Dynamic Performance of Continuous-Flow Mixing of Pseudoplastic

ARTICLE pubs.acs.org/IECR

Dynamic Performance of Continuous-Flow Mixing of Pseudoplastic Fluids Exhibiting Yield Stress in Stirred Reactors Dineshkumar Patel, Farhad Ein-Mozaffari,* and Mehrab Mehrvar Department of Chemical Engineering, Ryerson University, 350 Victoria Street, Toronto, Ontario, M5B 2K3 Canada ABSTRACT: The core objectives of this work were to characterize and optimize the continuous-flow mixing of pseudoplastic fluids exhibiting yield stress in stirred reactors. To achieve these objectives, the effects of impeller type (for the seven axial-flow impellers A100, A200, A310, A315, A320, 3AH, and 3AM and the four radial-flow impellers R500, RSB, RT, and Scaba), impeller speed (50
800 rpm), impeller diameter (T/3.2
T/1.6, where T is the tank diameter), impeller off-bottom clearance (H/3.4
H/1.7, where H is the fluid height in the vessel), inlet and outlet locations (for the four configurations top inlet
top outlet, top inlet
bottom outlet, bottom inlet
bottom outlet, and bottom inlet
top outlet), pumping directions for axial-flow impellers (upward and downward pumping), fluid height in the vessel (T/1.06
T/0.83), residence time (257
328 s), and jet velocity (0.317
3.24 m s
1) on the dynamic performance of the mixing vessel were explored. To identify nonideal flows, dynamic tests were conducted using the frequency-modulated random binary input of a brine solution with the feed. The mixing quality in the vessel was substantially improved by increasing the impeller diameter, increasing the residence time, optimizing the impeller off-bottom clearance, decreasing the fluid height, optimizing the jet velocity, and using the up-pumping axial-flow impeller. Applying these findings will lead to improved quality of products and more efficient use of power in continuous-flow mixing of yield-pseudoplastic fluids.

’ INTRODUCTION Continuous-flow mixing is prevalent in most of the chemical and allied process industries because it provides high production rates, improves process control, and saves operation time and labor costs.1 The complex rheology of non-Newtonian fluids such as pulp suspensions and certain polymer and biopolymer solutions creates nonideal flows (channeling, recirculation, and dead volume) that substantially influence the performance of continuous-flow mixers.2 The efficiency of continuous-flow mixing in stirred vessels depends on system geometries, fluid properties, and operating conditions. In a typical continuous-flow mixing vessel, the mean residence time (τm) is often related to the mixing time (tm) in batch mode. A typical value for τm/tm of approximately 10 is normally used as a criterion for an ideal mixing system.3
7 Results have shown that, for a value of τm/tm less than 10, channeling is likely to occur. The impeller type and size influence the performance of continuous-flow mixing systems as well. Studies of continuous-flow mixing of Newtonian fluids have shown that radial-flow impellers are able to work effectively whereas axial-flow impellers lead to channeling as a result of the location of the outlet directly below the impeller discharge.4
6 To minimize the extent of nonideal flows in continuous-flow mixing of non-Newtonian fluids, Saeed et al.8 recommended that an impeller with large pumping and circulation efficiencies such as the A320 impeller should be chosen. Ein-Mozaffari et al.2 observed that an increase in the impeller diameter improved the mixing performance for the agitation of pulp suspensions. Regarding the pumping direction of an axial-flow impeller, Aubin et al.9 reported that channeling through a bottom outlet was reduced in a continuous-flow stirred-tank reactor (CFSTR) when an impeller was employed in the up-pumping mode instead of the down-pumping mode. Studies on the effects of impeller r 2011 American Chemical Society

speed on continuous-flow mixing of non-Newtonian fluids showed that, even when the entire fluid was in motion at a higher impeller speed, channeling and dead zones still existed.10 The rheology of fluids also affects the efficiency of continuousflow mixing. Studies have shown that the extent of channeling increases and the fraction of fully mixed volume decreases as the fluid yield stress increased at a fixed impeller speed.10
12 The locations of the inlet and outlet5,11,13
15 and the number of feed inlets9 also affect the performance of continuous-flow mixing systems. Saeed et al.8 observed that the extent of nonideal flows was reduced when using a bottom outlet compared to a side outlet with an inlet at the top of the stirred tank. Saeed et al.8 and Ein-Mozaffari et al.10 investigated the effects of feed flow rates on the mixing of non-Newtonian fluids and found that decreasing the feed flow rates reduced the extent of nonideal flows (channeling and dead zones). It is apparent that the current design of continuous-flow mixing of non-Newtonian fluids is based on a limited amount of published information and trial-and-error methods. A poorly designed mixing system results in a decrease in product quality and an increase in power consumption. As a result, it would be highly beneficial to characterize and optimize the design of continuous-flow mixing systems for fluids with complex rheology so that good mixing with a predictable dynamic response profile can be attained. Therefore, this study explores the effects of important design parameters and operating conditions such as impeller type, impeller speed, impeller diameter, impeller offbottom clearance, inlet and outlet locations, pumping direction Received: November 27, 2010 Accepted: June 18, 2011 Revised: May 24, 2011 Published: June 18, 2011 9377

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Figure 1. Schematic diagram of the experimental setup for continuous-flow mixing: (1) electric motor, (2) mixing tank, (3) feed tank, (4) discharge tank, (5) tracer tank, (6) flexible coupling, (7) torque meter, (8) conductivity sensor, (9) progressing cavity pump, (10) metering pump, (11) solenoid valve, (12) data acquisition system, and (13) VFD control panel.

for axial-flow impellers, fluid height in the vessel, residence time, and jet velocity on the degree of channeling and the fraction of fully mixed volume in a continuous-flow stirred tank for a pseudoplastic fluid with yield stress using a dynamic test.

’ EXPERIMENTAL SETUP, DYNAMIC MODEL, AND PROCEDURE The experimental setup (Figure 1) previously described by Saeed et al.8 was employed in this study to perform dynamic tests on a continuous-flow mixing system. A transparent flat-bottomed cylindrical tank with a diameter (T) of 0.38 m and a height of 0.60 m was used as the mixing vessel. As shown in Figure 2, various axial-flow and radial-flow impellers were utilized to agitate the xanthan gum solution. To avoid creating a vortex, the tank was fitted with four equally spaced baffles (width of 0.04 m, thickness of 0.012 m, and length equal to the tank height) to the vessel wall. The tank was also fitted with inlet and outlet tubes. The inner diameter of the outlet was kept to 0.025 m. However, the inner diameter of the inlet was varied (from 7.94  10
3 to 25.4  10
3 m) to explore the effects of jet velocity on the continuousflow mixing system. To investigate the effects of inlet and outlet locations on continuous-flow mixing, the inlet was located at the top (r = 0.13 m, θ = 90°, and z = 0.38 m) and at the bottom (r = 0.05 m, θ = 105°, and z = 0.10 m) of the mixing vessel. The outlet was located at the bottom (r = 0.13 m, θ = 315°, and z = 0.00 m) and at the top side (r = 0.19 m, θ = 315°, and z = 0.35 m) of the mixing vessel. The mixing tank was equipped with a topentering impeller driven by a 2-hp motor, and the impeller speed was set to the desired revolutions per minute (rpm) using a variable-frequency drive (VFD). The impeller torque and speed were measured using a rotary torque transducer (Staiger Mohilo, Lorch, Germany) and a tachometer, respectively. During the

experiments, the fluid was pumped from the feed tank to the discharge tank through the mixing vessel. Dynamic tests were carried out by injecting a saline solution (NaCl solution as a tracer) into the fresh feed stream before it was pumped into the mixing vessel using a metering pump (Milton Roy, Ivyland, PA). The injection of the tracer was controlled by a computer-controlled on
off solenoid valve. The conductivity values of the input and output streams were measured as functions of time using flowthrough conductivity sensors (RoseMount Analytical, Irvine, CA), and these values were recorded using a data acquisition system controlled by LabVIEW software (National Instruments, Austin, TX) to estimate dynamic model parameters. Thermocouples were installed at the inlet and outlet of the mixing vessel to measure the fluid temperature. We did not observe any significant variations in temperature during the experiments for the given range of impeller speeds. All measurements were made at room temperature, 22 ( 1 °C. The fluids used in this study were xanthan gum solutions in water. Xanthan gum is a pseudoplastic fluid with yield stress, and its rheology can be described by the Herschel
Bulkley model16,17 : τ ¼ τy + KðγÞn ð1Þ where τ is the shear stress, τy is the yield stress, K is the consistency index, γ_ is the shear rate, and n is the power-law index. The average shear rate can be used to evaluate the apparent viscosity (η) of the Herschel
Bulkley fluid as : τy + KðγÞn τ : ð2Þ η¼ : ¼ γavg γavg According to Metzner and Otto’s18 classical equation (eq 3), the average shear rate (γ_ avg) close to an impeller in a mixing vessel is 9378

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Figure 2. Axial-flow and radial-flow impellers: (1) HG 3AH, (2) Lightnin A315, (3) Lightnin A320, (4) Lightnin A200, (5) Lightnin R500 (sawtooth), (6) Scaba 6 SRGT, (7) HG 3AM, (8) Lightnin A100, (9) Lightnin A310, (10) RSB (retreat swept-back), and (11) RT (Rushton turbine).

Table 1. Experimental Conditions description impeller types

range and types axial-flow impeller: A100, A200, A310, A315, A320, 3AH, and 3AM radial-flow impeller: R500, RSB, RT, and Scaba

impeller speed (N)

A100, 50
763 rpm; A200, 50
500 rpm; A310, 50
629 rpm; A315, 50
599 rpm; A320, 50
500 rpm; 3AH, 49
500 rpm; 3AM, 50
678 rpm; R500, 50
802 rpm; RSB, 50
560 rpm; RT, 50
416 rpm; Scaba, 49
331 rpm

impeller diameter (D) (A200 impeller) impeller off-bottom clearance (C) (3AH impeller)

T/3.2, T/2.5, T/2.1, and T/1.6 H/3.4, H /2.7, H /2.1, and H /1.7

impeller pumping direction (3AH and A200 impellers)

down- and up-pumping directions

fluid height in the stirred vessel (H) (3AH impeller)

T/1.06, T/0.93, and T/0.83

mean residence time (3AH impeller)

257, 292, and 328 s

jet velocity (Vj) (3AH impeller)

0.317, 1.66, and 3.24 m s
1

inlet locations (3AH impeller)

TI (r = 0.13 m, θ = 90°, and z = 0.38 m) BI (r = 0.05 m, θ = 105°, and z = 0.10 m)

outlet locations (3AH impeller)

directly proportional to the rotational speed of the impeller (N) : γavg ¼ kS N ð3Þ where kS is a function of the type of impeller. The rheological properties of xanthan gum solutions can be found in Saeed et al.8 The experimental conditions are summarized in Table 1. The dynamic model proposed by Ein-Mozaffari19 for continuous-flow mixing systems was used in this study. Patel et al.20

TO (r = 0.19 m, θ = 315°, and z = 0.35 m) BO (r = 0.13 m, θ = 315°, and z = 0.00 m)

explored the performances of different dynamic models proposed in the literature for continuous-flow mixing processes. They found that Ein-Mozaffari’s dynamic model was the most efficient model. Moreover, Saeed et al.8 reported that the dynamic responses predicted using the local velocities computed through the computational fluid dynamics (CFD) model were in good agreement with the experimentally determined values. The findings of that study8 based on the local velocities calculated using the continuity, momentum, and transport species 9379

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equations support the effectiveness of the dynamic model and experimental procedure employed in the present work to optimize and characterize the continuous-flow mixing of pseudoplastic fluids exhibiting yield stress. The combined transfer function for channeling and mixing zones in a continuous-time domain can be expressed mathematically as8,11,13,21

G¼


T1 s

fe + 1 + τ1 s

ð1
f Þð1
RÞ

e
T2 s 1 + τ2 s

ðRÞeT2 s 1
1 + τ2 s

ð4Þ

where G is the transfer function of the vessel, f represents the portion of the fluid that channels in the mixing tank, and 1
f is the fraction of the fluid that enters the mixing zone. A portion of the fluid, R, exiting the mixing zone can be recirculated within the mixing zone. Parameters τ1 and τ2 are the time constants for the channeling and mixing zones, respectively. Parameters T1 and T2 are the time delays for the channeling and mixing zones, respectively. The parameter R was set to zero, as recirculation of the fluid was not observed in the dynamic responses of the laboratory-scale mixing vessel.11,13,22 Two parameters were used to quantify the flow nonideality: f, the degree of channeling in the vessel, and Vfully mixed/V, the ratio of the fully mixed volume (Vfully mixed) in the vessel to the total solution volume (V) in the vessel. The fully mixed volume is given by8,11 Vfully mixed Q τ2 ð1
f Þ ¼ V V

ð5Þ

where Q is the solution flow rate through the mixing vessel. By measuring the input and output responses of the mixing vessel, the dynamic model parameters were estimated using the numerical method developed by Kammer et al.23 The total volume in the mixing vessel is the sum of the fully mixed volume plus the dead volume. By knowing the fully mixed volume, the dead volume in a mixing vessel is easily calculated. Based on eq 5, dead zones might exist within the vessel even when the extent of channeling is negligible. The system identification procedure comprises the following steps8 (1) exciting the system with a rectangular pulse, (2) designing a frequency-modulated random binary signal on the basis of the response of the system to the rectangular pulse by concentrating the excitation energy at frequencies where the Bode plot is sensitive to the parameters’ variations, (3) exciting the system by a frequency-modulated random binary signal, and (4) validating the dynamic model with a new input imposed by another random exciting signal to generate a new output and then comparing the measured and predicted outputs.

’ RESULTS AND DISCUSSION The estimation of power (P) is crucial for the design of mixing vessels in various industries. Power represents the rate of energy dissipated within a fluid from the impeller and is a function of the impeller speed (N), fluid rheology, and geometry of the impeller and tank. In this work, to calculate the power consumption (P), the impeller speed (N) and torque (M) were measured. The average shear rate was used to obtain the apparent viscosity (η) of the Herschel
Bulkley fluids as shown in eq 2. The modified

Figure 3. Power number (Po) versus Reynolds number (Re): (a) axialflow impellers, (b) radial-flow impellers (1.5% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93).

Reynolds number (Re) was calculated as Re ¼

FND2 kS FN 2 D2 ¼ η τy + KðkS NÞn

ð6Þ

The value of the Metzner
Otto proportionality constant kS was selected within the range of 7.1
11.5 according to the geometry of the impellers.24,25 The trend in the power number curve illustrated in Figure 3 is similar to the general trends reported by several researchers.26
28 It has been shown that Po µ Re
1 in the laminar regime (Re < 10), Po is constant in the turbulent regime (Re > 104), and Po changes to some extent in the transitional regime (Re between 10 and 104). Figure 3 shows that, at Re < 10, the solid line with a slope of
1 fits the data precisely, which implies that Po  Re is constant for the laminar regime. It also shows that, in the transitional regime, the power number changes slightly with Re. The impeller power numbers (A100, 0.27; A200, 1.36; A310, 0.57; A315, 0.65; A320, 0.99; 3AH, 1.33; 3AM, 0.38; R500, 0.32; RSB, 1.10; RT, 3.82; and Scaba, 4.67) shown in Figure 3 are within the range reported in the literature.24,29 The impeller speed is one of the most important parameters affecting the dynamic performance of the continuous-flow mixing system. Parts a and b of Figure 4 show the extent of channeling and the fraction of fully mixed volume, respectively, as functions of impeller speed. As expected, the channeling decreased and the fully mixed volume increased with an increase in impeller speed. At higher impeller speeds, the xanthan gum 9380

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Figure 4. Axial-flow impellers: Effects of impeller speed and impeller type on the extents of (a) channeling and (b) fully mixed volume (Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

solution was agitated vigorously and disrupted farther from the impeller, leading to improved mixing by reducing the extent of nonideal flows. Other researchers have observed similar phenomena.8,14,30 The optimum impeller speed at which the channeling approaches zero and the fully mixed volume approaches the total volume of the fluid within the mixing tank should be preferred, as further increases in the impeller speed will lead to more power consumption for the same extent of fully mixed volume. Besides the impeller speed, the type of impeller also influences the dynamic performance of continuous-flow mixing. Several types of impeller are used in industry; however, the determination of the most effective impeller should be based on an understanding of the process requirements and knowledge of the physical properties. Normally, axial-flow and radial-flow impellers are utilized for the agitation of fluids with low to medium viscosities. Seven axial-flow impellers (A100, A200, A310, A315, A320, 3AH, and 3AM) and four radial-flow impellers (R500, RSB, RT, and Scaba) were employed in this study, and the efficiency of each impeller in terms of the extent of channeling and fully mixed volume is depicted in Figures 4 and 5. It can be seen from Figure 4a,b that the A200 impeller was the least effective whereas the A320 impeller was the most effective in reducing the effects of channeling and dead volume among the axial-flow impellers. Hydrofoil impellers with a high solidity ratio have been recommended in the literature for the mixing of

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Figure 5. Radial-flow impellers: Effects of impeller speed and impeller type on the extents of (a) channeling and (b) fully mixed volume (Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

viscous fluids.31
33 Thus, we measured the solidity ratios of the five hydrofoil impellers (A320, 3AH, A315, A310, and 3AM) utilized in this study. The solidity ratios of A320, 3AH, A315, A310, and 3AM were 0.944, 0.902, 0.881, 0.668, and 0.643, respectively. It can be seen that the A320, 3AH, and A315 impellers have higher solidity ratios than the A310 and 3AM impellers. Moreover, the A320 impeller has the highest solidity ratio among all hydrofoil impellers used in this study. Figure 6 illustrates the effects of the solidity ratio of hydrofoil impellers on the extents of channeling and fully mixed volume at fixed power consumption. The results show that the A320, A315, and 3AH impellers (with high solidity ratios) were more effective than the A310 and 3AM impellers (with low solidity ratios) in reducing the effects of nonideal flows in the continuous-flow mixing of xanthan gum solutions. These results are in good agreement with those reported in the literature regarding the effects of the solidity ratio of hydrofoil impellers on the mixing quality. In Figure 4a,b, the power consumed per unit volume by the A320 impeller when channeling approached zero and fully mixed volume approached unity was the lowest power consumption among all axial-flow impellers. Alternatively, radial-flow impellers produce two circulating loops, one below and one above the impeller. The disk-type radial-flow impellers (Scaba and RT) provide a more uniform radial flow pattern and draw more power than those without disk 9381

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Figure 6. Effects of the solidity ratio of the hydrofoil impellers on the extents of channeling and fully mixed volume at fixed power consumption (Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

radial-flow impellers (RSB). The Scaba impeller is similar to the Rushton turbine, except that curved blades are substituted for vertical flat blades, resulting in a lower power number, while a very high-shear producing R500 impeller consists of a disk with serrations around its circumference.31 Figure 5 shows that, among the radial-flow impellers, the R500 impeller was the least effective, whereas the Scaba impeller was the most effective in reducing the effects of channeling and dead volume. The power consumed per unit volume by the Scaba impeller when the channeling approached zero and fully mixed volume approached unity was the lowest power consumption among all radial-flow impellers. Thus, the results show that, in reducing the effects of nonideal flows, the A320 impeller was the most effective among the axialflow impellers and the Scaba impeller was the most effective among the radial-flow impellers. However, these two most effective impellers would seldom be used under similar conditions. The axial-flow hydrofoil impellers are mostly capable for high pumping and low shear. Compared to axial-flow impellers, radial-flow impellers provide higher shear and turbulence levels with lower pumping. Therefore, based on the commercial price of each impeller, the process requirements, and the physical properties of the fluids, either an impeller producing high pumping and low shear such as the A320 impeller or a lowpumping and high-shear impeller such as the Scaba impeller should be chosen. The Scaba impeller provides better gas dispersion and higher gas-holding capacity than the A320 impeller in gas
liquid mixing operations. In addition to the impeller speed and impeller type, the impeller diameter also influences the dynamic performance of the continuous-flow mixing system. Choosing the optimum ratio of the impeller diameter to the tank diameter (D/T) can dramatically reduce the capital costs (impeller, gearbox, and motor) and operating costs (power requirement) of the processing unit. Reducing the impeller diameter cuts down the impeller weight, which leads to a reduction in the shaft’s normal frequency and allows for an increase in speed, whereas the selection of a smaller gearbox reduces the motor size. Parts a and b of Figure 7 demonstrate the effects of changing the impeller diameter

Figure 7. Effects of impeller diameter on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume at fixed power consumption as a function of D/T (A200, Q = 579 L h
1, 1.0% xanthan gum, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

(D = T/1.6, T/2.1, T/2.5, and T/3.2) on the extent of channeling and the fraction of fully mixed volume as a function of the power input for the A200 impeller, respectively, while Figure 7c shows the channeling and fraction of fully mixed volume as a function of D/T at the constant power input for the A200 impeller. The results show that the impeller with D = T/3.2 was the least effective, whereas the impeller with D = T/1.6 was the most effective in reducing the effects of channeling and dead volume. It is clear that, with an increase in impeller diameter, the extent of channeling decreased, and the fully mixed volume increased. An increase of the impeller diameter also increases the value of the average velocity of the circulation flow in the tank, which leads to improved mixing by eliminating channeling and dead volume. Moreover, the flow pattern with the A200 impeller becomes closer to that generated with a radial-flow impeller as the impeller 9382

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Industrial & Engineering Chemistry Research diameter increases.31 This radial-flow pattern also reduces the degree of channeling compared to that achieved by an axial-flow pattern. Ein-Mozaffari et al.2 observed a similar phenomenon, where an impeller with a larger diameter provided better performance than an impeller with a smaller diameter for the continuous-flow mixing of a pulp suspension (a non-Newtonian fluid) in a laboratory chest. The range of rotational speed for impellers with D = T/3.2 was narrower than that for other impeller diameters because, at higher impeller speeds, the system generated a lot of mechanical vibrations, severe turbulent flow, and surface air entrainment. In such a situation, it is almost risky to conduct the experiment at higher impeller speeds. The impeller clearance (C) from the bottom of the tank has a significant impact on the dynamic performance of the continuous-flow mixing system. In the mixing of a pseudoplastic fluid with yield stress, placing the impeller too low results in the majority of the fluid remaining unmixed on the upper part of the tank. Placing the impeller too high causes a deep vortex, which leads to surface aeration even at lower impeller speeds and also results in the creation of dead zones at the bottom of the tank, especially the bottom corner of the tank. Hence, placing the impeller at an optimum clearance (C) can dramatically reduce the channeling and dead zones in the continuous-flow mixing of viscous fluids. Four different impeller positions from the base of the tank, namely, C = H /1.7, H /2.1, H /2.7, and H/3.4, were tested with the 3AH impeller. Parts a and b of Figure 8 show the effects of the impeller clearance on the extent of channeling and the fraction of fully mixed volume, respectively. Figure 8c shows the channeling and the fraction of fully mixed volumes as a function of C/H at the constant power input for the 3AH impeller. These results show that, as the clearance of the impeller increased from H/3.4 to H/2.1, the nonideal flows such as channeling and dead volume decreased and reached a minimum value at C = H/2.1. A further increase in the clearance of the impeller (to H/1.7) had an adverse effect on the extent of the nonideal flows. This result is similar to those obtained by EinMozaffari and Upreti,29 who observed a reduction in the mixing time with increasing impeller clearance (from H/3 to H/2) for a pitched blade turbine in the mixing of a pseudoplastic fluid with yield stress. Houcine et al.34 also observed identical phenomena in the batch mixing of Newtonian fluids with a pitched blade turbine. Amanullah et al.35 also investigated the effects of impeller clearance on the cavern volume in the mixing of shear-thinning viscous fluid for C/T = 0.24
0.49 (0.2% Carbopol, D/T = 0.49) and C/T = 0.17
0. 33 (0.1% Carbopol, D/T = 0.33). In both cases, increasing the impeller clearance from the vessel base was beneficial in generating larger cavern volumes at a given power input. The locations of the inlet and outlet, two of the vital geometric parameters of a mixing tank, play a crucial role in the continuous-flow system. Ein-Mozaffari et al.11,13 and Saeed and Ein-Mozaffari30 found that the locations of the inlet and outlet have a significant effect on the extent of nonideal flows in the continuous-flow mixing of non-Newtonian fluids. Thus, this study examined the effects of four different configurations, namely, (1) TI
TO (top inlet
top outlet), (2) TI
BO (top inlet
bottom outlet), (3) BI
BO (bottom inlet
bottom outlet), and (4) BI
TO (bottom inlet
top outlet), on the extent of nonideal flows. The effects of the inlet and outlet locations on the extent of channeling and the fraction of fully mixed volume are shown in parts a and b, respectively, of Figure 9. Figure 9c displays the degree of channeling and fully mixed volume for

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Figure 8. Effects of impeller clearance on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume as a function of C/H at 50 rpm (3AH, Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

each configuration at 400 rpm for the 3AH impeller. It can be seen from the results that, for identical operating conditions, the BI
TO configuration was the most effective in reducing the extent of the nonideal flows, whereas the TI
TO configuration was very prone to a high degree of channeling and dead volume. The BI
BO configuration was more susceptible to a high degree of channeling and dead volume than the TI
BO configuration. The TI
TO and BI
BO configurations enabled large percentages of the feed to be conveyed directly to the outlet without being drawn into the mixing zone (or through the impeller). Conversely, in the case of the BI
TO and TI
BO configurations, the feed was forced to flow through the mixing zone before leaving the vessel. Even in the case of the BI
TO configuration, the feed had to face intense fluid discharge from the impeller and pass through the mixing zone in the direction 9383

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Figure 9. Effects of inlet and outlet locations on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume for each configuration at 400 rpm (3AH, Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s).

opposite to the gravitational force. Based on the data presented in Figure 9c, the BI
TO configuration is the optimum inlet
outlet configuration. Overall, it seems that the locations of the inlet and outlet should be chosen in such a way that a line drawn from the inlet to the outlet passes through the impeller (or the intense mixing zone). Khopkar et al.15 simulated the flow generated by an axial flow impeller to investigate the effects of the inlet and outlet locations on the mixing of Newtonian fluid and reported that the mixing was improved when the inlet was located at the bottom and the outlet as an overflow instead of

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Figure 10. Effects of impeller pumping direction on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume for each pumping direction for the 3AH and A200 impellers at 400 rpm (Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, Vj = 0.317 m s
1, residence time = 292 s, input
output locations = TI
BO).

having the inlet at the top and the outlet at the bottom of the tank. For an axial-flow impeller, the impeller rotational direction or the impeller pumping direction (either up-pumping or downpumping) also has a significant effect on the dynamic performance of continuous-flow mixing when the outlet is located at the bottom of the tank. The up-pumping impeller avoids creating a vortex, which can cause air entrainment and mechanical 9384

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Industrial & Engineering Chemistry Research vibration. The effects of pumping direction for the A200 and 3AH impellers on the extent of channeling and the fraction of fully mixed volume are presented in parts a and b, respectively, of Figure 10. Figure 10c dsiplays the extent of channeling and the fraction of fully mixed volume for each pumping direction at 400 rpm for the A200 and 3AH impellers. The results show that the up-pumping impellers were more effective than the downpumping impellers in terms of reducing the nonideal flows such as channeling and dead volumes. The mixing performance in the case of the up-pumping impellers was improved because the feed stream was directly facing the up-pumping stream from the impeller discharge and provided better mixing in the upper part of the tank. Moreover, the outlet was located at the bottom of the tank; therefore, the feed stream had to pass through the intense up-flow from the impeller discharge before reaching the outlet. This feature is particularly useful for surface feed applications. These results are identical to those reported in the literature. For instance, Aubin et al.9 studied the effects of up-pumping and down-pumping (Mixel TT) impellers on the efficiency of a CFSTR using a Newtonian fluid. They reported that channeling through a bottom outlet can be reduced in the CFSTR when the impeller is employed in the up-pumping mode instead of the down-pumping mode. The fluid height (H) in the vessel also affects the dynamic performance of continuous-flow mixing. The actual volume to be agitated in the vessel depends on the height of the fluid, in addition to the vessel diameter (T). Three different fluid heights in the mixing vessel, namely, H = T/0.83, T/0.93, and T/1.06, were tested with the 3AH impeller. To maintain a constant residence time of the fluid, the inlet flow rates (Q) were changed accordingly (Q = 508, 579, and 649 L h
1). Parts a and b of Figure 11 show the effects of the fluid height on the extent of channeling and the fraction of fully mixed volume, respectively. Figure 11c displays the extent of channeling and the fraction of fully mixed volume as a function of H/T for the 3AH impeller at a constant power input and residence time. The results show that, as the fluid height in the vessel was increased, the extent of channeling and dead volume also increased, and the fraction of fully mixed volume decreased. This is due to poor mixing above the impeller when the height of the fluid was increased but the impeller clearance was kept constant. However, choosing an optimum ratio of the fluid height (H) to the tank diameter (H/T) is important because a low fluid height in the vessel reduces the production capacity, whereas an increase in the fluid height increases nonideal flows. Generally, for any single impeller, a fluid height/vessel diameter (H/T) aspect ratio of about 1 is selected, and multiple impellers might be recommended if the aspect ratio is much higher than 1.31 The residence time also has a significant effect on the dynamic performance of continuous-flow mixing. The total time spent by a molecule within the boundary of the reactor (time taken by a molecule to reach the outlet from the inlet) is known as the residence time, which is calculated from the ratio of the fluid volume (V) in the vessel to the feed flow rate (Q). The residence time can be adjusted by changing either the feed flow rate or the fluid volume. In this study, three different residence times (257, 292, and 328 s) were tested by changing the fluid height (H = 36, 41, and 46 cm) at constant feed flow rate (Q = 579 L h
1). The effects of residence time with the 3AH impeller on the extent of channeling and the fraction of fully mixed volume are displayed in parts a and b, respectively, of Figure 12. Figure 12c presents the channeling and fully mixed volume as a function of the residence

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Figure 11. Effects of fluid height (H) in the mixing vessel on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume as a function of H/T at a power of 224 W/m3 (constant residence time = 292 s but different fluid flow rates of Q = 508, 579, and 649 L h
1; 3AH; 1.0% xanthan gum; D = T/2.1; C = H/2.7; Vj = 0.317 m s
1; input
output locations = TI
BO).

time at constant power. As expected, as the residence time of the fluid in the vessel increased, the extent of channeling and dead volume decreased, whereas the fraction of fully mixed volume increased. As the residence time increased, the fluid had more time to stay within the mixing vessel and had more chances to interact with the intense mixing zone around the impeller. As a result, a higher residence time led to more fully mixed volume in the mixing vessel (Figure 12b). As shown in Figure 12c, higher residence times are able to reduce nonideal flows in continuousflow mixing vessels. The mixing of fluids necessitates mechanical energy, which is applied through impeller rotation to achieve the desired process result. An alternative method for transferring mechanical energy to the fluid is to use a pump to generate a high-velocity jet of fluid 9385

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Industrial & Engineering Chemistry Research

Figure 12. Effects of fluid residence time in the mixing vessel on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume as a function of the residence time at power 16 W/m3 [at constant fluid flow rate (Q) = 579 L h
1 but different fluid heights (H) = 36, 41, and 46 cm; 3AH; 1.0% xanthan gum; D = T/2.1; C = H/2.7; Vj = 0.317 m s
1; input
output locations = TI
BO).

in the vessel at the same flow rate by reducing the inlet diameter.31 The jet velocity (Vj) can influence the efficiency of a continuous-flow mixing system. This study applied three different jet velocities (Vj = 0.317, 1.66, and 3.24 m s
1) to determine their effects on the dynamic performance of continuous-flow mixing. The normal TI
BO configuration was used, in which the outlet was located at the bottom of the tank. The data in parts a and b, respectively, of Figure 13 represent the effects of the jet velocity on the extent of channeling and the fraction of fully mixed volume, respectively, and Figure 13c shows the channeling and the fraction of fully mixed volume as a function of the jet velocity for the 3AH impeller at 400 rpm. The results show that, for the same operating conditions, as the jet velocity (Vj) was increased from 0.317 to 1.66 m s
1, the

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Figure 13. Effects of inlet jet velocity on the extents of (a) channeling, (b) fully mixed volume, and (c) channeling and fully mixed volume as a function of the jet velocity at 400 rpm (3AH, Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, residence time = 292 s, input
output locations = TI
BO).

channeling decreased, and the fully mixed volume increased. When an inlet stream is fed into a tank at high velocity, it is expected that the surrounding bulk fluid will be entrained into the feed zone, thus improving the mixing. Furthermore, the high jet velocity will transport the feed promptly to the impeller region, where it will be exposed to high turbulence and be better mixed. However, a further increase in the jet velocity from 1.66 to 3.24 m s
1 had an adverse effect on the mixing performance, as the channeling increased and the fully mixed volume decreased. A potential problem related to high jet velocities is that the jet can very easily pass through the impeller-swept volume and reach the outlet, which is located at the bottom of the tank, thereby bypassing the impeller turbulent zone. As a result, the channeling increases, and the fully mixed volume decreases at very high jet velocities. There is a possibility of overcoming this potential problem by either increasing the impeller speed so that it is sufficient to break the jet path or relocating the outlet. However, 9386

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where there was no outlet, which reduced the extent of the channeling. Moreover, the feed that bypassed the impeller zone and directly reached the bottom of the tank had to face the intense discharge from the impeller before leaving the tank from the top side outlet, and thus, the mixing in the tank was improved. For the purpose of comparison, Figure 15 presents the channeling as a function of jet velocity for two different configurations (TI
BO and TI
TO) at 200 rpm impeller speed. This figure shows that, even at a high jet velocity, the TI
TO configuration was able to reduce the channeling dramatically compared to that observed with the TI
BO configuration.

Figure 14. Effects of inlet jet velocity on the extents of (a) channeling and (b) fully mixed volume (3AH, Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, residence time = 292 s, input
output locations = TI
TO).

Figure 15. Effects of inlet jet velocity on the extents of channeling for different output locations (200 rpm, 3AH, Q = 579 L h
1, 1.0% xanthan gum, D = T/2.1, C = H/2.7, H = T/0.93, residence time = 292 s).

higher impeller speeds create a deep vortex, which leads to surface aeration. Hence, further investigation was done by relocating the outlet using the TI
TO configuration for the same operating conditions. For the new TI
TO configuration, the results presented in parts a and b of Figure 14 show the effects of the jet velocity on the extent of channeling and the fraction of fully mixed volume, respectively. Now, it is clear that, when the jet velocity was increased from 0.317 to 3.24 m s
1, the extent of channeling and dead volume decreased, and the fraction of fully mixed volume increased. Still, the feed with the high jet velocity passed through the impeller-swept volume and reached the bottom of the tank,

’ CONCLUSIONS The efficiency of the continuous-flow mixing of non-Newtonian fluids with yield stress in reducing nonideal flows and increasing the fully mixed volume was successfully measured through dynamic tests. The results and importance of each studied factor are as follows: (i) Impeller Type. The selection of the most effective impeller among the various choices is the most critical factor. This study showed that, for reducing the nonideal flows in the continuous-flow mixing system, the A320 impeller was the most effective impeller among the seven axial-flow impellers and the Scaba impeller was the most effective among the four radial-flow impellers. Depending on the commercial price of impellers, the process requirements, and the physical properties of the fluids, either an impeller producing high pumping and low shear such as the A320 impeller or a low-pumping and highshear impeller such as the Scaba impeller should be chosen. (ii) Impeller Diameter. Tests on the effect of impeller diameter (D = T/1.6, T/2.1, T/2.5, and T/3.2) for A200 impellers revealed that the channeling decreased and the fully mixed volume increased as the impeller diameter increased. Thus, a larger-diameter impeller makes a continuous-flow mixer more efficient. (iii) Impeller Off-Bottom Clearance. The mixing quality was improved when the clearance of the impeller was increased from H/3.4 to H/2.1. A further increase in the clearance of the impeller (H/1.7) had an adverse effect on the mixing quality. Therefore, the optimum value of the impeller off-bottom clearance should be chosen to improve the mixing quality. (iv) Direction for Axial-Flow Impellers. Dynamic tests made with the A200 and 3AH impellers showed that up-pumping impellers were more effective than downpumping impellers for reducing nonideal flows. Hence, the mixing quality in a continuous-flow mixer can be improved by using an up-pumping impeller. (v) Fluid Height in the Vessel. Three different fluid heights (H = T/0.83, T/0.93, and T/1.06) in the mixing vessel were tested with the 3AH impeller at constant residence time. It was observed that, as the fluid height in the vessel was increased, the extent of nonideal flows also increased. Thus, increasing the fluid height in the vessel at constant residence time cannot improve the mixing quality. (vi) Residence Time. Three different residence times (257, 292, and 328 s), obtained by changing the fluid height (H = 36, 41, and 46 cm) at constant feed flow rate (Q = 579 L h
1), were also tested to determine their effects on nonideal flows. As the residence time of the fluid in the 9387

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Industrial & Engineering Chemistry Research vessel was increased, the mixing quality was found to improve. (vii) Jet Velocity. The effect of the jet velocity (Vj = 0.317, 1.66, and 3.24 m s
1) on the dynamic performance of the continuous-flow mixing system was also investigated for two configurations: TI
BO and TI
TO. The results showed that, for the same operating conditions, as the jet velocity (Vj) was increased from 0.317 to 1.66 m s
1, the mixing quality improved for both configurations. A further increase in the jet velocity from 1.66 to 3.24 m s
1 had an adverse effect on the mixing quality for the TI
BO configuration; however, this potential problem was overcome by relocating the outlet using the TI
TO configuration. Consequently, increasing the jet velocity does not always mean improving the mixing quality in the continuous-flow mixer; however, the location of the outlet also plays an important role. (viii)Inlet and Outlet Locations. An extensive study on the locations of the inlet and outlet showed that the BI
TO (bottom inlet
top outlet) configuration was the most effective whereas the TI
TO (top inlet
top outlet) and BI
BO (bottom inlet
bottom outlet) configurations enabled large percentages of feed to be conveyed directly to the outlet without being drawn into the mixing zone. (ix) Impeller Speed. The results also showed that the channeling decreased and the fully mixed volume increased with increasing impeller speed. Applying the findings of this study will reduce the effects of nonideal flows and help reduce the variability in the continuousflow mixing of non-Newtonian fluids.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: fmozaff[email protected]. Tel.: (416) 979-5000 Ext. 4251. Fax: (416) 979-5083.

’ ACKNOWLEDGMENT The financial support of the Natural Science and Engineering Research Council of Canada (NSERC) and Ontario Graduate Scholarship in Science and Technology (OGSST) is gratefully acknowledged. ’ NOTATION C = impeller off-bottom clearance (m) D = impeller diameter (m) f = percentage of channeling (fraction) G = transfer function H = fluid height in the vessel (m) K = consistency index (Pa sn) kS = Metzner
Otto constant M = torque (N m) n = power-law index N = impeller rotational speed (s
1) P = power (P = 2πNM) (W) Po = power number (Po = P/FN3D5) Q = volumetric flow rate (m3 s
1) r = cylindrical coordinate (m) R = percentage of recirculation (fraction) Re = Reynolds number T = tank diameter (m)

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T1, T2 = time delays (s) tm = mixing time (s) Vfully mixed = fully mixed volume (m3) Vj = jet velocity (m s
1) V total = fluid volume inside the mixing tank (m3) z = cylindrical coordinate (m) Greek Letters γ_ = shear rate (s
1) γ_ avg = average shear rate (s
1) η = apparent viscosity (Pa s) θ = cylindrical coordinate (deg) F = fluid density (kg m
3) τ = shear stress (Pa) τ1, τ2 = time constants (s) τm = mean residence time (s) τy = fluid yield stress (Pa) Abbreviations

BI = bottom inlet BO = bottom outlet CFSTR = continuous-flow stirred tank reactor HG = Hayward Gordon rpm = revolutions per minute RSB = retreat swept-back RT = Rushton turbine TI = top inlet TO = top outlet VFD = variable-frequency drive

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