Pump Capacity and Power Consumption of Two Commercial In-line

Article pubs.acs.org/IECR

Pump Capacity and Power Consumption of Two Commercial In-line High Shear Mixers Qin Cheng, Shuangqing Xu, Jintao Shi, Wei Li, and Jinli Zhang* School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, P. R. China ABSTRACT: Two main commercial in-line high shear mixer (HSM) configurations, including the dual rows ultrafine teethed and the single-row blade-screen in-line units, were investigated under the pump-fed mode in order to disclose the pump capacity and power consumption characteristics. Results indicate that the pump capacity of the teethed in-line HSM is rather poor, with maximum pumping heads of 2.31−2.72 m and a maximum pumping efficiency of 1.5%. By contrast, the blade-screen in-line HSM demonstrates maximum heads around 4.33−4.76 m and a maximum pumping efficiency of 7.3%. The power number data of both units with the bearing loss subtracted can be correlated by the Froude number modified power consumption model. The predicted power numbers show good agreement with the experimental data for both in-line HSMs. The results obtained here are fundamental for the performance assessment as well as the design and selection of in-line HSMs.

1. INTRODUCTION As a promising equipment to develop novel process intensification techniques, high shear mixers (HSMs) have attracted increasing attention in chemical, biochemical, agricultural, and food-processing industries.1−14 HSMs have great potential to intensify chemical reactions with fast inherent reaction rates but relatively slow mass transfer due to their locally intense turbulence and shear.14−17 The applications of HSMs have been broadened from typical physical processes including homogenization, dispersion, emulsification, grinding, dissolving, and cell disruption to the chemical reaction processes. Patented fine chemical productions using HSMs have been booming recently.18−25 However, the current understanding of HSMs still needs to be advanced in order to predict or assess the device performance. The process development, scale-up, and operation of HSMs are mostly relied on engineering judgments and trial-and-errors other than sound engineering principles, which lead to high development costs, start-up problems, lost time to market, and considerable material waste.1,26,27 HSMs can be generally categorized into batch and in-line units. Compared with batch units, in-line HSMs have the advantages of continuous operation, short residence time, and high throughput.2,28 Commercial in-line HSMs are usually designed as either the teethed or blade-screen configuration. The presence of blades on the rotor is a significant feature affecting the device performance.1,2,29 In-line HSMs with blades, such as Silverson series, can simultaneously pump and disperse materials. While for the teethed in-line units, an external pump is often needed for feeding.1 In practice, it is often convenient and preferable to use a separate pump to adjust the residence time of the materials for dispersion and reactive mixing by controlling the flow rate independently, while varying the rotor speed controls the level of energy input and the resulting turbulence and shear instead. Power consumption, which is an important parameter for the performance assessment and motor selection of an in-line HSM, can be measured by the electric,30 calorimetric,29,31 or torque method.28,32,33 The electric method directly measures © 2012 American Chemical Society

the apparent voltage and current (assuming alternating current motors used) but suffers from the problem caused by the varied motor efficiency and power factor with respect to load.30 The calorimetry technique, which insulates the system and measures the temperature rise over time, is not so reliable in accuracy due to the effectiveness of the insulation and the changes of fluid physical properties with temperature.34 The method based on measuring the torque is preferred and believed to be more accurate in the open literature.28,32,33 In an in-line HSM, the flow rate can be controlled independently of the rotor speed. Experimental results show that power consumptions of in-line HSMs depend on not only the rotor speed but also the processing flow rate.28−33 Sparks32 studied the power consumption of several single-row teethed and blade-screen in-line HSMs using water, where the axially straight teeth slots and the round screen holes were rather coarse (with opening percentages over 50%). On the basis of the kinetic energy of a fluid element on the rotor tip, a power consumption correlation in proportion to ρQN2D2 was obtained, where ρ is the density (kg/m3), Q is the volumetric flow rate (m3/s), N is the rotor speed (s−1), and D is the rotor diameter (m). However, as criticized by Hall et al.31 and Kowalski et al.,28 this expression predicted incorrect zero power consumption at zero flow rate. Kowalski30 proposed that the total power consumption of an in-line HSM consisted of three parts: the power required to rotate the rotor against the liquid in the gap (“tank term”, PT); the power requirements from the flow of fluid through the gap (“flow term”, PF); and the power loss by vibration and noise, kinetic energy losses at the entrance and exit, and the accuracy of measurements, etc. (“losses term”, PL). As shown in eq 1, the “tank term” PT is analogous to the power consumption in a stirred vessel, while the “flow term” PF accounts for the pumping action of the in-line mixer. Received: Revised: Accepted: Published: 525

August 30, 2012 November 25, 2012 December 12, 2012 December 12, 2012 dx.doi.org/10.1021/ie3023274 | Ind. Eng. Chem. Res. 2013, 52, 525−537

Industrial & Engineering Chemistry Research

Article

Figure 1. Geometric details of (a and c) the stator and (b and d) the rotor in (a and b) the teethed and (c and d) the blade-screen in-line high shear mixers.

mm) with 1 mm slots; while the stator has two rows of 30 teeth (15° backward inclined; with outer diameters of the inner and outer teeth rows of 53.5 and 66 mm) with 2 mm slots. The shear gap width (i.e., the annular space between the assembled rotor and stator) is 0.5 mm; and the tip-to-base clearance (i.e., the axial space from the rotor tip to the stator base or that from the stator tip to the rotor base) is 1 mm. Geometric details of the stator and rotor teeth are shown in Figure 1a and b. Alternatively, the mixer can be assembled into a blade-screen configuration, where the rotor has a single row of 6 blades (15° backward inclined; with the same rotor outer swept diameter of 59.5 mm) while the single-row stator screen (with the same stator outer swept diameter of 66 mm) has two rows of 3 mm × 3 mm square holes with 30 holes in each row. The shear gap width and tip-to-base clearance are kept the same as those of the teethed design, i.e., 0.5 mm and 1 mm, respectively. The opening areas are calculated as both 23.6% of the outer circular face for the teethed and screen stators. Figure 1c and d show the geometric details of the blades and screen holes. 2.2. Materials and Properties. The Newtonian fluids of pure water and glycerin (Sinopharm Chemical Reagent Co., Ltd.) aqueous solutions and the non-Newtonian fluids of carboxymethyl cellulose (CMC, Tianjin Bodi Chemical Co., Ltd.) aqueous solutions were used. The densities of all fluids were measured by the pycnometer method. A viscometer (LVDV-II+Pro, Brookfield) and a rheometer (MARS III, Thermo Scientific) were utilized for the rheology measurements of the Newtonian and non-Newtonian fluids, respectively. For the Newtonian working fluids, the viscosities and densities were measured at temperatures from 20 to 50 °C

where Pshaft is the shaft power (W), Pfluid is the net power delivered to fluid including the contributions by PT and PF (W), Poz is the power number at zero flow rate, and k1 is the model constant. Experimental results from several recent publications have shown the rationality of this model.28,29,31,33 However, it is worth noting that, the in-line HSMs investigated in these studies all have blades on the rotors providing positive pumping efficiencies, e.g., either the typical blade-screen configuration, or the modification from the typical teethed unit to include an additional “pumping wheel”. In this paper, two main commercial in-line HSMs, including the teethed and the blade-screen configurations, were investigated under the pump-fed mode in order to study the pump capacity and power consumption characteristics. By an analogy with a centrifugal pump, the pump capacity of the inline HSMs was characterized by the pumping head and pumping efficiency. The Froude number adjusted power consumption model was utilized for the power prediction.

2. EXPERIMENTAL SECTION 2.1. Experimental Apparatus. The experimental in-line HSM is a custom-built pilot-scale unit of FDX series provided by FLUKO. The rotor and stator of the mixer are designed as interchangeable so that the two main commercial rotor−stator designs can be expediently tested in the same model. Originally, the mixer is a rotor−stator teethed design, where the rotor consists of two rows of 52 teeth (axially straight; with outer diameters of the inner and outer teeth rows of 47 and 59.5 526

dx.doi.org/10.1021/ie3023274 | Ind. Eng. Chem. Res. 2013, 52, 525−537


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Table 1. Values of the Constants to Correct Viscosity (or Apparent Viscosity) and Density under Different Temperatures viscosity (or apparent viscosity) working fluids

a1

a2

a3

Gly no. 1 Gly no. 2 Gly no. 3 water CMC no. 1 CMC no. 2

−55.4 −44.5 −67.8 2.4 122.3 −175.3

0.05 0.05 0.09 −0.02 −0.22 0.28

11653 8325 10392 −1062 −16513 27223

density n

R2

b1

b2

0.693 0.741

0.999 1.000 0.999 0.999 1.000 1.000

1351 1326 1059 554 754 648

−0.09 −0.20 1.00 3.20 2.01 2.65

and found to fit well using eqs 2 and 3, respectively, where μ is the viscosity from 0.001 to 0.4 Pa·s, ρ the density from 988 to 1252 kg/m3, T is the absolute temperature from 293 to 323 K, and a1 ∼ a3 and b1 ∼ b3 are the fitted constants as shown in Table 1. a ln μ = a1 + a 2T + 3 (2) T

ρ = b1 + b2T + b3T μa = Kγav

n−1

=e

2

a1+ a 2T + a3 / T

γav

−8.6 −6.7 −2.5 −5.7 −3.8 −4.8

× × × × × ×

10−4 10−4 10−3 10−3 10−3 10−3

1.000 1.000 0.999 0.999 1.000 0.996

utilized to account for bearing losses in this paper. It was found that, when using the low viscous water as working fluid, the type of the fitted stator (i.e., the teethed or screen configuration) showed no obvious influence on the measured bearing loss. 2.4. Data Processing. The head of the experimental in-line HSM was calculated as H = (h2 − h1) +

(3) n−1

R2

b3

p2 − p1 ρg

+

u 2 2 − u12 + 2g

∑ Hf

(5)

where H is the head of the mixer (m), h is the mounting height of the pressure gauge (m), p is the measured pressure (Pa), u is the mean flow velocity calculated from the corrected volumetric flow rate and the inlet or outlet tube diameter (m/s) (d1 = 25 mm, d2 = 20 mm), ΣHf is the head loss by friction and local resistance in the inlet and outlet tubes35 (m), ρ is the density of the working fluid (kg/m3), g is the gravitational acceleration (= 9.81 m/s2). Subscripts 1 and 2 denote the inlet and outlet conditions, respectively. The shaft power and net power delivered to fluid were expressed as

(4)

For the non-Newtonian working fluids, the physical properties were measured at temperatures from 15 to 30 °C. The densities demonstrated relatively small difference from 1008 to 1017 kg/ m3 and were also fitted by eq 3. The rheologies of the CMC solutions were found to obey power law as indicated by eq 4, where μa is the apparent viscosity (Pa·s), K is the consistency index from 0.227 to 1.360 Pa·sn, γav the average shear rate (s−1), and n the power law index. The temperature dependency of K was expressed in the similar form as eq 2 and the small difference of n was averaged out within the temperature ranges.33 The values of the constants for fitting the physical properties of the non-Newtonian fluids were also listed in Table 1. 2.3. Experimental Procedure. The pump capacity of the teethed in-line HSM was rather poor,1 therefore the mixer was fed by a centrifugal pump. The blade-screen HSM was also operated under the pump-fed mode. The in-line HSM was installed in the recirculation loop of a 60 L storage tank, where two brass coil pipes were utilized in parallel for heat removal and temperature control. Under the pump-fed mode, the volumetric flow rates of the working fluids were controlled by a valve downstream of the pump and measured by a rotameter. The temperatures and pressures at the inlet and outlet of the in-line HSM were monitored via temperature probes and precision pressure gauges, respectively. The rotor speed of the HSM (up to ∼3500 rpm) was controlled by an inverter. The shaft torque and the rotor speed were measured on the drive shaft using an AKC-215 transducer (China Academy of Aerospace Aerodynamics) and recorded by the data-logging system at a frequency of 1 Hz. The actual volumetric flow rates of the fluids other than water from the rotameter reading were carefully calibrated by measuring the volume and flow time under the same temperature ranges as those during the power measurements. The bearing losses were measured at zero flow rate by rotating the shaft at different rotor speeds without the rotors attached. The underlying assumption is that the power consumption by drag on the shaft should be negligibly small compared to the bearing loss. Therefore, the measured power without rotors when using pure water as the working fluid was

Pshaft = 2πNM

Pfluid = 2πNM − 2πNM n

(6) (7) −1

where Pshaft is the shaft power (W), N is the rotor speed (s ), and M is the torque (N·m). Pfluid is the net power delivered to fluid (W), and Mn is the torque for the bearing loss correction, measured using water with no rotor attached (N·m). The pumping efficiency, η, and the power number, Po, were then determined by η=

QρgH Pshaft

Po =

(8)

Pfluid ρN3D5

(9)

The power-law Reynolds number of the non-Newtonian CMC solutions, Repl, was given by Repl =

ρN 2 − nD2 K

(10)

In this paper, calculations of the power number Po and the Reynolds number Re (= ρND2/μ) or Repl were based on the rotor outer swept diameter of 59.5 mm. The corrected fluid physical properties based on the averaged inlet and outlet temperatures were utilized in data processing.

3. RESULTS AND DISCUSSION 3.1. Pump Capacity. The head, by an analogy with a centrifugal pump, is characteristic for the pump capacity of an 527



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Figure 2. Head of the teethed in-line high shear mixer.

in-line HSM. Figure 2 shows the head of the teethed in-line HSM when processing different working fluids. The head increases with rotor speed and decreases with flow rate. At lower rotor speeds of 500−1000 rpm, the teethed unit mostly causes a pressure drop rather than a pumping action at almost all fluid flow rates investigated here (see the negative heads in Figure 2), confirming the poor pumping capacity of the teeth design. At the maximum flow rate of each fluid, the mixer demonstrates negative head under a broad range of rotor speeds (even up to 2500 rpm). The maximum pumping heads

of the mixer are just 2.31−2.72 m at the maximum rotor speed of 3500 rpm and zero flow rate of each fluid. As shown in Figure 3, the pumping efficiencies of the teethed unit at lower rotor speeds of 500−1000 rpm are predominantly negative and decrease with flow rate to even lower than −20%. A peak pumping efficiency of 1.5% is observed at 3500 rpm when processing water at 1000 L/h or CMC no. 2 at 889.77 L/ h. In comparison, Sparks32 reported a peak pumping efficiency of 6.7% at 3500 rpm and the water flow rate of 1800 L/h for an in-line teethed HSM of similar scale (with the rotor outer swept diameter of 61.44 mm), where the rotor and stator had single 528



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Figure 3. Pumping efficiency of the teethed in-line high shear mixer.

significantly or remains relatively stable with flow rate. At the lower rotor speeds of 500−1000 rpm, the blade-screen unit does not pump fluids well, either. The maximum pumping heads of the blade-screen unit are 4.33−4.76 m at 3500 rpm, over 60% higher than those of the teethed unit. As presented in Figure 5, the pumping efficiency of the blade-screen HSM shows an increase with the flow rate at higher rotor speeds as well as with the fluid viscosity (or apparent viscosity), which is an obvious difference from that of the teethed HSM. A peak pumping efficiency of 7.3% is observed at 3500 rpm and water flow rate of 2000 L/h. By contrast, Kowalski et al.28 reported a pumping efficiency of 11.5% at 5000 rpm and water flow rate of 2000 L/h for a double-row blade-screen Silverson in-line unit of

rows of 18 coarse, axially straight teeth. Therefore, the dual rows and ultrafine teethed design (with the stator teeth backward inclined) in the custom-built teethed HSM breaks the already-poor pumping action and should be responsible for the low pumping efficiency here. It deserves mention that the low pumping efficiency is no longer a problem when using a separate pump for feeding. Furthermore, the custom-built inline teethed HSM studied in this article can avoid the channeling and/or short circuiting defects that may occur in the single-row, coarse teethed units,1,27,36 which is of more practical importance in the reactive mixing processes. The pumping head of the blade-screen HSM, as shown in Figure 4, also increases with rotor speed but decreases less 529



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Figure 4. Head of the blade-screen in-line high shear mixer.

the stator slots or holes to counteract the pumping action. However, it is the dissipation of this energy that promotes mixing.1 As a matter of fact, the dispersing performance of the teethed in-line HSMs is never inferior to the blade-screen units, which explains their widespread applications and their survival after decades of developments. As for the industrial applications involving large flow rates and/or high viscosities of the fluids, even the blade-screen in-line HSMs cannot provide sufficient pump capacity, considering the upper limit of the industrial operating rotor speed. Therefore, the external pump-fed mode is essential for both the teethed and blade-screen in-line HSMs in practice. 3.2. Power Consumption. The input shaft power into the mixer is an important parameter for motor selection. Figure 6 presents the shaft power of the teethed in-line HSM as a

similar scale (with the rotor outer swept diameter of 63.5 mm) and opening percentage on the screen (∼21%). This pumping efficiency difference can be reasonably attributed to configurational difference of the blades (e.g., rows, total numbers, orientations and axial heights, etc.), considering the weak dependence of pumping efficiency on the rotor speed higher than 3000 rpm (see Figure 5d). The better pump capacity is certainly an advantage of the blade-screen configuration over the teethed one; however, it is worth noting that, in-line HSMs are basically designed for dispersion and mixing rather than pumping.32 The pumping efficiencies of the teethed and blade-screen in-line HSMs are both much lower than those of conventional centrifugal pumps. In the in-line HSMs, the tangential velocities resulting from rotor rotation are redirected radially as the fluid passes through 530



Article

Figure 5. Pumping efficiency of the blade-screen in-line high shear mixer.

exponential increase with the rotor speed. Power law fits were then conducted between the shaft power and the rotor speed for each flow rate of each working fluid. The indexes are found varied with the working fluid, i.e, 1.2−1.3 for Gly nos. 1 and 2 and 1.5−1.6 for Gly no. 3, water, and CMC nos. 1 and 2. Figure 7 shows the normalized shaft power (not power number) Pshaft/ρN3D5 as a function of the Reynolds number in the double logarithmic coordinate. A linear relationship is observed between the logarithms of Pshaft/ρN3D5 and Re (or Repl) for all working fluids. Regressions show that Pshaft/ρN3D5 is proportional to Re−1.5 for Newtonian fluids and to Repl−1.2 for non-Newtonian CMC solutions. The net power delivered to

function of the rotor speed when processing different working fluids. The shaft power shows an increase with the rotor speed, flow rate and fluid viscosity (or apparent viscosity). For example, the shaft power ranges from 166 to 258 W at N = 3500 rpm when the water flow rate increases from 0 to 2000 L/ h (see Figure 6d). The shaft power at N = 2000 rpm, Q = 1218.48 L/h for Gly no. 3 is 120 W; while at N = 2000 rpm and an approximate flow rate of Q = 1213.64 L/h for Gly no. 2, this increases to 199 W (see Figure 6b and c). The shaft power at N = 3000 rpm and zero flow rate is 199 and 160 W for CMC nos. 1 and 2, respectively (see Figure 6e and f). Under the same flow rate for each working fluid, the shaft power demonstrates an 531



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Figure 6. Shaft power of the teethed in-line high shear mixer as a function of the rotor speed.

fluid, obtained with the bearing loss subtracted, presents similar variations as the shaft power and is therefore not shown here. Power law fits of the net delivered power versus rotor speed give indexes of 1.1−1.2 for Gly nos. 1 and 2 and 1.6−2.0 for Gly no. 3, water, and CMC nos. 1 and 2. The index near 2 for the working fluid of water is consistent with earlier results from the pump-fed teethed HSMs reported by Sparks.32 The power curve, usually expressed as the relationship between the power number and the Reynolds number, is often used to predict the power requirements for given fluid properties, impeller dimensions, and operation parameters.

The power number data of the teethed in-line HSM with the bearing loss subtracted are presented as a function of the Reynolds number in Figure 8. The data exhibit exponential decrease at lower Reynolds number and approach to constant at higher Reynolds number. The constant power number of the teethed in-line HSM approximates Poz(t) = 0.147 under the Reynolds number above 8.3 × 104. The flow is considered as turbulent when processing water in the Reynolds number ranges from 2.7 × 104 to 2.1 × 105. The constant of k1 in Kowalski’s power consumption model can be obtained by fitting the turbulent power data. It deserves to note that the 532



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expressed in dimensionless forms as eqs 11 and 12, respectively, where Fl is the flow number defined as Fl = Q/ND3. Poz = Poz(l) + Poz(t ) = KPRe c1Fr c2 + Poz(t) c1

c2

Po = KPRe Fr + Poz(t) + k1Fl

(11) (12)

The power number data at zero flow rate for the three Newtonian fluids other than water are fitted using eq 11, which gives KP = 322.57, c1= −0.39, and c2= −0.65. While for the nonNewtonian CMC solutions, the power-law Reynolds number Repl is used instead of Re in data fitting. With the fixed values of c1, c2, Poz(t), and k1 in eq 12, the KP values of 40.43 and 25.16 are obtained from regressions for the teethed HSM when processing CMC nos. 1 and 2, respectively. It is expected that eq 12 should be capable of predicting the power numbers from the laminar, transition to turbulent regime. However, the exponent of −0.39 on the Reynolds number is not low enough to diminish the laminar term on the right of eq 12 for a smooth transition to the power number expression in the fully turbulent regime as eq 13.

Figure 7. Normalized shaft power of the teethed in-line high shear mixer as a function of the Reynolds number.

Po = Poz(t ) + k1Fl

(13)

Therefore, eq 13 was utilized for the power predictions in the fully turbulent regime with Re ranging from 2.7 × 104 to 2.1 × 105; while in the laminar to transition regime with Re from 105 to 7.3 × 103 or Repl from 46 to 2.0 × 103 eq 12 was used. The power data from Gly no. 3, with Re ranging from 1.4 × 104 to 1.0 × 105, is found to be better fitted by eq 12. This is probably because the flow may not be fully turbulent away from the rotor−stator head in the bulk region of the mixer chamber. As shown in Figure 9, the calculated power numbers from this

Figure 8. Power number of the teethed in-line high shear mixer as a function of the Reynolds number.

measured power with and without rotors are rather close at zero water flow rate. Consequently, the power numbers calculated using the net delivered power show fluctuation and do not conform to the turbulent power model well. Fortunately, this zero water flow rate is not important in practice, since the in-line HSMs are usually utilized for processing more viscous fluids,1 or operated at higher flow rates aiming for high throughputs.2,28 Therefore, the power number data under zero water flow rate are excluded in the model constant fitting, and this yields k1 = 14.49. Cooke et al.33 suggested the power requirement at zero flow rate in the transition regime consisting of the contributions by a laminar and a turbulent part, with the laminar Poz inversely proportional to the Reynolds number while the turbulent Poz almost constant. However, discontinuity of the power curve in Figure 8 indicates that Poz is not a sole function of the Reynolds number. Myers et al.37 reported similar discontinuity in the measured power curve for a batch HSM and the Froude number (Fr = N2D/g) adjusted method was introduced in order to yield a smooth correlation. Similar treatment is conducted in this article and the laminar Poz is presented as a function of both the Reynolds number and Froude number. According to Kowalski’s power consumption model (see eq 1), the power numbers at zero and nonzero flow rates can then be

Figure 9. Comparison between the experimental and predicted power numbers for the teethed in-line high shear mixer.

“zonal correlation” approach show good agreement with the experimental results, with an overall average error of 20.1%. The few inaccurate predictions are observed only for the case under the lowest rotor speed of 500 rpm. Shown in Figure 10, the shaft power of the blade-screen HSM presents similar variations as those of the teethed unit, i.e., an increase with rotor speed, flow rate, and fluid viscosity (or apparent viscosity). In comparison, the shaft power of the blade-screen and teethed in-line HSMs are relatively close when processing the fluids of water, Gly nos. 2 and 3 and CMC no. 2; 533



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Figure 10. Shaft power of the blade-screen in-line high shear mixer at different rotor speeds.

for Newtonian fluids and to Repl−1.2 for non-Newtonian CMC solutions. Power-law fits of the net delivered power to fluid by the blade-screen HSM versus rotor speed give indexes of 1.1−1.3 for Gly nos. 1 and 2 and 1.6−2.0 for Gly no. 3, water, and CMC nos. 1 and 2, similar to those of the teethed unit. Figure 12 shows the power curve of the blade-screen HSM. The constant turbulent power number is found to be Poz(t) = 0.241 under the Reynolds number above 1.4 × 105. With the power number data at zero water flow rate excluded, k1 = 8.38 is obtained by fitting the turbulent power data from the working fluid of water

while for Gly no. 1 and CMC no. 1, the teethed HSM draws more shaft power than the blade-screen unit under all rotor speeds and flow rates. The shaft power of the blade-screen HSM shows similar power law relationship with rotor speed, with indexes of 1.1−1.3 for Gly nos. 1 and 2 and 1.4−1.6 for Gly no. 3, water, and CMC nos. 1 and 2. The normalized shaft power of the blade-screen HSM is also plotted versus the Reynolds number in the double logarithmic coordinate, as shown in Figure 11. Similar trends to those for the teethed unit are observed, i.e., the proportionality of Pshaft/ρN3D5 to Re−1.5 534



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Figure 11. Normalized shaft power of the blade-screen in-line high shear mixer as a function of the Reynolds number.

Figure 13. Comparison between the experimental and predicted power numbers for the blade-screen in-line high shear mixer.

Table 2. Turbulent Power Consumption Model Constants for the Teethed and Blade-Screen In-line High Shear Mixers in-line high shear mixers

Poz(t)

k1

dual ultrafine teethed single row blade-screen dual fine Silverson33 dual standard Silverson33

0.147 0.241 0.145 0.241

14.49 8.38 8.79 7.75

the other hand, for the single-row blade-screen HSM, the Poz(t) value of 0.241 is equal to that for the Silverson 150/250 MS inline mixer fitted with dual standard screens; while the k1 value of 8.38 is slightly higher than 7.75 for the dual standard Silverson.33 Considering the fact that the flow number is rather small in the high Re turbulent regime, the contribution by the “flow term” to the power consumption is small. Therefore, the blade-screen HSM in this article draws similar power as that from the dual standard Silverson.

Figure 12. Power number of the blade-screen in-line high shear mixer as a function of the Reynolds number.

(Re = 2.8 × 104−2.0 × 105). Due also to the discontinuity in the power curve, eq 11 is adopted for correlating the power number data at zero flow rate for the three Newtonian fluids other than water, which yields KP = 624.81, c1= −0.53, and c2= −0.56. With the fixed values of c1, c2, Poz(t), and k1 in eq 12, the KP values of 39.42 and 54.33 were obtained from regressions for the blade-screen HSM when processing CMC nos. 1 and 2, respectively. The “zonal correlation” approach, as previously described for the power prediction of the teethed HSM, is also adopted for the estimation of the power consumption of the blade-screen HSM. As shown in Figure 13, good agreement is observed between the measured and predicted power numbers, with an overall average error of 16.3%. Table 2 lists the values of the turbulent power consumption model constants for both the teethed and blade-screen HSMs, along with those reported in the literature for comparison purpose. The turbulent power number Poz(t) of 0.147 for the ultrafine teethed in-line HSM is very close to 0.145 for the Silverson 150/250 MS in-line mixer fitted with dual fine screens. Whereas the k1 value of 14.49 is much higher than 8.79 for the dual fine Silverson,33 indicating a more significant dependence of the power consumption on the processing flow rate for the ultrafine teethed unit. Under the fully turbulent regime with the same flow number, the ultrafine teethed HSM draws over 60% higher power than the dual fine Silverson. On

4. CONCLUSIONS The pump capacity and power consumption of the dual rows ultrafine teethed and the single-row blade-screen in-line HSMs were investigated under the pump-fed mode. Both HSM configurations do not pump well at lower rotor speeds of 500− 1000 rpm. The heads of both HSMs increase with the rotor speed. As the flow rate increases, the head of the teethed unit drops more significantly than that of the blade-screen unit. The pump capacity of the teethed HSM is rather poor, with maximum pumping heads of 2.31−2.72 m and a maximum pumping efficiency of 1.5%. At the maximum flow rate of each fluid, the teethed unit demonstrates negative heads and pumping efficiencies under a broad range of rotor speed. By contrast, the blade-screen HSM presents maximum heads around 4.33−4.76 m and a maximum pumping efficiency of 7.3%. The normalized shaft power Pshaft/ρN3D5 of both in-line HSMs shows the proportionality to Re−1.5 for the Newtonian fluids and to Repl−1.2 for the non-Newtonian CMC solutions. The power number data of both units with the bearing loss subtracted can be correlated with a Froude number modified power model. The predicted power numbers from the “zonal correlation” approach show good agreement with the experimental data for both in-line HSMs. The power 535



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Poz(l) = laminar power number at zero flow rate, − Poz(t) = turbulent power number at zero flow rate, − p = pressure, Pa Q = volumetric flow rate, (m3/s) T = absolute temperature, K u = mean flow velocity, m/s

consumption of the dual rows ultrafine teethed HSM shows more significant dependence on the flow rate than the dual fine Silverson unit of the similar scale. In the high Re turbulent regime with the same flow number, the ultrafine teethed HSM draws over 60% higher power than the dual rows Silverson with fine screen; while the single-row blade-screen HSM draws similar power as that from the dual rows Silverson with standard screen. For a successful design and scale-up of the high shear process, one should take into consideration both the pump capacity and power consumption characteristics of the in-line HSMs together. For the applications where the materials are relatively easy to disperse and the throughput is not very large, the blade-screen HSMs with optimized pumping capacity would be good choice due to their simultaneous pumping and dispersing capability. While for the applications where high energy inputs are required (e.g., high viscosity, large throughput, some multiphase systems, etc.), the in-line HSMs with optimized mixing capability are needed and the pump-fed operation mode is preferred, whether the teethed or bladescreen configuration is chosen.

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Greek Symbols

α, β = constants, − γav = average shear rate, s−1 η = pumping efficiency, − μ = viscosity, Pa·s μa = apparent viscosity, Pa·s ρ = density, kg/m3 ΣHf = head loss by friction and local resistance, m

Subscripts

1 = inlet conditions 2 = outlet conditions Dimensional Groups

AUTHOR INFORMATION

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Corresponding Author

*Tel.: 86-22-27890643. Fax: 86-22-27890643. E-mail address: [email protected].

Fl = Q/ND3 = flow number Fr = N2D/g = Froude number Po = Pfluid/ρN3D5 = power number Re = ρND2/μ = Reynolds number Repl = ρN2−nD2/K = power-law Reynolds number

REFERENCES

(1) Atiemo-Obeng, V. A.; Calabrese, R. V. Rotor-stator mixing devices. In Handbook of Industrial Mixing: Science and Practice; Paul, E. L., Atiemo-Obeng, V. A., Kresta, S. M., Ed.; John Wiley & Sons: NJ, 2004. (2) Zhang, J.; Xu, S.; Li, W. High shear mixers: A review of typical applications and studies on power draw, flow pattern, energy dissipation and transfer properties. Chem. Eng. Process. 2012, 57−58, 25. (3) Adler-Nissen, J.; Mason, S. L.; Jacobsen, C. Apparatus for emulsion production in small scale and under controlled shear conditions. Food Bioprod. Process. 2004, 82, 311. (4) Gingras, J.-P.; Tanguy, P. A.; Mariotti, S.; Chaverot, P. Effect of process parameters on bitumen emulsions. Chem. Eng. Process. 2005, 44, 979. (5) El-Jaby, U.; Cunningham, M.; Mckenna, T. F. L. Comparison of emulsification devices for the production of miniemulsions. Ind. Eng. Chem. Res. 2009, 48, 10147. (6) Hall, S.; Cooke, M.; El-Hamouz, A.; Kowalski, A. J. Droplet break-up by in-line Silverson rotor−stator mixer. Chem. Eng. Sci. 2011, 66, 2068. (7) Baldyga, J.; Orciuch, W.; Makowski, L.; Malskibrodzicki, M.; Malik, K. Break up of nano-particle clusters in high-shear devices. Chem. Eng. Process. 2007, 46, 851. (8) Baldyga, J.; Makowski, L.; Orciuch, W.; Sauter, C.; Schuchmann, H. Deagglomeration processes in high-shear devices. Chem. Eng. Res. Des. 2008, 86, 1369. (9) Baldyga, J.; Orciuch, W.; Makowski, L.; Malik, K.; Ö zcan-Taşkin, G.; Eagles, W.; Padron, G. Dispersion of nanoparticle clusters in a rotor-stator mixer. Ind. Eng. Chem. Res. 2008, 47, 3652. (10) Hassan, A.; Hassan, A. High shear process for producing micronized waxes. US 20100125157A1, May 20, 2010. (11) Lee, F. P.-H.; Wong, R. W.-N.; Kao, S. V. Process for preparing phase change inks. US 20070030322A1, Feb. 8, 2007. (12) Kamahara, T.; Takasuga, M.; Tung, H. H.; Hanaki, K.; Fukunaka, T.; Izzo, B.; Nakada, J.; Yabuki, Y.; Kato, Y. Generation of fine pharmaceutical particles via controlled secondary nucleation under high shear environment during crystallizationProcess development and scale-up. Org. Process Res. Dev. 2007, 11, 699. (13) Lo, E.; Mattas, E.; Wei, C.; Kacsur, D.; Chen, C.-K. Simultaneous API particle size reduction and polymorph transformation using high shear. Org. Process Res. Dev. 2012, 16, 102.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is financially supported by NSFC (20836005, 21076144) and the Special Funds for Major State Basic Research Program of China (2012CB720300). The authors gratefully acknowledge FLUKO Equipment Shanghai Co., Ltd., for providing the custom-built in-line high shear mixer of FDX series and offering technical support. The authors also wish to thank associate professor Lvhong Zhang and Miss Jing Zhang from Tianjin University for the kind assistance and useful discussion and colleagues from Chemical Engineering Experimental Center (CEEC) of Tianjin University for the debugging of the data-logging system.

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NOMENCLATURE a1−a3, b1−b3, c1−c2, KP, k1 = constants, − D = outer diameter, m d = inner diameter of the inlet or outlet tube, m g = gravitational acceleration, m/s2 H = head, m h = mounting height, m K = consistency index, Pa·sn M = torque, N·m Mn = torque measured without the rotor, N·m N = rotational speed, s−1 n = power-law index, − PF = power requirements from the flow of liquid through the gap, W Pfluid = net delivered power to fluid, W PL = power loss, W Pshaft = shaft power, W PT = power required to rotate the rotor against the fluid resistance, W Poz = power number at zero flow rate, − 536



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Pump Capacity and Power Consumption of Two Commercial In-line

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