that the corotation mode can generate stronger axial circulation flow, which is beneficial for the drawdown of floating particles, whereas the outer impeller would weaken the main circulation flow produced by the inner impeller under the counter-rotation mode. In addition, it was observed in experiments that a large and deep central vortex appeared at the center of the liquid surface under the corotation mode, whereas only a few small and shallow vortices appeared at the liquid surface under the counter-rotation mode, and the vortices would constantly appear and dissipate with the rotation of the outer impeller, as shown in Figure 5. On the basis of the above analysis, it is not difficult to understand that the existence of a strong main circulation flow and large central vortex leads to a better drawdown performance of floating particles under the corotation mode. (2) The Nijd and PVjd of the PBTD impeller are much lower than those of the PBTU impeller. This phenomenon can be explained by the research results of Ozcan-Taskin.27 When the impeller is arranged near the liquid surface, the main circulation flow generated by the PBTU impeller diffuses from the center of the liquid surface to the periphery and then moves downward after it touches the wall. However, the intensity of the circulation flow at this time has been weakened and the ability to drawdown particles has been reduced. In contrast, the PBTD impeller forms a vortex at the center of the liquid surface and directly draws the particles down into the vessel. Therefore, its critical drawdown speed and power are lower than those of the PBTU impeller. To investigate the effect of inner and outer impeller on the power consumption, their respective proportions to the total power consumption were calculated and listed in Table 6. As can be seen, the inner impeller accounts for the major power consumption, whereas the outer impeller has little effect on the power consumption. This is because P is proportional to N3, and the inner impeller speed is several times that of the outer impeller speed in the experiment. Therefore, compared with Table 6. Power Consumption of Inner and Outer Impeller No (s−1)

Ni (s−1)

Po (W m−3)

Pi (W m−3)

XPo (%)

XPi (%)

0.667 0.5 0.333 0.167 0 −0.167 −0.333 −0.5 −0.667

3.125 3.208 3.292 3.375 3.375 3.458 3.542 3.458 3.458

16.622 11.756 6.903 3.327 0 1.037 2.539 3.325 1.793

166.238 193.404 228.687 267.123 285.64 303.893 365.481 316.395 318.327

9.09 5.73 2.93 1.23 0 0.34 0.69 1.04 0.56

90.91 94.27 97.07 98.77 100 99.66 99.31 98.96 99.44

PBTD, Di = 200 mm, Ds = 125 mm, μl = 0.2 Pas, C0 = 0.03 L L−1, dp = 2.16 mm. a

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Figure 6. Critical drawdown speed and power corresponding to different inner impellers (Di = 200 mm, Ds = 125 mm, μl = 0.2 Pa s, C0 = 0.05 L L−1, dp = 2.16 mm).

Figure 7. Critical drawdown speed and power under different inner impeller diameters (PBTD, Ds = 125 mm, μl = 0.2 Pa s, C0 = 0.05 L L−1, dp = 2.16 mm).

Figure 8. Critical drawdown speed and power at different impeller submergences (PBTD, Di = 200 mm, μl = 0.2 Pa s, C0 = 0.05 L L−1, dp = 2.16 mm).

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Figure 9. Critical drawdown speed and power under different system viscosity (PBTD, Di = 200 mm, Ds = 125 mm, C0 = 0.05 L L−1, dp = 2.16 mm).

Figure 10. Critical drawdown speed and power at different solid concentrations (PBTD, Di = 200 mm, Ds = 125 mm, μl = 0.1 Pa·s, dp = 2.16 mm).

used for the drawdown of floating particles does not exceed half of the vessel diameter. 3.4. Effect of Inner Impeller Submergence. The impeller submergence Ds refers to the vertical distance from the center of inner impeller to the free liquid surface. Nijd and PVjd at different impeller submergences and outer impeller speeds were measured and illustrated in Figure 8. As can be seen from Figure 8, with increasing impeller submergence, the Nijd and PVjd of the coaxial mixer become larger. The increasing impeller submergence results in the overall downward migration of the circulation flow area developed by the inner impeller, and the liquid phase velocity, turbulence intensity and surface vortices at the liquid surface are weakened accordingly. At this time, a higher rotation speed is required to form enough vortices and circulation flow to achieve the critical state. Meanwhile, a large impeller submergence means that a large hydrostatic pressure occurs at the position of the inner impeller. Thus, the resistance encountered in the mixing process is also large. Because of the above two reasons, the PVjd also increases continuously with increasing impeller submergence. It should be pointed out that

the inner impeller with small diameter must be higher, and a deeper vortex will be produced accordingly in the center of the liquid surface. The increase in the outer impeller speed would further increase the depth of the central vortex. If the central vortex is deep enough to expose the small diameter inner impeller to the air, the particles near the vessel wall cannot be drawn down completely, and the air will continuously be sucked into the stirred material, accompanied by the obvious crushing sound of bubbles and the vibration of the stirring shaft. This process is similar to the cavitation phenomenon of a pump, which will cause some damage to the impeller. Therefore, it should not continue to increase the speed of the anchor to make the solid−liquid system reach the critical state under such working conditions. In general, it is beneficial for the critical drawdown of floating particles to select the inner impeller with larger diameter. However, once the diameter of the inner impeller is large to a certain extent, the influence of the outer impeller speed on Nijd and PVjd becomes insignificant, and the advantages of the coaxial mixer compared with the single-shaft mixer also disappears. Therefore, it is better that the inner impeller diameter of the coaxial mixer 11067

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Figure 11. Critical drawdown speed and power at different particle sizes (PBTD, Di = 200 mm, Ds = 125 mm, μl = 0.1 Pa s).

a thicker solid layer accumulates at the liquid surface, which requires a higher rotation speed to destroy the solid layer. The increase of Nijd results in a larger PVjd. However, the increasing solid concentration decreases the average density of the mixing system, and therefore the resistance on the blade declines slightly and the increase of PVjd is reduced. Figure 10 also illustrates that the Nijd decreases less with increasing outer impeller speed when the solid concentration is low, whereas it decreases more with increasing outer impeller speed at higher solid concentration, which means that the advantages of the coaxial mixer in systems with low solid volume fraction are not obvious. Accordingly, it is more suitable for the drawdown and dispersion of floating particles in systems with high solid volume fraction. 3.7. Effect of Particle Size. The particle size is also a common factor influencing the solid−liquid mixing. However, it can be learned from the existing literature that the particle size has a small influence on the critical drawdown suspension state of floating particles.2 Figure 11 shows the Nijd and PVjd at different particle sizes, concentrations and outer impeller speeds, where A, B, C represent the particle size dp of 2.16, 1.15, and 0.69 mm, respectively, and α, β, γ represent the particle concentration C0 of 0.01, 0.05, and 0.09 ·L−1, respectively. As can be seen from Figure 11, under the conditions of three particle concentrations, both the Nijd and PVjd increase with increasing particle size, but the difference between different particle sizes was small. As the particle size becomes larger, the resistance acting on the particles increases, which makes the particles more difficult to be pulled down and dispersed. On the other hand, according to the buoyancy formula F = (ρl − ρs)gV, the net buoyancy on a solid particle increases with increasing volume, which means a greater impeller speed is required to achieve the critical drawdown of particles. 3.8. Correlation for Critical Drawdown Speed Nijd. To quantify the effect of the inner impeller diameter, impeller submergence, liquid viscosity, solid concentration, particle size, and outer impeller speed, we established a correlation for predicting Nijd through multivariable regression fitting, which can reflect the relationship between Nijd and different influencing factors. The correlation is similar to the one proposed by Zwietering,6 and is shown as follows:

a small impeller submergence may lead to the inability of floating particles to disperse to the whole vessel under critical drawdown state, causing the clear liquid area to appear in the lower part of the vessel. In addition, the minor impeller submergence easily exposes the inner impeller to the air, which not only adversely affects the drawdown of floating particles but also reduces the service life of the mixing system. The minimum impeller submergence investigated in this paper is 95 mm, and no clear liquid area appears for that case. 3.5. Effect of System Viscosity. Most of the present studies on the drawdown and dispersion of floating particles are carried out in water, ignoring the influence of system viscosity on the particle motion. However, in the actual industrial processes, many mixing systems are viscous. Figure 9 shows the Nijd and PVjd under different system viscosities. Figure 9 indicates that both the Nijd and PVjd of the coaxial mixer become larger with increasing system viscosity. Under the same condition, the increasing liquid-phase viscosity will lead to a decline in Reynolds number. The main circulation flow and the liquid surface fluctuation are weakened on the one hand and on the other hand the vorticity magnitude at the center of the liquid surface is also weakened, which means that the two driving forces for the drawdown and dispersion of floating particles proposed by Ozcan-Taskin et al.7 are weakened simultaneously. This makes it more difficult for particles to be drawn down into the vessel. The increasing liquid phase viscosity increases the viscous force between molecules, and the density of the stirred material increases as well, both of which increase the resistance of the blade and the corresponding mixing power. In addition, it is not difficult to understand that the effect of system viscosity on the critical drawdown of floating particles becomes less with increasing outer impeller speed, which means that the coaxial mixer is more competitive in high viscous system compared with the single-shaft mixer. 3.6. Effect of Solid Concentration. Solid concentration, also known as solid volume fraction, refers to the volume of solid particles contained in a unit volume of the mixture. Figure 10 shows the Nijd and PVjd at different solid concentrations and outer impeller speeds. Figure 10 indicates that with the increasing solid concentration, the Nijd and PVjd of the coaxial mixing system become larger. The increase of solid concentration means that 11068

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Industrial & Engineering Chemistry Research Nijd = SDi aDsbν cX dd peNo f

impeller submergence of the inner impeller were determined. The main conclusions are as follows: (1) Compared with a single-shaft mixer, the coaxial mixer under corotation mode could produce stronger main circulation flow and a larger central vortex, thereby achieving the drawdown and dispersion of floating particles with lower critical speed and power, which has obvious competitive advantages. (2) Under the same conditions, the critical drawdown speed and power of the coaxial mixer, respectively, with an inner impeller of the radial-flow Rushton impeller, axialflow TXL impeller and mixed-flow PBTD impeller reduced in sequence, which means that the mixed-flow impeller under down-pumping mode is more suitable for the critical drawdown of floating particles in viscous systems and should be selected preferentially as the inner impeller of the coaxial mixer. (3) The diameter and impeller submergence of the inner impeller were the main factors affecting the critical drawdown of floating particles in viscous systems. A larger diameter of the inner impeller and a smaller impeller submergence were beneficial to reduce the critical drawdown speed and power. However, when the diameter of the inner impeller was too large, the advantages of the coaxial mixer over the single-shaft mixer would not be obvious. Thus, the diameter of the inner impeller is not recommended to exceed half of the diameter of the vessel. Similarly, the impeller submergence of the inner impeller should not be too small but should be determined on the premises of taking into account the service life of the mixing system and the dispersion of particles in the whole vessel. (4) With increasing system viscosity and solid concentration, the drawdown of floating particles became more difficult, and both the critical drawdown speed and power of the coaxial mixer would increase. However, the higher the system viscosity and solid concentration, the more are the critical drawdown speed and power decreased with increasing outer impeller speed. This indicates that the coaxial mixer is more competitive in systems with high viscosity and solid concentration, and should be preferred in actual industrial production. (5) The overall trends of the Nijd and PVjd increase with increasing particle size. However, because of the small variation range of particle size, the influence of particle size on the drawdown process of floating particles can be ignored.

(11)

where S is a proportionality coefficient, which represents the influence of system geometry variables; ν is liquid kinematic viscosity; and X is solid mass fraction, which indicates the effect of C0. The influence of major variables can be obtained from the following correlation: Nijd = 0.835Di−2.389Ds 0.553ν 0.127X 0.056d p0.006No−0.071

(12)

R represents the fitting degree of the regression curve to the experimental value. The closer R2 is to 1, the better the fitting effect is. It can be learned from the fitting result that R2 is 0.98, which means a good fitting degree. In addition, the exponent of Di is largest, which suggests that the inner diameter has the greatest influence on the critical drawdown speed, whereas the effect of particle size is negligible. Figure 12 shows the comparison between the experimental value of Nijd and the fitted value of Nijd for the data from Figure 2

Figure 12. Comparison between experimental values and predicted values.

6 to Figure 11. It can be seen that the error of all the points are within 15%. The ranges of variables applicable to the correlation are Di in 134−200 mm, Ds in 95−185 mm, μ in 0.1−0.5 Pa·s, dp in 0.69−2.16 mm, Co in 0.01−0.09 L/L, N0 in 0.167−0.667 s−1.

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4. CONCLUSIONS The drawdown and dispersion of floating particles in viscous systems are common in process industries, but with the increase in system viscosity and solid concentration, it is difficult for traditional single-shaft mixers to meet the demands. In this paper, for the first time, the coaxial mixer was adopted in the drawdown and dispersion of floating particles in viscous systems. The effects of operation mode, inner impeller type, outer impeller speed, inner impeller diameter, impeller submergence, system viscosity, solid concentration and particle size on the critical drawdown of floating particles were investigated experimentally and the mechanisms were analyzed. At the same time, on the basis of the principles of low energy consumption and practical operability, the suitable operation mode, type, diameter, and

AUTHOR INFORMATION

Corresponding Author

*Email: [email protected]. Tel.: +46 462228604. ORCID

Bengt Sunden: 0000-0002-6068-0891 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the National Natural Science Foundation of China (21776246) and the Fundamental Research Funds for the Central Universities (2019QNA4020) 11069

DOI: 10.1021/acs.iecr.9b01867 Ind. Eng. Chem. Res. 2019, 58, 11060−11071

Article

Industrial & Engineering Chemistry Research

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NOMENCLATURE C0 = solid concentration, L L−1 CG = distance of frame paddle from tank bottom, mm Cl = syrup concentration, L L−1 d32 = Sauter mean solid diameter, mm dp = particle diameter, mm Da = diameter of stirring shaft, mm Di = diameter of inner impeller, mm Ds = impeller submergence, mm H = liquid level height, mm HG = height of arc section of frame paddle, mm Mi = net torque of inner impeller, N m Mi,0 = idling torque of inner impeller, N m Mi,1 = loading torque of inner impeller, N m Mo = net torque of outer impeller, N m Mo,0 = idling torque of outer impeller, N·m Mo,1 = loading torque of outer impeller, N m Ni = rotation speed of inner impeller, s−1 Nijd = critical drawdown speed of inner impeller, s−1 No = rotation speed of outer impeller, s−1 Ni = ratio of inner impeller speed to outer impeller speed P = stirring power, W Pi = power of inner impeller, W Po = power of outer impeller, W PV = unit volume power, W m−3 PVjd = critical drawdown power of the system, W t = thickness of frame paddle, mm T = vessel diameter, mm V = material volume, m3 Wa = diameter of frame paddle, mm Wb = breadth of frame paddle, mm WC = width of horizontal section of frame paddle, mm Re = total Reynolds number X = ratio of solid mass to liquid mass XPi = fraction of inner impeller power, % XPo = fraction of outer impeller power, % S = proportionality coefficient R2 = adjusted coefficient of determination

Greek Letters

ρl = syrup density, kg m−3 ρs = solid density, kg m−3 ρ = stirred material density, kg m−3 μl = syrup viscosity, Pa s ν = kinematic viscosity, m2 s−1

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DOI: 10.1021/acs.iecr.9b01867 Ind. Eng. Chem. Res. 2019, 58, 11060−11071

Article

Industrial & Engineering Chemistry Research (29) Qiao, S. C.; Wang, R. J.; Yan, Y. F.; Yang, X. X. Computational fluid dynamics analysis to effects of geometrical design and physical property on complete suspension of floating solids in stirred tanks. Asia-Pac. J. Chem. Eng. 2014, 9, 866.

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DOI: 10.1021/acs.iecr.9b01867 Ind. Eng. Chem. Res. 2019, 58, 11060−11071