Experimental Study on the Entrainment Characteristics of Ultrafine

Dec 28, 2012 - ABSTRACT: The entrainment characteristics of Geldart group C powder from solid mixtures (groups A and C) were investigated in a fluidiz...
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Experimental Study on the Entrainment Characteristics of Ultrafine Powder in a Fluidized Bed with Vibrator and Agitator Fuming Yang, Li Wang,* Shaowu Yin, Yanhui Li, Chuanping Liu, and Lige Tong School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China ABSTRACT: The entrainment characteristics of Geldart group C powder from solid mixtures (groups A and C) were investigated in a fluidized bed (inner diameter of 40 mm and height of 150 mm) equipped with two vibrators and an agitator. Silicon powders of mean size 2.2 and 0.9 μm were adopted as entrained material (group C), hollow alumina pellets of mean sizes 359, 505, 650, 775, 996, and 1200 μm were used as coarse particles (group A), and industrial nitrogen was applied as carrier gas. At ambient temperature (20 °C) and atmospheric pressure, the effects of the size of coarse particles (D, 359−1200 μm), mass ratio of coarse to fine particles (M, 0−1.5), ratio of static bed height to diameter (H, 0.875−1.625), rotational speed of agitator (ω, 27−54 rps), vibration intensity (Γ, 0−5.0) and superficial velocity of nitrogen gas (V, 0.22−0.55 m/s) on the entrainment characteristics were experimentally studied in sequence. In the scope of this work, the increase of M, Γ, or V could always improve the entrainment characteristics, while there exists an optimal value for D, H, or ω to obtain the optimum entrainment characteristics. The entrainment rate constant is an order of magnitude larger than that without vibration and agitation, which shows the significant effects of vibration and agitation on the improvement of entrainment characteristics. A relational expression is derived to unify the experimental data, which gives a good fitting result. fluidized bed feeder, and the effects on entrainment characteristics were investigated. The entrainment characteristics in gas−solid fluidized bed have been investigated extensively. Shin et al.22 performed experiments on the entrainment characteristics of fine powder from solid mixtures in a conical and a cylindrical fluidized bed, respectively. They discovered that the entrainment rate increased as the gas velocity increased but decreased as the content of fine powders in the cylindrical fluidized beds increased and was unaffected by changing the static bed height. At a given gas flow rate, the entrainment rate constants from cylindrical fluidized beds were 5−12 times higher than those of conical fluidized beds; therefore, a cylindrical fluidized bed should be adopted in the fluidized bed feeder. Choi et al.23−25 investigated the qualitative effect of temperature on the particle entrainment rate at the freeboard gas exit of a gas fluidized bed. According to their results, the particle entrainment rate increased, after an initial decrease, as the temperature increased. The temperature at the minimum entrainment rate increased as the gas velocity increased. The effect of temperature on the particle entrainment rate decreased as either the gas velocity or the particle density increased. An empirical equation was developed by nonlinear regression using the previous experimental results, which related the entrainment rate constant to temperature, gas velocity, and particle size. The equation may be used to predict particle entrainment rates in both cold and hot model bubbling fluidized beds reasonably well, whereas it was not applicable for cohesive particles because no interparticle forces were considered. Choi et al.26

1. INTRODUCTION The dispersed cloud of powder feeding into an aerosol flow reactor (e.g., the fluidized bed reactor used in continuous preparation of ultrafine silicon nitride powder1) should meet three requirements: (1) low velocity, for the purpose of long residence time in the reactor; (2) small size, so as to complete the conversion within a reasonable time; (3) high powder gas ratio, which is in favor of the production efficiency and gas utilization. Various types of feeders are available for the feeding of powder, such as mechanical feeders,2,3 pneumatic feeders,4 and fluidized bed feeders,5,6 but each feeder can generally deal with specific types of materials. The mechanical feeder limits itself for medium sized particles and tends to plug if it is used in the transport of fine powder. The pneumatic feeder fits to large scale system, and it is confined to high gas consumption and low powder gas ratio. The fluidized bed feeder offers an advantage of aerated feeding of medium sized to fine solids with high powder gas ratio, simple construction, flow rate uniformity, and good operability. In some applications of fluidized bed, such as combustion and catalytic cracking, the particles entrainment tends to be considered as shortcoming,7 while it is an advantage in the fluidized bed feeders. It is well-known that fine power belongs to group C in Geldart’s classification, which is difficult to be fluidized or conveyed because of the considerable interparticle forces, such as London−van der Waals, electrostatic interactions and liquid bridging forces.8,9 The interparticle forces put forward many problems in the fluidization and entrainment of group C particles, such as channeling, slugging, and spouting.10 A series of methods have been developed to improve the fluidization characteristics, including addition of coarse particles,11,12 fine powder coating,13 vibration,14−16 agitation,17 sound waves,18,19 and magnetic20 and electric fields.21 In this work, a combination of vibration, agitation, and coarse particles was introduced into © 2012 American Chemical Society

Received: Revised: Accepted: Published: 1359

December December December December

24, 16, 28, 28,

2011 2012 2012 2012

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Figure 1. Schematic of experimental apparatus.

Table 1. Main Properties of Silicon Powder and Inert Medium species

avg. diam. (μm)

theoretical density (kg/m3)

min. fluidization velocity, Umf (m/s)

terminal velocity, Ut(m/s)

Geldart’s classification

Si powder Si powder Al2O3 pellet Al2O3 pellet Al2O3 pellet Al2O3 pellet Al2O3 pellet Al2O3 pellet

2.2 0.9 1200 996 775 650 505 359

2320 2320 560 560 560 560 560 560

3.91 × 10−06 6.54 × 10−07 0.269 0.185 0.112 0.079 0.048 0.024

3.58 × 10−04 5.99 × 10−05 24.5 16.9 10.3 7.22 4.36 2.20

C C A A A A A A

Figure 2. Size distribution of the ultrafine silicon powder.

particles influenced the entrainment characteristics. The entrainment rate constant increased as gas velocity increased and reached the order of magnitude of 10−3 kg/m2·s. The exertion of vibration and agitation on fluidized bed would change the bed structure, affect the sizes of agglomerates, and influence the entrainment characteristics. Currently, there is a lack of research on the roles of vibration and agitation on the entrainment characteristics of group C powders, on which this work conducted some experimental studies. The experimental results were compared with that of Liu et al.,12

also studied the effect of secondary gas injection on the particle entrainment rate, finding that the particle entrainment rate decreased with an increase of the secondary gas fraction. At a given secondary gas fraction, the entrainment rate decreased, after an initial increase, as the static bed height increased. Kim et al.27 discovered that the entrainment rate decreased exponentially with the freeboard height. Liu et al.12 studied effects of the addition of large particles on the entrainment characteristics of fine silicon powder (mean diameter of 3.7 μm) and found that both the type and addition fraction of large 1360

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because both Liu et al.12 and this work used silicon powder as entrained materials, the mean diameters of which are close to each other.

2.2.2. Entrainment Rate Constant. The entrainment rate constant (Ki, kg/m2·s)22 is defined in eq 2.

2. EXPERIMENT SETUP AND PROCEDURE 2.1. Experimental Apparatus. The experimental apparatus, which was composed of fluidized bed, gas supply system, and collector, is schematically shown in Figure 1. The body of the fluidized bed consisted of a Plexiglas column of 40 mm inner diameter (i.d.) and 150 mm height. The distributor was a perforated Plexiglas plate with an aperture of 1 mm and opening area ratio of 6.69%. A 1000 mesh screen was used to cover the surface of the distributor to prevent powder leaking from the bed into the plenum chamber. A discharge port (10 mm i.d.) normal to the axis of the bed was located at a height of 130 mm above the distributor plate. Two vibrators (rated voltage 12 V; rated speed 36 rps) were symmetrically mounted on the side of the column, at a height of 60 mm above the distributor plate. An agitation motor (rated voltage 12 V; rated speed 54 rps) was fixed on the upper flange of the column, on which attached a stirring bar (145 mm in length and 38 mm in profile diameter). The entire bed was supported by four springs. The collector was made of needle felt, which had a good effect of collection efficiency on the entrained powder used in this work. Ultrafine silicon powder was employed as the entrained materials, hollow Al2O3 pellets were adopted as the coarse particles, and industrial nitrogen gas (purity 99.5%) was used as the carrier gas. The physical properties of the silicon powders and Al2O3 pellets are listed in Table 1, in which the minimum fluidization velocity (Umf, m/s) and terminal velocity (Ut, m/s) were calculated through the formulas in ref 28. The size distributions of ultrafine silicon powders were shown in Figure 2. An experiment was conducted as follows: To begin, silicon powder and alumina particles were put into a drying chamber at 150 °C for 24 h to remove any adsorbed water. Then, a weighed quantity of premixed silicon powder and alumina particles was introduced into the bed. The tee valve was initially set fully open to atmosphere, and the flowmeter, vibrator, and agitator were set at predetermined values. The collector was weighed by an electronic balance with an accuracy of 0.001 g (denoted as m1). The test was then started by diverting the nitrogen flow into the bed and turning on the vibrators and agitator. After 2 min, a run was completed by turning off the gas, vibrator, and agitator. The collector was weighed again (denoted as m2). These procedures were repeated three times for each run, and the average of these repeated runs was taken as the final value for the calculations of the entrainment characteristics. 2.2. Experimental Parameters. 2.2.1. Vibration Intensity. Vibration intensity Γ is a dimensionless number, defined using the following:14

where m1 (kg) is the mass of collector at the beginning of an experiment, m2 (kg) is the mass of collector at the end of the experiment, Δt (s) is the time duration of the experiment, and S (m2) is the cross-sectional area of the column.

Γ = A(2πf )2 /g

K i = (m2 − m1)/(ΔtS)

(2)

3. RESULTS AND DISCUSSION Using control variable method, the effects of coarse particles size (D), mass ratio of coarse to fine particles (M), ratio of static bed height to diameter (H), rotational speed of agitator (ω), vibration intensity (Γ), and superficial velocity of nitrogen gas (V) on the entrainment characteristics were experimentally studied as follows. 3.1. Size of Coarse Particles (D). The addition of group A or B particles into group C could break agglomerates and enhance entrainment characteristics accordingly. Maintaining the variables M = 1.00, H = 1.125, ω = 54 rps, Γ = 5.0, and V = 0.44m/s, the effect of the size of coarse particles on the entrainment characteristics is depicted in Figure 3. When the

Figure 3. Effect of the size of coarse particles on the entrainment characteristics.

average diameter of coarse particles increases from 359 to 775 μm, Ki increases from 0.029 kg/m2·s to 0.050 kg/m2·s and from 0.035 kg/m2·s to 0.057 kg/m2·s for 2.2 and 0.9 μm silicon powder, respectively. This is most likely because the bigger coarse particles have a larger inertial impact on the agglomerates. Increasing the size of the coarse particles leads to a continuous reduction of the number of them. When the diameter of coarse particles is larger than 775 μm, there are too few coarse particles to achieve the purpose of improving the entrainment characteristics. 3.2. Mass Ratio of Coarse to Fine Particles (M). Keeping D = 775 μm, H = 1.125, ω = 54rps, Γ = 5.0, and V = 0.44m/s, the relationship between entrainment characteristics and the mass ratio of coarse to fine particles is shown in Figure 4. When M increases from 0 to 1.00, Ki increases from 0.038 kg/m2·s to 0.051 kg/m2·s for 2.2 μm silicon powder, while when M increases from 0 to 1.25, Ki increases from 0.035 kg/m2·s to 0.062 kg/m2·s for 0.9 μm silicon powder. At given D and H, increasing M is equivalent to increasing the number of coarse

(1)

where A and f are the amplitude and frequency of vibration, respectively, and g is the gravimetric acceleration. According to the study of Hakim et al.,29 the effect of breaking agglomerates improved when the amplitude of vibration was in the range of 0.75−2.00 mm. In this work, the amplitude of vibration was maintained at 1 mm, and the frequencies of vibration were 0, 27.8, 30.6, 33.3, and 36.1 Hz, respectively. 1361

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= 0.44m/s, the relationship between the entrainment characteristics and the rotational speed of the agitator is shown in Figure 6, which indicates that Ki decreases, after an initial increase, as

Figure 4. Effect of mass ratio of coarse to fine particles on the entrainment characteristics.

particles, which would enhance the breakage of agglomerates, but it would give little effect when M exceeded 1.00 for 2.2 μm silicon powder and 1.25 for 0.9 μm silicon powder. 3.3. Ratio of Static Bed Height to Diameter (H). Keeping D = 775 μm, M = 1.00, ω = 54rps, Γ = 5.0, and V = 0.44m/s, the relationship between entrainment characteristics and the ratio of static bed height to diameter is shown in Figure 5, which indicates that H has an influence on the entrainment

Figure 6. Effect of rotational speed of agitator on the entrainment characteristics.

ω increases. The phenomena may be explained that, when the rotational speed is lower than 45 rps, the force that stirring bar exerts to bed materials increases as rotational speed increases, which enhances the effect of breaking agglomerates, while when the rotational speed exceeds 45 rps, the intense centrifugal force presses the cohesive powder to side wall and a hard layer of silicon powder forms, which decreases the amount of silicon powder that could be entrained. 3.5. Intensity of Vibrator (Γ). Vibration is often utilized in the fluidization of fine particles to improve the fluidization qualities. This may act to increase the collision frequency between agglomerates or between agglomerates and coarse particles, thereby reducing the size of the agglomerates. In this set of experiments, keeping D = 775 μm, M = 1.00, H = 1.375, ω = 45 rps, and V = 0.44m/s, the relationship between the entrainment characteristics and the vibration intensity is shown in Figure 7. When Γ increases from 0 to 5.0, Ki increases from 0.045 kg/m2·s to 0.071 kg/m2·s for 2.2 μm silicon powder, and increases from 0.051 kg/m2·s to 0.085 kg/m2·s for 0.9 μm silicon powder. The collision frequency between agglomerates increases as the vibration intensity increases, which reduces the agglomerate size and improves the entrainment characteristics. 3.6. Superficial Velocity of Nitrogen Gas (V). In this section, the effect of superficial velocity of nitrogen gas on the entrainment characteristics was studied. Keeping D = 775 μm, M = 1.00, H = 1.375, ω = 45 rps, and Γ = 5.0, the relationship between entrainment characteristics and superficial velocity of nitrogen gas is shown in Figure 8. When V increases from 0.22m/s to 0.55m/s, Ki increases from 0.019 kg/m2·s to 0.085 kg/m2·s for 2.2 μm silicon powder, while Ki increases from 0.04 kg/m2·s to 0.092 kg/m2·s for 0.9 μm silicon powder, which is consistent in tendency with the result of Liu et al.12 and Shin et al.22 High gas velocity enhances turbulence of the flow, which increases the collision between agglomerates and reduces the sizes of agglomerates. In addition, high gas velocity leads to the entrainment of larger agglomerates. At given superficial gas velocity, the entrainment rate constant increases by an order of magnitude (from 10−3 kg/m2·s to 10−2 kg/m2·s) relative to that

Figure 5. Effect of ratio of static bed height to diameter on the entrainment characteristics.

characteristics. When H is lower than 1.375, Ki increases as H increases, but when H is higher than 1.375, Ki decreases as H increases. The tendency is same for 2.2 and 0.9 μm silicon powder. The curve is consistent with the results derived by Choi et al.26 (there is an optimal value) but different from the results of Shin et al.22 (no change with H), which is probably because of the difference in properties of bed materials. 3.4. Rotational Speed of Agitator (ω). An agitator is commonly used to facilitate the fluidization of fine powders by breaking up agglomerates and changing bed structure. The influence of the rotational speed of the agitator on the entrainment characteristics is investigated in this section. Keeping D = 775 μm, M = 1.00, H = 1.375, Γ = 5.0, and V 1362

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respectively, when j varies from 1 to 7; Aj, Bj, and C are fitting parameters. The χ2 tolerance value of 1 × 10−9 and adjusted R2 of 0.908 are reached, which demonstrates a good fitting result. The fitting parameters are shown in Table 2.

4. CONCLUSIONS The effects of the size of coarse particles (D, 359−1200), mass ratio of coarse to fine particles (M, 0−1.5), ratio of static bed height to diameter (H, 0.875−1.625), rotational speed of agitator (ω, 27−54rps), vibration intensity (Γ, 0−5.0), and superficial velocity of nitrogen gas (V, 0.22−0.55m/s) on the entrainment characteristics (entrainment rate constant, Ki, and powder gas ratio, R) were experimentally studied in order. It was observed that Ki increases as M, Γ, or V increases, while it decreases after an initial increase as D, H, or ω increases, the increase of M, Γ, or V improves the entrainment characteristics, while there exists a favorable value for D, H, or ω to obtain the optimum entrainment characteristics. The effects of the six independent parameters could be explained as follows: D: the bigger coarse particles have a larger inertial impact on the agglomerates, while increasing the size of the coarse particles led to a continuous reduction of the number of them. M: increasing M is equivalent to increasing the number of coarse particles, which would enhance the breakage of agglomerates. H: the effect of H needs to be studied further; it is different among the researchers. ω: when the rotational speed is lower, the force that stirring bar exerts to bed materials increases as rotational speed increases, which enhances the effect of breaking agglomerates, while when the rotational speed exceeds 45 rps, the intense centrifugal force presses the cohesive powder to side wall and a hard layer of silicon powder forms, which decreases the amount of silicon powder that could be entrained. Γ: it may act to increase the collision frequency between agglomerates or between agglomerates and coarse particles, thereby reducing the size of the agglomerates. V: high gas velocity enhances turbulence of the flow, which increases the collision between agglomerates and reduces the sizes of agglomerates. In addition, high gas velocity leads to the entrainment of larger agglomerates. The entrainment rate constant is an order of magnitude larger than that without vibration and agitation, which demonstrates the significant effects of vibration and agitation on the improvement of entrainment characteristics. The three requirements of low velocity, small size, and high powder gas ratio for silicon powder feeding are realized. A relational expression is derived to unify the experimental data, which gives a good fitting result.

Figure 7. Effect of vibration intensity on the entrainment characteristics.

Figure 8. Effect of superficial velocity of nitrogen gas on the entrainment characteristics.

without vibration and agitation,12 which shows remarkable effects of vibration and agitation on the improvement of entrainment rate constant. To unify the data, eq 3 is adopted to conduct multifactor nonlinear fitting: 7

y=

∑ xj(Aj + Bjxj) + C (3)

j=1

where y represents the entrainment rate constant, Ki; xj is independent variable that represents D, M, H, ω, Γ, V, or d, Table 2. Fitting Parameters j y xj Aj Bj C

1 D 1.84 × 10−4 −1.14 × 10−7

2 M 0.0208 −0.00579

3

4 Ki ω 0.0126 −1.40 × 10−4 −0.125

H 0.356 −0.126

1363

5

6

7

Γ 0.0103 −0.00101

V 0.338 −0.209

d −0.871 0.278

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(12) Liu, Y. D.; Kimura, S. Fluidization and Entrainment of Difficultto-Fluidize Fine Powder Mixed with Easy-to-Fluidize Large Particles. Powder Technol. 1993, 75, 189. (13) Liu, H. E.; Li, Y.; Guo, Q. J. Fluidization Quality Improvement for Cohesive Particles by Fine Powder Coating. Ind. Eng. Chem. Res. 2006, 45, 1805. (14) Mawatari, Y.; Tsunekawa, M.; Tatemoto, Y.; Noda, K. Favorable Vibrated Fluidization Conditions for Cohesive Fine Particles. Powder Technol. 2005, 154, 54. (15) Mawatari, Y.; Koide, T.; Tatemoto, Y.; Uchida, S.; Noda, K. Effect of Particle Diameter on Fluidization under Vibration. Powder Technol. 2002, 123, 69. (16) Mawatari, Y.; Koide, T.; Tatemoto, Y.; Takeshita, T.; Noda, K. Comparison of Three Vibrational Modes (Twist, Vertical, and Horizontal) for Fluidization of Fine Particles. Adv. Powder Technol. 2001, 12, 157. (17) Kim, J.; Han, G. Y. Effect of Agitation on Fluidization Characteristics of Fine Particles in a Fluidized Bed. Powder Technol. 2006, 166, 113. (18) Russo, P.; Chirone, R.; Massimilla, L.; Russo, S. The Influence of the Frequency of Acoustic Waves on Sound-Assisted Fluidization of Beds of Fine Particles. Powder Technol. 1995, 82, 219. (19) Zhu, C.; Liu, G. L.; Yu, Q.; Pfeffer, R.; Dave, R. N.; Nam, C. H. Sound Assisted Fluidization of Nanoparticle Agglomerates. Powder Technol. 2004, 141, 119. (20) Zhu, Q. S.; Li, H. Z. Study on Magnetic Fluidization of Group C Powders. Powder Technol. 1996, 86, 179. (21) Colver, G. M. The Effect of van der waals and Charge Induced Forces on Bed Modulus of Elasticity in AC/DC Electrofluidized Beds of Fine PowdersA Unified Theory. Chem. Eng. Sci. 2006, 26, 2301. (22) Shin, M. K.; Kim, E. M.; Koo, B. S.; Han, G. Y.; Yoon, K. J.; Lee, D. H. Entrainment Characteristics of Fine Particles in Cylindrical and Conical Inert-Medium Fluidized Beds. Ind. Eng. Chem. Res. 2007, 46, 1408. (23) Choi, J. H.; Choi, K. B.; Kim, P.; Shun, D. W.; Kim, S. D. The Effect of Temperature on the Particle Entrainment Rate in a Gas Fluidized Bed. Powder Technol. 1997, 92, 127. (24) Choi, J. H.; Ryu, H. J.; Shun, D. W.; Son, J. E.; Kim, S. D. Temperature Effect on the Particle Entrainment Rate in a Gas Fluidized Bed. Ind. Eng. Chem. Res. 1998, 37, 1130. (25) Choi, J. H.; Chang, I. Y.; Shun, D. W.; Yi, C. K.; Son, J. E.; Kim, S. D. Correlation on the Particle Entrainment Rate in Gas Fluidized Beds. Ind. Eng. Chem. Res. 1999, 38, 2491. (26) Choi, J. H.; Kim, K. J.; Kim, S. D. Effect of Secondary Gas Injection on the Particle Entrainment Rate in a Gas Fluidized Bed. Powder Technol. 1997, 90, 227. (27) Kim, Y. T.; Song, B. H.; Kim, S. D. Entrainment of Solids in an Internally Circulating Fluidized Bed with Draft Tube. Chem. Eng. J. 1997, 66, 105. (28) Jin, Y.; Zhu, J. X.; Wang, Z. W.; Yu, Z. Q. Fluidization Engineering Principles; Tsinghua University Press: Beijing, 2001. (29) Hakim, L. F.; Portman, J. L.; Casper, M. D.; Weimer, A. W. Aggregation Behavior of Nanoparticles in Fluidized Beds. Powder Technol. 2005, 160, 149.

AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-10-62334425. Fax: +86-10-62329145. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the financial support of this work from the Natural Science Foundation of China (Grant No. 51076010) and the National Basic Research Program of China (973 Program, Grant No. 2012CB720406).

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NOMENCLATURE A = vibration amplitude [m] d = mean diameter of silicon powder [μm] D = mean diameter of hollow alumina pellets [μm] f = vibration frequency [Hz] g = acceleration of gravity [m/s2] H = ratio of static bed height to diameter Ki = entrainment rate constant [kg/m2/s] m1 = mass of the collector at the beginning of an experiment [kg] m2 = mass of the collector at the ending of an experiment [kg] M = mass ratio of coarse to fine particles R = powder gas ratio [kg/kg] S = cross-sectional area of the column [m2] Δt = duration of an experiment [s] Umf = minimum fluidization velocity [m/s] Ut = terminal velocity [m/s] V = velocity of nitrogen gas [m/s]

Greek Letters

ω = rotational speed of agitator [rps] Γ = vibration intensity

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REFERENCES

(1) Yin, S. W.; Wang, L.; Tong, L. G.; Sun, S. F. Preparation of Silicon Nitride Powder by a Direct Nitridation Process Based on Fluidization Technology. J. Beijing University Chem. Technol. 2008, 35, 70. (2) Gundogdu, M. Y. Design Improvements on Rotary Valve Particle Feeders Used for Obtaining Suspended Airflows. Powder Technol. 2004, 139, 76. (3) Dai, J. J.; Grace, J. R. Biomass Screw Feeding with Tapered and Extended Sections. Powder Technol. 2008, 186, 56. (4) Parker, C.; Reist, L. T. Development and Operation of an Improved Turntable Dust Feeder. Powder Technol. 2000, 107, 36. (5) Suri, A.; Horio, M. A Novel Cartridge Type Powder Feeder. Powder Technol. 2009, 189, 497. (6) Francis, T. M.; Kreider, P. B.; Lichty, P. R.; Weimer, A. W. An Investigation of a Fluidized Bed Solids Feeder for an Aerosol Flow Reactor. Powder Technol. 2010, 199, 70. (7) Milioli, F. E.; Foster, P. J. Entrainment and Elutriation Modeling in Bubbling Fluidized Beds. Powder Technol. 1995, 83, 233. (8) Geldart, D. Types of Gas Fluidization. Powder Technol. 1973, 7, 285. (9) Seville, J. P. K.; Willett, C. D.; Knight, P. C. Interparticle Forces in Fluidization: A Review. Powder Technol. 2000, 113, 261. (10) Wang, Z.; Kwauk, M.; Li, H. Fluidization of Fine Particles. Chem. Eng. Sci. 1998, 53, 377. (11) Zhou, T.; Li, H. Z. Effects of Adding Different Size Particles on Fluidization of Cohesive Particles. Powder Technol. 1999, 102, 215. 1364

dx.doi.org/10.1021/ie301733t | Ind. Eng. Chem. Res. 2013, 52, 1359−1364