Pilot-Scale Examination of Mixing Liquid into Pulp Fiber Suspensions

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Pilot-Scale Examination of Mixing Liquid into Pulp Fiber Suspensions in the Presence of an In-Line Mechanical Mixer Wisarn Yenjaichon,* John R. Grace, C. Jim Lim, and Chad P. J. Bennington† Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia, Canada V6T1Z3 ABSTRACT: The quality of liquid mixing into the main stream for an in-line mechanical mixer was investigated for water and pulp suspensions over a range of mass concentrations (0−3.0%), main-stream velocities (0.5−3.0 m/s), jet velocities (3.8−12.6 m/s), and rotational speeds (0−800 rpm) based on electrical resistance tomography and a modified mixing index, derived from the coefficient of variation of conductivity values. The mixing quality was worse when the jet penetrated to the far wall of the pipe for all fiber mass concentrations investigated, whereas this only applied at higher mass concentrations without the impeller. For water flow, the residence time had a significant effect on mixing at higher impeller speeds. With the impeller present, the mixing quality in pulp suspensions improved substantially and was similar to that for water when the flow approached the turbulent regime, with a considerably lower main-stream velocity required for mixing compared to a tee mixer alone. At higher mass concentrations, the energy supplied was insufficient to provide the same level of turbulence as that in water, even at the highest main-stream velocity and impeller speed examined. Improved mixing with increasing impeller speed primarily occurred in the high-shear zone around the impeller, with turbulence decaying rapidly downstream, likely aided by reflocculation. and a radioactive tracer8 as well as alternative techniques such as temperature profiling around process piping.3,9,10 Most techniques are not continuous, because pulp samples need to be taken from the process, and time-consuming because of the large number of samples at different locations required to give a clear picture of mixing. Temperature profiling is noninvasive, continuous, and less tedious, but it quantifies mixing only at the pipe periphery and not over the entire cross section, and a suitable temperature difference between the chemical and pulp suspension must exist. Electrical resistance tomography (ERT) is a nonintrusive technique used to determine the distribution of electrical conductivity in process vessels from measurements at the vessel periphery. The ERT system injects an electrical current from a pair of neighboring electrodes and measures the voltage differences between the remaining pairs of electrodes. This process is repeated by injecting a current for the other pairs of neighboring electrodes, and the cross-sectional distribution of the electrical conductivity is determined.11 ERT has been utilized extensively in various processes including pulp and paper systems. Recently, this technique has been used to evaluate the mixing performance of in-line mixers in pulping processes. Yenajaichon et al.12 evaluated the mixing efficiency of an industrial static mixer in a chlorine dioxide bleaching stage. ERT was successful in monitoring the temporal variation of the mixing index, based on the coefficient of variation (CoV), as a function of the operating conditions, including the chemical flow rate, suspension flow rate, and fiber mass concentration. Kourunen et al.13 applied ERT to assess the performance of a pilot-scale medium-consistency mixer and

1. INTRODUCTION Good mixing is essential in pulp bleaching. Poor mixing in a bleach plant causes poor chemical contacting, leading to poor product qualities such as lower pulp brightness and cleanliness. Additional bleaching chemicals are often applied to improve these qualities. However, excessive use of chemicals increases production costs and has an undesirable effect on the product strength. Mixing in bleaching processes is usually accomplished by in-line mixers ahead of bleaching towers, reactors with sufficient residence time to complete the bleaching. Chemicals are injected ahead of, or inside, these static and high-shear mixers. The mixers predistribute the chemicals to achieve optimum product quality and chemical usage. In modern bleaching processes, in-line mixers have replaced continuously stirred vessels because of their increased energy dissipation rate per unit volume. Details of mixers in bleaching operations were summarized by Bennington.1,2 Static mixers are normally used in low-consistency applications (fiber mass concentration, Cm, 3 contacts per fiber and flocculation when the shear stress was less than the suspension yield stress. When the softwood suspension flow in an empty pipe was considered at Up = 3.0 m/s, the shear stress exceeded the suspension yield stress, providing relative motion among fibers and turbulent flow. At Up = 1.0 m/s, however, the flow was in the mixed flow regime, with a rigid plug in the core where the shear stress was less than the suspension yield stress.16 The rotating impeller disrupted the plug and provided turbulence in the high-shear (P2) zone, with reflocculation likely occurring downstream because energy dissipation was not sustained. Figure 7 shows the influence of the main-stream velocity on the degree of mixing of a softwood pulp suspension at Cm = 2.0% for virtually identical impeller speeds and jet-to-pipe velocity ratios and identical diameter ratio. At this concentration, the flow was essentially plug before passing through the impeller for all main-stream velocities investigated. The rotating impeller disrupted the plug, and the mixing quality improved substantially with increasing main-stream velocity compared to the tee mixer alone, where the mixing quality was poor and improved only slightly as the main-stream velocity increased.16 Enhanced mixing with increasing main-stream velocity at this concentration occurred mainly in the high-shear (P2) zone, whereas mixing improved only slightly downstream for Up ≥ 2.0 m/s compared to that for Cm = 0.5%, likely because of the reestablishment of a plug downstream of the impeller. At Up = 3.0 m/s, the quality of mixing in the pulp suspension was considerably better with the impeller than without it at the same main-stream velocity. The mixing was slightly worse than

Figure 4. Modified mixing index as a function of the dimensionless distance downstream of injection for various jet-to-pipe velocity ratios, R, with water at Dr = 0.05 and N = 400 rpm.

and hence the main-stream velocity, had less effect on mixing, and the mixing quality depended strongly on the jet-to-pipe velocity ratio. The mixing quality improved significantly with increasing velocity ratio as the mixing mode changed from wall source (R < 4) to jet mixing (4 ≤ R ≤ 10) and jet impaction (R > 10). The results for the in-line mechanical mixer were similar to those for a tee mixer described previously.16 However, a significant difference was observed at R = 12.2 when the jet stream reached the far wall of the pipe ahead of the impeller. The mixing quality was worse than that for the jet penetrating to the center of the pipe, behavior not observed for the tee mixer alone. The mixing was more efficient when the jet penetrated to the core of the pipe, likely because of higher energy dissipation when the jet impinged on the rotating impeller. At very high velocity ratios (R > 16), energy dissipation from jet impingement on the pipe wall and rotating impeller was profound, resulting in efficient downstream mixing. Tomographic images showing jet penetration and downstream mixing appear in Figure 5. Because of misalignment between the electrode position in the ERT reconstruction process and the actual electrode position in each sensor plane, the top of the pipe in the tomographic image is rotated counterclockwise by 11° from the vertical axis, and a corresponding corrective rotation is applied to all tomographic images. From these images, the injected tracer or brine solution is represented by the high-conductivity region in red and yellow, whereas the main stream is represented by the lowconductivity blue region. The tracer was injected and reached the impeller between planes 1 and 2. The disappearance of the red and yellow colors from plane 2 to plane 8 showed improved mixing downstream. The jet penetrated to the core of the pipe at R = 6.15, reached the far wall of the pipe ahead of the 489

dx.doi.org/10.1021/ie300843z | Ind. Eng. Chem. Res. 2013, 52, 485−498

Industrial & Engineering Chemistry Research

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Figure 5. Tomographic images for water with Dr = 0.05 and N = 400 rpm at R = (a) 6.15, (b) 12.2, and (c) 24.6. The locations of planes P1−P8 are shown in Figure 1.

difference was likely due to faster energy dissipation when the jet penetrated to the core of the pipe and impinged on the rotating impeller at R = 6.3, as discussed above for water flow. Figure 9 shows the mixing quality for a softwood suspension with Cm = 0.5%, Up = 0.5 m/s, and higher velocity ratios. Mixing improved significantly with increasing jet velocity, likely because energy dissipation from jet impaction and the rotating impeller disintegrated the plug in the dilute pulp suspension. The energy supplied was not, however, enough to provide turbulence, even in the high-shear (P2) zone, with reflocculation occurring downstream, as shown by considerably worse mixing than that for water beyond P3.

that for water at P2 and P3 but significantly worse downstream, suggesting that reflocculation likely occurred rapidly downstream of the impeller, with robust fiber networks impeding mixing. 3.3. Effect of the Jet Velocity on the Mixing Quality in Pulp Suspensions. Figure 8 portrays the effect of the jet-topipe velocity ratio on the mixing quality for a softwood suspension at Cm = 0.5%, Up = 1.0 m/s, and N = 400 rpm. The mixing was significantly better when the mixing mode changed from the wall source (R = 3.4) to jet mixing (R = 6.3). It was worse, however, at a higher velocity ratio when the jet reached the far wall of the pipe, whereas this behavior was not observed at the same mass concentration for a tee mixer alone.16 The 490



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Figure 8. Modified mixing index as a function of the dimensionless distance downstream of injection for a softwood pulp suspension with Cm = 0.5%, Up = 1.0 m/s, Dr = 0.05, and various jet-to-pipe velocity ratios.

Figure 6. Modified mixing index as a function of the dimensionless distance downstream of injection for a softwood pulp suspension with Cm = 0.5% and water (w) at Dr = 0.05 and N = 400 rpm with various main-stream velocities and almost identical jet-to-pipe velocity ratios.

At higher concentrations (Cm ≥ 1.0%), the jet velocity had less influence on mixing. Figure 10 plots the modified mixing index at various velocity ratios for a 2.0% softwood suspension at Up = 0.5 m/s and virtually identical impeller speeds. The degree of mixing clearly improved with the addition of the mechanical mixer. However, mixing improved only slightly with increasing jet velocity because the fiber networks were still robust and energy dissipation from jet impaction was insufficient to disrupt the fiber networks. The mixing quality was worse when the jet reached the far wall of the pipe ahead of the impeller at R = 12.2, likely because of the robust fiber networks causing the jet to adhere to the far wall downstream, behavior similar to that for a tee alone.16 Tomographic images comparing the tracer distribution for the same operating conditions are presented in Figure 11. For a jet reaching the far wall of the pipe at R = 12.2, the high-conductivity regions were concentrated at the upper part of the images and persisted as a clump downstream, as illustrated in Figure 11a. At R = 16.5, the jet impinged on the far wall and recirculated to the core of the pipe. Energy dissipation from the jet impingement and rotating impeller likely caused less nonuniformity, as shown by more spreading of the high-conductivity regions in the cross sections downstream of the P2 plane in Figure 11b. Although a higher velocity ratio of 24.1 provided slightly better mixing than R = 8.1 for a jet penetrating to the core of the pipe, this condition

Figure 9. Modified mixing index as a function of the dimensionless distance downstream for a softwood pulp suspension with Cm = 0.5% and water (w) at Up = 0.5 m/s, Dr = 0.05, and various jet-to-pipe velocity ratios.

may be undesirable from a practical point of view because impingement on the opposite pipe wall creates significant stress there. The design of an in-line mechanical mixer should therefore be based on the velocity ratio for the jet penetrating to the axis of the pipe, as summarized by Yenjaichon et al.17

Figure 7. Modified mixing index as a function of the dimensionless distance downstream with and without the impeller for softwood pulp suspension for Cm = 2.0% and water (w) at Dr = 0.05, various main-stream velocities, and almost identical jet-to-pipe velocity ratios and rotational speeds. 491



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the impeller. At a lower main-stream velocity (Up = 0.5 m/s), a long residence time in the high-shear zone provided profoundly improved mixing with increasing impeller rotational speed, as shown in Figure 12a. Decay of turbulence likely occurred, accompanied by reflocculation downstream, as is clearly shown by worse mixing downstream of P4 for a pulp suspension than for water at N = 800 rpm. The crowding number of 27.6 for the 1.0% hardwood pulp suspension exceeded 16, the gel crowding number, suggesting that fibers interacted and began to flocculate when the shear stress was lower than the suspension yield stress downstream of the impeller. For this velocity, the quality of mixing with the perpendicularly oriented static mixer was lower than that for all nonzero rotational speeds investigated. The suspension flowed through the gaps between the impeller and inner pipe wall at relatively low velocity, and the turbulence created by the static mixer was significantly less than that provided by the mechanical mixer. At a higher mainstream velocity (Up = 2.0 m/s), the residence time was low enough that the impeller speed had little influence on the mixing quality. An increase in the rotational speed, however, slightly enhanced downstream mixing, as shown in Figure 12b. The mixing quality was similar for the first three planes (P2− P4) and then became slightly better with increasing impeller speed. A comparison of suspension mixing at N = 400 and 800 rpm with water (dashed lines) at the same impeller speeds

Figure 10. Modified mixing index as a function of the dimensionless distance downstream for a softwood pulp suspension at Cm = 2.0%, Up = 0.5 m/s, Dr = 0.05, almost constant impeller rotation speeds, and various jet-to-pipe velocity ratios

3.4. Effect of the Impeller Rotational Speed on the Mixing Quality in Pulp Suspensions. Figure 12 shows the effect of the impeller speed on the mixing quality for a hardwood suspension with Cm = 1.0%. The mixing was poor for a tee mixer alone but improved substantially in the presence of

Figure 11. Tomographic images for a softwood pulp suspension at Up = 0.5 m/s, Cm = 2.0%, and Dr = 0.05 with (a) R = 12.2 and N = 403 rpm and (b) R = 16.5 and N = 410 rpm. The locations of planes P1−P8 are shown in Figure 1. 492



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Figure 13. Modified mixing index as a function of the dimensionless distance downstream of injection for a softwood pulp suspension with Cm = 3.0% and water (w) at Dr = 0.05 and almost identical velocity ratios with various impeller speeds at Up = (a) 1.0 and (b) 2.0 m/s.

Figure 12. Modified mixing index as a function of the dimensionless distance downstream of injection for a hardwood pulp suspension with Cm = 1.0% and water (w) at Dr = 0.05 and almost constant velocity ratios with various impeller speeds at Up = (a) 0.5 and (b) 2.0 m/s.

water flow at the identical main-stream velocity, however, the perpendicular configuration only matched the mixing provided by the mechanical mixer at N = 400 rpm, as shown in Figure 3a. At a higher main-stream velocity (Up = 2.0 m/s), the impeller improved mixing significantly, as shown in Figure 13b, with slightly enhanced downstream mixing compared to a lower main-stream velocity. The impeller speed, however, had little effect on mixing, likely because of shorter residence time in the high-shear zone. 3.5. Effect of the Fiber Mass Concentration on the Mixing Quality. Figure 14 plots the modified mixing index for various fiber mass concentrations of a softwood pulp suspension at Up = 1.0 m/s, N = 400 rpm, nearly identical jet-to-pipe velocity ratios, and identical diameter ratio. The mixing quality improved significantly as the consistency decreased. The fiber mass concentration strongly influenced the mixing when turbulent flow could not be achieved. Figure 15 shows the influence of consistency on the mixing quality for a shorter-fiber hardwood suspension at a higher impeller speed, 800 rpm. The mixing quality improved profoundly as Cm decreased from 2.0 to 1.0%, at which the energy supplied was sufficient to disrupt the plug and provide turbulence. The mass concentration did not, however, have a strong effect on the mixing quality for Cm ≤ 1.0% because the suspension flow was turbulent, with mixing quality similar to that for water. For Cm ≤ 1.0%, the mixing quality was similar for the first three planes (P2−P4 in Figure 1) downstream of the injection. Mixing for the hardwood pulp suspension with Cm = 1.0% was worse downstream than that for Cm = 0 and 0.5%, likely because of the reduction of turbulence accompanied by

showed that turbulence was achieved in the high-shear zone for both impeller speeds, but reflocculation likely occurred faster downstream at N = 400 rpm (downstream of P5) than at N = 800 rpm (downstream of P7), because of reduced downstream turbulence. Figure 13 shows the influence of the rotational speed on the mixing quality for a long-fiber softwood suspension with a higher mass concentration of 3.0%. Mixing with the parallel static impeller was poor, not significantly better than that for the tee mixer alone, as shown in Figure 13a. At Up = 1.0 m/s, the mixing quality improved with increasing impeller speed, predominantly occurring in the high-shear (P2) zone, with lack of downstream mixing compared to a lower-concentration, shorter-fiber hardwood suspension and water, because strong fiber networks reestablished immediately downstream of the impeller. The energy provided by the impeller and flow (main stream and jet) were unable to disrupt the networks in the high-shear zone, even at an impeller speed as high as 800 rpm, as shown by considerably worse mixing at P2 than for water at a lower impeller speed (N = 400 rpm). Further increasing the impeller speed likely improves mixing and provides a level of turbulence similar to that for water. However, this probably occurs only in the high-shear zone without improved downstream mixing. At this main-stream velocity, the highconcentration suspension flow, carrying high momentum, provided high energy dissipation when it impinged on the perpendicularly oriented static impeller, with the mixing quality similar to that of the mechanical mixer at N = 800 rpm. For 493



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0.5%, the flow was turbulent and the tracer distributed uniformly downstream of P2, as illustrated by uniform green in the cross sections, similar to that upstream of tracer injection (P1) in Figure 16a, indicating efficient mixing downstream of the impeller. Figure 16b shows the low-conductivity region in blue downstream of P2, likely a plug caused by fiber reflocculation at a higher fiber mass concentration, 3.0%. This region occurred immediately downstream of P2, indicating rapid reflocculation as the energy dissipation was not sustained. Figure 17 illustrates the influence of the fiber mass concentration on the mixing quality for a softwood suspension at a higher main-stream velocity of 3.0 m/s and virtually identical impeller speeds. For Cm ≤ 1.0%, the energy supply rate was sufficient to disintegrate the fiber networks and provide turbulence in the high-shear zone. Reflocculation and decaying turbulence then probably occurred rapidly for Cm = 1.0%, as shown by the mixing quality being worse downstream of the P3 sensor plane compared to water and a 0.5% pulp suspension in the turbulent flow regime. At higher mass concentrations (Cm ≥ 2.0%), on the other hand, the energy supplied was insufficient to provide the same level of turbulence as that for water, even in the high-shear zone immediately downstream of the impeller. Reflocculation also likely occurred more rapidly than that for the 1.0% pulp suspension, with significantly lower mixing quality downstream. 3.6. Hardwood versus Softwood Fibers. Figure 18 shows that the mixing quality for the short-fiber hardwood pulp suspension was considerably better than for the softwood suspension at Cm = 1.0%, Up = 0.5 m/s, and N = 400 rpm. This was likely due to less robust fiber networks. However, the energy from the impeller and the flow was not able to disintegrate the fiber networks and provide turbulence in the suspension, as shown from the mixing quality being significantly worse than that for water in turbulent flow. The influence of the fiber type on the degree of mixing for a lower mass concentration of 0.5% and a higher main-stream velocity of 2.0 m/s is presented in Figure 19. In this case, the fiber properties did not have such a strong influence on the mixing quality because the turbulence was generated in both softwood and hardwood suspensions, with the mixing quality approaching that for water. Table 1 summarizes the influences of jet penetration, flow regime, and impeller speed on the mixing quality with an in-line mechanical mixer. For water, a jet penetrating to the center of the pipe clearly provided better mixing than the jet attaching to the pipe wall, and mixing was even better when the jet impinged on the far wall at a higher jet-to-pipe velocity ratio. A similar effect of jet penetration on mixing was observed for pulp suspensions, with considerably worse mixing when the jet reached the far wall of the pipe for the plug flow regime, likely because of the reestablishment of robust fiber networks downstream of the impeller causing the jet to adhere to the wall. Jet impingement on the far wall, however, did not provide significantly better mixing than that for jet penetration to the core of the pipe, likely because the energy supplied was insufficient to disrupt the fiber networks for both cases. The flow regime had a strong influence on mixing in pulp suspensions. For similar jet penetration, mixing worsened substantially as the flow regime changed from turbulent to mixed and plug flow. For the mixed flow regime, increasing the impeller speed clearly enhanced mixing in both the high-shear (P2) zone and downstream, whereas mixing improved predominantly in the high-shear zone for the plug flow.

Figure 14. Modified mixing index as a function of the dimensionless distance downstream for softwood pulp suspensions at Up = 1.0 m/s, R = 6, N = 400 rpm, and Dr = 0.05 for various fiber mass concentrations.

Figure 15. Modified mixing index as a function of the dimensionless distance downstream for hardwood pulp suspensions at Up = 1.0 m/s, R = 6, N = 800 rpm, and Dr = 0.05 for various fiber mass concentrations.

reflocculation, occurring because the energy required to maintain turbulence was not sustained at the higher mass concentration. The crowding number of 13.8 for Cm = 0.5% was less than 16, indicating that fibers were free to move relative to one another, so that the suspension was essentially dilute. On the other hand, the crowding number for the 1.0% hardwood pulp suspension exceeded the gel crowding number of 16. Accordingly, reflocculation likely occurred only at Cm = 1.0%. The mixing quality with the mechanical mixer for a hardwood suspension flow at Cm = 0.5% was similar to that for water without fibers, whereas mixing with a tee mixer and turbulent flow was better for a dilute hardwood suspension than for water.17 For tee mixing alone, mixing is achieved by turbulent shear. The shorter- and smaller-diameter fibers could alter the turbulence structure in the bulk, carrying turbulent eddies with them and colliding with each other, thereby promoting turbulent dispersion. For the mechanical mixer, however, the energy dissipated near the rotating impeller probably dominated, modifying the turbulence structure in the bulk and leading to similar mixing quality for water and a dilute hardwood suspension. Tomograhic images showing turbulent and plug flow for hardwood suspensions are presented in Figure 16. For Cm = 494



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Figure 16. Tomographic images for hardwood pulp suspensions at Up = 1.0 m/s, R = 6, N = 800 rpm, and Dr = 0.05 with Cm = (a) 0.5% and (b) 3.0%. The locations of planes P1−P8 are shown in Figure 1.

Figure 17. Modified mixing index as a function of the dimensionless distance downstream for softwood pulp suspensions at Up = 3.0 m/s, R = 4, Dr = 0.05, and virtually identical rotational speeds for various fiber mass concentrations.

Figure 18. Modified mixing index as a function of the dimensionless distance downstream for softwood and hardwood pulp suspensions at Cm = 1.0% Up = 0.5 m/s, R = 12, and N = 400 rpm.

residence time in the high-shear zone became significant, with mixing improving considerably as the main-stream velocity decreased. Mixing improved substantially with increasing impeller speed at a low main-stream velocity (1.0 m/s), likely because of increased residence time in the high-shear zone, whereas the rotation speed had less effect at a higher mainstream velocity (3.0 m/s). At a low impeller speed (400 rpm), mixing improved substantially with increasing velocity ratio as

4. CONCLUSIONS For water in turbulent flow, the quality of mixing for a lowspeed impeller (400 rpm) was almost independent of the mainstream velocity for identical jet-to-pipe velocity and diameter ratios because the residence time in the high-shear zone had little influence. At a higher impeller speed (800 rpm), the 495



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m/s was required without the impeller. At a higher mass concentration (Cm = 2.0%), the fiber plug was disrupted and mixing improved profoundly with increasing main-stream velocity, but downstream mixing was poor, likely because of rapid reflocculation. For a dilute softwood pulp suspension (Cm = 0.5%), mixing improved with increasing jet velocity, whereas the jet velocity had little influence at Cm = 2.0%. The mixing quality worsened when the jet penetrated to the far wall of the pipe for all mass concentrations investigated. For a dilute hardwood pulp suspension with Cm = 1.0%, mixing was improved by the addition of an impeller. A stationary impeller provided better mixing when perpendicular than when parallel to the flow. As the rotational speed increased, mixing improved significantly, in both the high-shear zone and downstream, for a low main-stream velocity (Up = 1.0 m/s), whereas it was only slightly better at Up = 2.0 m/s, likely because of less residence time in the high-shear zone. At a higher mass concentration of 3.0% for a long-fiber softwood pulp suspension, enhancement of mixing with increasing rotation speed occurred mainly in the high-shear zone, with almost negligible improvement downstream. The fiber mass concentration and properties profoundly affected mixing when there was insufficient supply of energy to provide turbulence. Mixing improved substantially with decreasing consistency and was better for shorter hardwood pulp fibers than for softwood fibers. The mass concentration and fiber properties did not, however, strongly influence the mixing quality when the flow was turbulent because the

Figure 19. Modified mixing index as a function of the dimensionless distance downstream for softwood and hardwood pulp suspensions with Cm = 0.5% Up = 2.0 m/s, R = 2, and N = 400 rpm.

the mode changed from wall source to jet mixing and jet impaction. However, the mixing was worse when the jet stream reached the far wall of the pipe upstream of the impeller at a jet-to-pipe velocity ratio of 12.2. For pulp fiber suspensions, mixing depended strongly on the flow regime. Mixing downstream improved profoundly when the plug was disrupted, approaching that for water when the flow became turbulent. With the addition of an impeller, the turbulent flow regime was obtained for a 0.5% softwood pulp suspension at a main-stream velocity of 2.0 m/s, whereas 4.0

Table 1. Summary of the Influences of Jet Penetration, Flow Regime, and Impeller Speed on Mixing modified mixing index, M′ parameter investigated jet penetration in water

jet penetration in a pulp suspension

flow regime

impeller speed (mixed flow)

impeller speed (plug flow)

a

suspension concentration, Cm (%) 0 (water)

2.0 (SW)

0.5 (SW) 0.5 (SW) 0.5 (SW) 2.0 (SW) 1.0 (HW)

3.0 (SW)

impeller speed, N (rpm) 400

main-stream velocity, Up (m/s)

jet-to-pipe velocity ratio, R

flow regime

jet penetration

2.0, 3.0

2.06

turbulent

1.0, 2.0 0.5, 1.0

6.15 12.2

0.5

24.6 8.14

x/D = 2.41a

x/D = 12.2

x/D = 22.1b

4.41

0.87

0.51

3.02 3.32

0.4 0.62

0.21 0.25

1.43

0.12

0.06

plug

attaching to the near wall center reaching the far wall impinging on the far wall almost center

6.96

6.87

6.61

reaching the far wall impinging on the far wall almost center almost center

8.88

9.17

9.75

7.59

6.67

6.02

2.5 2.34

1.49 0.92

1.17 0.58

almost center almost center reaching the far wall reaching the far wall reaching the far wall almost center

2.84 5.58 5.79

0.87 4.45 5.56

0.44 4.36 5.1

4.04

1.47

1.26

2.41

0.26

0.16

8.89

9.24

9.55

almost center almost center

7.78 4.95

7.26 4.89

7.42 4.69

408

0.5

403

0.5

12.2

418

0.5

24.1

400

1.0 2.0

3.99 4.13

mixed turbulent

no impeller

3.0 1.0 1.0

4.13 6.14 12.5

turbulent plug mixed

406

1.0

12.5

802

1.0

12.0

no impeller

1.0

6.35

406 802

1.0 1.0

6.14 6.12

plug

High-shear zone (P2). bFurthest distance downstream (P8). 496



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turbulence disrupted the plug, with the mixing quality approaching that for water. Unlike tee mixing, the quality of mixing with an in-line mechanical mixer for a dilute hardwood suspension flow was not significantly better than that for water.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. † Deceased.

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ACKNOWLEDGMENTS The authors thank NSERC, FPInnovations (Paprican Division), and Howe Sound Pulp and Paper Ltd. for support. We are also grateful to Drs. James Olson and Mark Martinez for providing access to the flow-loop facility in the Pulp and Paper Centre, University of British Columbia.

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NOMENCLATURE Cj salt concentration in the side stream for jet flow [kg/m3] Cm suspension mass concentration or consistency [%] Cp salt concentration in the main stream or pipe flow [kg/ m3] d fiber diameter [m] D pipe diameter [m] Dj injection tube diameter [m] Dr jet-to-pipe diameter ratio L fiber length [m] MFS mixing index for fully segregated flow defined by eq 4 [%] Mm measured mixing index defined by eq 3 [%] Ms system mixing index measured in the absence of tracer [%] M′ modified mixing index defined by eq 2 [%] N rotational speed [rpm] Nc crowding number defined by eq 1 Qj volumetric flow rate of the side stream [m3/s] Qp volumetric flow rate of the main stream [m3/s] n number of image pixels R jet-to-pipe mean velocity ratio, i.e., Uj/Up Rej jet Reynolds number Rep pipe Reynolds number Up main-stream or pipe velocity [m/s] Uj side-stream or jet velocity [m/s] x distance downstream of injection [m] yi local mixture electrical conductivity [mS/cm] y̅ average electrical conductivity [mS/cm] Greek Symbols

σ standard deviation of the conductivity in a tomographic image [mS/cm] ω fiber coarseness [kg/m]

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REFERENCES

(1) Bennington, C. P. J. Mixing and Mixers. In Pulp Bleaching: Principle and Practice; Dence, C. W., Reeve, D. W., Eds.; TAPPI Press: Atlanta, GA, 1996; p 539. (2) Bennington, C. P. J. Mixing in the pulp and paper industry. In Handbook of Industrial Mixing: Science and Practice; Paul, E. L., AtiemoObeng, V. A., Kresta, S. M., Eds.; John Wiley and Sons: Hoboken, New Jersey, 2004; p 1187. (3) Torregrossa, L. O. Effect of mixing efficiency on chlorine dioxide bleaching. Proceedings of TAPPI Pulping Conference, Houston, TX, 1983; TAPPI Press: Atlanta, GA, 1983; p 635. 497



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Pilot-Scale Examination of Mixing Liquid into Pulp Fiber Suspensions

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