Time-Periodic Mixing of Shear-thinning Fluids

Time-Periodic Mixing of Shear-thinning Fluids

0263–8762/04/$30.00+0.00 # 2004 Institution of Chemical Engineers Trans IChemE, Part A, September 2004 Chemical Engineering Research and Design, 82(A9...

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0263–8762/04/$30.00+0.00 # 2004 Institution of Chemical Engineers Trans IChemE, Part A, September 2004 Chemical Engineering Research and Design, 82(A9): 1199–1203

TIME-PERIODIC MIXING OF SHEAR-THINNING FLUIDS G. ASCANIO1, S. FOUCAULT2 and P. A. TANGUY2 1

Center of Applied Sciences and Technological Development, National University of Mexico, Mexico City, Mexico 2 Unit Research on Industrial Flow Processes, Ecole Polytechnique of Montreal, Montreal, Canada

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ixing times and energy consumption of inelastic shear-thinning fluids in stirred vessels were experimentally investigated using time-periodic conditions. The impeller rotated initially at a speed sufficient to allow the well-mixed region around the impeller to be formed and then the impeller was stopped and turned on periodically. Mixing times were evaluated by the colorimetry technique based on the fast acidbase reaction, which also allowed the presence of either dead or segregated regions in the vessel to be revealed. The effects of impeller type, its position and speed as well as the fluid power-law index were all considered in this work. Both the mixing times and the energy consumption can be drastically reduced when weakly shear-thinning fluids are mixed at low speed under intermittent conditions. Results obtained with the best operating conditions are compared to steady stirring, showing the potentialities and drawbacks of the proposed approach. Keywords: shear-thinning fluids; chaotic mixing; well-mixed regions; segregated regions.

INTRODUCTION Mixing of viscous and non-Newtonian fluids in laminar and transition regimes is usually difficult to achieve. Wellmixed regions are formed around the impeller that, in some cases, may remain visible even after several hours of mixing (Elson et al., 1986). No-flow regions called dead zones appear far from the impeller due to the dampening of momentum transfer by viscous effects. As a consequence very long or infinite mixing times are obtained. To eliminate these mixing problems and achieve complete homogenization in a minimal time, wider impellers or higher rotational speeds can be used, both of which lead to an increase in the power draw. Moreover if the impeller speed is increased the fluid is submitted to higher shear rate, which can be a drawback for shearsensitive media. It has been shown that well-mixed regions tend to grow as the impeller is stopped and turned on cyclically (Lamberto et al., 1996). Alvarez et al., (2002) observed that well-mixed regions can be readily disrupted when the impeller is slightly displaced from the center and Ascanio et al. (2002) showed that mixing times can be significantly reduced if the flow is continuously perturbed by rotating the impeller in alternating directions. In such cases, the use of eccentric impellers is equivalent to using baffled tanks. These approaches were based on pioneering studies on chaotic laminar mixing, in which it was demonstrated that homogenization could be quickly achieved by using  Correspondence to: Professor P.A. Tanguy, PO Box 6079, Stn. Centreville, Montreal, QC Canada H3C3A7. E-mail: [email protected]

eccentric cylinders rotating in alternating directions for short periods (Ottino et al., 1988; Swanson and Ottino, 1990; Muzzio et al., 1991; Muzzio et al., 1992). All these works dealt with Newtonian fluids. One of the main reasons for using eccentric impellers is that they provide the best mixing action where a vortex is not required or not desirable. Only a few reports on chaotic mixing flows with non-Newtonian shear-thinning fluids can be found in the literature. Niederkorn and Ottino (1994) used computer simulations to determine the effect of shear-thinning viscosity for two dimensional and time-periodic conditions. They found that the quality of mixing degrades as the flow behavior index decreases. Using concentric cylinders rotating in both directions, Yurun and Zhumin (2001) demonstrated a large impact of pseudoplasticity on flow stretching confirming the results obtained by Niedekorn and Ottino (1994). The above contributions suggest that the use of dynamic perturbations may improve significantly the mixing of nonNewtonian fluids. The purpose of the present work is to investigate experimentally the impact of dynamic perturbations on the mixing of shear-thinning fluids, based on a stop and go protocol (time-periodic mixing). MATERIALS AND METHODS The experimental setup used for the present work is shown in Figure 1. It consists of an unbaffled transparent vessel of 165 mm diameter and 210 mm height, which can be horizontally displaced. The agitation system is composed of an impeller fitted to a rigid shaft and driven by an AC motor coupled to a solid-state frequency changer with a

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ASCANIO et al.

Figure 1. Experimental setup.

closed-loop control receiving a feedback signal from a speed encoder. The motor is installed on a plate that can be vertically displaced, so that the impeller height can be easily adjusted. A torquemeter having a range of 0– 2 N m is coupled to the agitation shaft to determine the power draw. In the study, two different impellers were used; a Rushton turbine (RT) as radial flow impeller and a pitched blade turbine (PBT) as axial/radial flow impeller. Aqueous solutions of carboxymethyl cellulose (CMC, Noviant, Inc.) and xanthan gum (Keltrol RD, CPKelco, Inc.) were chosen as mild and pronounced shear-thinning fluids, respectively. The rheological properties of both solutions were determined with the Advanced Rheometer model AR-2000 (TA Instruments) in a Couette configuration of 30 mm and 28 mm for the inside and outside diameter, respectively. The flow behavior index of the power-law (n) was 0.8 for the CMC solution and 0.2 for the xanthan gum solution. The consistency index (k) was 0.11 and 1.52 Pa sn for the CMC and the xanthan gum solutions, respectively. The shear rheological properties were measured in a shear rate range from 102 to 103 s21. From the dynamic tests, the storage modulus (G0 ) was found to be very small in the operating speed range and the ratio G0 /G00 was found to be much smaller than unity, so that the elastic effects were negligible (G0 is the elastic modulus and G00 the viscous or storage modulus). The concentration of both solutions was chosen in such a way that they did not exhibit elasticity or yield stress. The solutions were prepared in a stirred vessel without vortex avoiding the formation of air bubbles. Mixing times were evaluated by means of a colordiscoloration technique based on a fast acid-base indicator reaction (Ascanio et al., 2002). Images of the flow in the tank at different times were made with a digital camera

in order to assess the presence of flow segregations or dead regions. For the steady stirring mixing experiments, the impeller rotated at 200 rpm and 600 rpm and it was placed in the centerline of the vessel and at one-third of liquid height. For the time-periodic mixing, the operating conditions were as follows: . . . .

Impeller position: x  1/4 T, 1/3 H y 1/2 H Impeller rotational speed (N1): 200 rpm or 600 rpm Impeller rotation time (t1): 10 s or 30 s. Sequence: The system was initially stirred at 200 rpm until the well-mixed region around the impeller was formed (2 min approximately) and then the periodic oscillation of the impeller was started. A period consisted of stopping the impeller and restarting at 200 rpm or 600 rpm for 10 s or 30 s.

The experiments under steady stirring and time-periodic mixing were performed at a Reynolds number ranging from 165 to 1200. RESULTS AND DISCUSSION Tables 1 and 2 show the mixing time and energy draw data under steady stirring and intermittent mixing, respectively. In both cases, the energy draw was determined by the following expression: E ¼ 2pN ttm

(1)

where N is the rotational speed in s21, t is the torque in N m and tm is the mixing time in s. From Table 1 it is observed that in some cases mixing is particularly inefficient under steady stirring conditions

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A9): 1199–1203

TIME-PERIODIC MIXING OF SHEAR-THINNING FLUIDS Table 1. Mixing times and power draw under steady stirring conditions. Run

Impeller

N (rpm)

A1 A2 A3 A4 A5 A6 A7 A8

RT RT RT RT PBT PBT PBT PBT

600 600 200 200 600 600 200 200



n

Mixing time (s)

Energy draw (J)

0.8 0.2 0.8 0.2 0.8 0.2 0.8 0.2

11 27 1 1 20 22 1 1

79.48 110.27 — — 51.52 44.23 — —

no homogenization was achieved after several mixing hours.

particularly at low agitation speed, corresponding to the transition regime (runs A3, A4, A7 and A8). In these cases, the well-mixed region formed in the beginning remained visible even after several hours of mixing, no homogenization was achieved and the mixing time was considered infinite. As Table 2 shows, this problem can be overcome by using intermittent conditions. In runs B1 and B2 a moderate shear-thinning fluid was mixed at low speed using a radial flow impeller in the stop/go protocol. A mixing time of 40 s and an energy draw of 20.10 J was

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obtained using the cycle with a short rotating time (run B1), while a longer mixing time (tm ¼ 69 s) and energy draw of 34.68 J was obtained with a long rotating time (run B2). By comparing these mixing times to that obtained under steady stirring (run A3), one can observe the potential of intermittent mixing, especially when short mixing periods are used. Figure 2 shows a mixing sequence of run B1, in which it can be observed that the well-mixed region formed in the beginning tends to grow as the flow is dynamically perturbed and finally it is observed that the segregated zone at the top of the tank disappears after four mixing cycles. A similar trend is noticed when using a mixed flow impeller. Although an infinite mixing time was obtained under steady stirring of moderate and pronounced shear-thinning fluids (runs A7 and A8), long but finite mixing times were obtained when the flow was perturbed. A good example of this fact can be noted in run B14, in which a mixing time of 578 s and an energy draw of 145.26 J was obtained with a PBT off-centered and placed at 1/2 H. In this case a moderate shear-thinning fluid was considered. As shown in Figure 3, the well-mixed region formed around the impeller grows and segregated zones vanish thoroughly after two mixing cycles. Although Figures 2c and 3c appear quite similar, a segregated region observed at the bottom of the

Figure 2. Mixing of CMC solution using intermittent conditions with a Rushton turbine centered (Run B1): a) 10 s; b) 20 s; c) 30 s.

Figure 3. Mixing of CMC solution using intermittent conditions with a PBT off-centered (Run B14): a) 20 s; b) 40 s; c) 60 s.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A9): 1199–1203

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ASCANIO et al. Table 2. Mixing times and power draw under intermittent conditions.

Run

x

B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 B11 B12 B13 B14 B15 B16

0 0 0 0 0 0 0 0 1/4 T 1/4 T 1/4 T 1/4 T 1/4 T 1/4 T 1/4 T 1/4 T



y 1/3 1/3 1/3 1/3 1/2 1/2 1/2 1/2 1/3 1/3 1/3 1/3 1/2 1/2 1/2 1/2

H H H H H H H H H H H H H H H H

Impeller

N1 (rpm)

t1 (s)

n

Mixing time (s)

Energy draw (J)

RT RT PBT PBT PBT PBT RT RT RT RT PBT PBT PBT PBT RT RT

200 200 600 600 200 200 600 600 200 200 600 600 200 200 600 600

10 30 10 30 10 30 10 30 10 30 10 30 10 30 10 30

0.8 0.8 0.8 0.8 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.8 0.8 0.8 0.8

40 69 8 8 1 1 24 50 1 1 27 41 736 578 34 29

20.10 34.68 22.61 22.61 — — 101.53 211.53 — — 55.41 84.15 184.97 145.26 262.76 224.12

no homogenization was achieved after several mixing hours.

tank in Figure 3c required almost 9 min to be disrupted as the fluid is continuously perturbed. However, a different trend is observed when using pronounced shear-thinning fluids mixed with either a Rushton turbine or a PBT. Under steady stirring conditions, mixing times using either a Rushton turbine (runs A3 and A4) or a PBT (runs A7 and A8) were considered as infinite. Although the flow was dynamically perturbed with the impeller centered (runs B5 and B6) or off-centered (runs B9 and B10), no improvement was obtained. On the other hand, in general terms relatively short mixing times are obtained when using steady stirring conditions at high speed (A1, A2, A5 and A6). As runs B3 and B4 show, the mixing time can be drastically reduced with a PBT rotating at 600 rpm. The mixing time of run B3 and B4 is 60% shorter compared to that of run A5 and the energy required to achieve total homogenization is 55% lower. In other cases, the use of the proposed protocal with the impeller rotating at high speed can affect the mixing efficiency. Longer mixing times and much higher energy draw is required for runs B15 and B16 compared to run A1, in which the CMC solution was mixed with a Rushton turbine. However, better results can be obtained with the xanthan gum solution, which can be seen by comparing runs B7 and A2. A positive effect is observed when the impeller is slightly displaced from the conventional position (centered impeller at 1/3 H) in both radial and axial directions. However, in some cases mixing time can degrade if the impeller is strongly displaced in the radial direction. This can be seen when comparing runs B15 and B16 with A1 (in all cases a Rushton turbine was used). In the case of a mixed flow impeller (PBT), a negative effect is obtained if the agitator is displaced from the centerline. The mixing time of runs B3 and B4 is 65% shorter than that obtained under steady stirring conditions (run A6). However, longer mixing times are required if the impeller is displaced from the tank centerline. This can be seen by comparing run B11 and B12 with run A6, in which mixing times 30% and 85% longer were obtained. These results are in good agreement with those reported by Ascanio et al. (2002). The reader is referred to Ascanio et al. (2002)

and Alvarez et al. (2002) for a detailed analysis on the effect of the impeller position on mixing time. In the present work is difficult to observe this effect because the impeller was placed at extreme positions.

CONCLUSIONS An unconventional configuration was used for improving mixing times and power draw of inelastic shear-thinning fluids in stirred vessels. It has been demonstrated that the well-mixed region formed around the impeller at the beginning is readily disrupted when the flow is dynamically perturbed. Overall, the proposed configuration has been proven to be an efficient alternative to steady mixing, with better results obtained with moderate shear-thinning fluids mixed at low speed. However, special attention must be paid when using impellers rotating at high speed in order to avoid longer mixing times and higher energy requirements. It is also important to point out that the present configuration is limited mainly for use with open industrial tanks. In the case of pressurized tanks, the use of the present configuration could be an industrial challenge since the mechanical seals used in such tanks are not usually designed for intermittent conditions. It should also be considered that the agitation shaft can be submitted to considerable dynamic stresses as the impeller is offcentered.

NOMENCLATURE D H k n N T tm x y

Impeller diameter, m Liquid height, m Consistency index (power law), Pa sn Flow behavior index (power-law), dimensionless Rotational speed, rpm Tank diameter, m Mixing time, s Impeller radial position, m Impeller axial position, m

Greek Letter

t

torque, Nm

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A9): 1199–1203

TIME-PERIODIC MIXING OF SHEAR-THINNING FLUIDS REFERENCES Alvarez, M., Arratia, P.E. and Muzzio, F.J., 2002, Laminar mixing in eccentric stirred tank systems, Can J Chem Eng, 80: 546 –557. Ascanio, G., Brito-Baza´n, M., Brito-De La Fuente, E., Carreau, P.J. and Tanguy, P.A., 2002, Unconventional configuration studies to improve mixing times in stirred tanks, Can J Chem Eng, 80: 558– 565. Elson, T.P., Cheesman, D.J. and Nienow, A.W., 1986, X-ray studies of well-mixed region sizes and mixing performance with fluids possessing a yield stress, Chem Eng Sci, 41, 2555–2562. Harnby, N., Edwards, M.F. and Nienow, A.W., 1992, Mixing in Process Industries (Butterworth Heinemann, UK). Lamberto, D.J., Muzzio, F.J., Swanson, P.D. and Tonkovich, A.L., 1996, Using time-dependent RPM to enhance mixing in stirred vessels, Chem Eng Sci, 51: 733–741. Muzzio, F.J., Swanson, P.D. and Ottino, J.M., 1991, The statistics of stretching and starting in chaotic flows, Phys Fluids A, 3: 822–834. Muzzio, F.J., Meneveau, C., Swanson, P.D. and J.M. Ottino, J.M., 1992, Scaling and multifractal properties of mixing in chaotic flows, Phys Fluids A, 4: 1439–1456.

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Niederkorn, T.C. and Ottino, J.M., 1994, Chaotic mixing of shear-thinning fluids, AIChE J, 40: 1782–1793. Ottino, J.M., Leong, C.W., Rising H. and Swanson, P.D., 1988, Morphological structures produced by mixing in chaotic flows, Nature, 333: 419–425. Swanson, P.D. and Ottino, J.M., 1990, A comparative computational and experimental study of chaotic mixing of viscous fluids, J Fluid Mech, 213: 227 –249. Yurun, F. and Zhumin, L., 2001, Non-Newtonian effects on chaotic mixing between eccentric cylinders, Chin J Chem Eng, 9: 306 –309.

ACKNOWLEDGMENTS The financial support of NSERC and DGAPA (National University of Mexico) is gratefully acknowledged. The manuscript was received 29 March 2004 and accepted for publication after revision 30 June 2004.

Trans IChemE, Part A, Chemical Engineering Research and Design, 2004, 82(A9): 1199–1203