Numerical Simulation of Particle Mixing Behavior in High Speed Shear Mixer and Cylinder Mixer

Abstract

The mixing effect of powder materials is crucial in the iron ore granulation process, which determines the composition and particle size distribution, thereby affecting the quality of the sinter. To study the mixing effect of powder particles in a high speed shear mixer (HSSM) and cylinder mixer (CM), numerical simulation based on discrete element method was adopted in this work. For the CM, the particle movement consists of slipping and slumping. For the HSSM, the particle movement consists of rolling and cascading. The particle movement intensity coefficient of the HSSM is larger than that of CM, indicating that the movement of the particles in HSSM is more intensive. For HSSM case with four blades, the variation coefficient of homogeneity increases as rotational speed increases. The number of blades has little effect on the particle movement intensity coefficient and variation coefficient of homogeneity. In comparison to the CM, the variation coefficient of the HSSM reduce the most. It means that the mixing effect of HSSM is better than the CM. These findings are helpful for the improvement of the mixing and granulation efficiency in the iron ore sintering process.

1. Introduction

The mixing of powder materials is a crucial process in many industries such as pharmaceutical, food, agriculture and metallurgy. In the metallurgical ironmaking process, iron ore sinter, which is the main raw materials used to produce liquid molten iron, is produced in the sintering machine from the mixture of iron ore, flux and fuel.^1,2) Before the sintering, the iron ore fines should mix with coke and limestone, and then granulate with the addition of water to improve sinter bed permeability. The objective of granulation is to properly control the homogeneous composition and suitable size of the granules.^3,4,5) Hence, the mixing effect is crucial in the granulation process, which determines the composition and particle size distribution, thereby affecting the quality of the sinter.^6,7,8) However, the flow and mixing behaviors of granular systems have turned out to be surprisingly complex phenomena, a change in the vessel shape, operational conditions or granular particles’ properties can readily result in different mixing effect.^9,10,11) Thus, it is necessary to understand the mixing behavior of granular particles for optimal control of the iron ore fine granulation process.

At present, cylinder mixer is a widespread apparatus in sintering plants, and it has the advantages of simple equipment structure and low cost.¹²⁾ However, the quasi-particles produced by the traditional cylinder mixer under heavy load are with some disadvantages such as uneven size distribution and serious component segregation.^13,14) It not only greatly reduces the efficiency of mixing and granulating process, but also reduces the service life by forming a thick inner ring made of the lime and water in the drum.^7,15,16,17) It is well known that mixing and granulation can achieve easily under the heavy loading in a horizontal high shear mixer which is widely used in the pharmaceutical, food, agriculture and chemical industries.^{18,19,20,21,22)} The most attractive of high shear mixer is the intensive mixing effect of iron ore particles in both axial and radial directions due to the force of the agitation blades on particles, and the self-cleaning features of the agitation blades. Considering the advantages of the high speed shear mixer, it should be a potential option in iron ore mixing and granulation process.

In the past, several studies have been reported to investigate particle flow and mixing behavior in the high speed shear mixer.^23,24,25) Nilpawar et al.²⁶⁾ used a high speed camera and particle image velocimetry (PIV) software to investigate the effect of binder type on granular flows and found that binder viscosity influenced granular bed velocities. Darelius et al.²⁷⁾ measured the velocity field and predicted the torque of the impeller based on the velocity data. However, physical experiments are difficult to understand the particle flow and mixing at the microscopic scale. Recently, numerical simulation based on discrete element method (DEM) has been widely used to study particle mixing and segregation processes.^28,29,30) Sato et al.³¹⁾ developed a three-dimensional DEM model to study the torque of an agitator, particle velocity profiles and forces acting on a particle under different agitator rotational speeds. Chan et al.³²⁾ investigated the internal flow patterns and behavior of different scale batch, horizontal high shear mixers. They found that the relative particle velocity is correlated, independent of scale, to the relative swept volume per rotation. However, most studies focused on the pharmaceutical and chemical industries, and there are few researches on mixing and segregation of iron ore particles during granulation process in the field of metallurgy. Besides, the effect of the number of blades on particle mixing efficiency and the comparison of mixing efficiency between cylinder mixer and high shear mixer have not been investigated.

In this work, numerical simulation based on discrete element method is used to study the mixing effect in a high speed shear mixer and cylinder mixer. In the simulations, the particle motion, mixing area distribution and the coefficient of variation are calculated to discuss particle flow pattern and mixing behavior under different number of blades and their rotational speeds in high speed shear mixer. Besides, the particle mixing performance is compared between high speed shear mixer and cylinder mixer. It is significant to improve the mixing effect of the traditional mixture granulation process and explore the feasibility of the new mixing granulation device.

2. Model Description

Particles in the cylinder mixer and high speed shear mixer are treated as discrete phase and their motion is described by the DEM based on the Newton’s second laws. The iron ore particles are modelled using a commercial software packages EDEM^®. During the motion and mixing process, a particle may collide with neighboring particles or the wall. Each particle in the DEM model undergoes both translational and rotational motion. The governing equations for motion of particle i can be written as follows:   

$$m_i\frac{d{u}_i}{dt}=\sum _j(F_{ij}^N+F_{ij}^T)+m_{i}g$$(1)

  

$$I_i\frac{d{\omega }_i}{dt}=\sum _j(R_i\times F_{ij}^T)+{\tau }_{r,ij}$$(2)

Where m_i, R_i, I_i, u_i and ω_i are the mass, radius, moment of inertia, linear velocity, and angular velocity of particle i, respectively. g is the acceleration of gravity. $F_{ij}^N$ and $F_{ij}^T$ are the normal and tangential forces resulting from the contact of particle i with particle j. The effect of rolling friction is included in the torque term τ_r,ij.

This work focuses on the first stage of iron ore granulation, namely the mixing process. As the water is not considered in the mixing process, there is no cohesive force or liquid bridge force between particles. Hence, Hertz-Mindlin contact model is applied in this work. The normal contact force F_cn and the normal damping force F_dn are given as follows:   

$$F_{cn}=\frac{4}{3}{E}^{*}\sqrt{R^{*}}{\delta }_n{}^{\frac{3}{2}}$$(3)

  

$$F_{dn}=-2\sqrt{\frac{6}{5}}\beta \sqrt{S_n{m}^{*}}{u}_n^{rel}$$(4)

Where δ_n and $u_n^{rel}$ are the normal overlap and the normal component of relative particle velocity. Besides, the particle equivalent radius R^*, the equivalent Young’s modulus E^* and the equivalent mass m^* are defined as:   

$$R^{*}\text{= }{\left(1/R_i+1/R_j\right)}^{-1}$$(5)

  

$$E^{*}\text{= }{\left((1-v_i^2)/E_i+(1-v_j^2)/E_j\right)}^{-1}$$(6)

  

$$m^{*}\text{= }{\left(1/m_i+1/m_j\right)}^{-1}$$(7)

The normal stiffness S_n and coefficient β are given by:   

$$\beta =\frac{-lne}{\sqrt{{ln}^{2}e+{\pi }^2}}$$(8)

  

$$S_n=2E^{*}\sqrt{R^{*}{\delta }_n}$$(9)

The tangential contact force F_ct, the tangential damping force F_dt and the tangential stiffness S_t are given by Eqs. (10), (11) and (12). In the simulations, the tangential force is limited by Coulomb friction μ_sF_cn, where μ_s is the coefficient of static friction. The tangential rolling friction is expressed by applying a torque to the contacting surfaces, as shown in Eq. (13).   

$$F_{ct}=-S_t{\delta }_t$$(10)

  

$$F_{dt}=-2\sqrt{\frac{5}{6}}\beta \sqrt{S_t{m}^{*}}{u}_t^{rel}$$(11)

  

$$S_t\text{=}8G^{*}\sqrt{R^{*}{\delta }_n}$$(12)

  

$${\tau }_{r,ij}=-{\mu }_r{F}_{ij}^N{R}_i{\omega }_i$$(13)

Where δ_t and $u_t^{rel}$ are the tangential overlap and the tangential component of relative particle velocity. G^* is the equivalent shear modulus. μ_r, R_i and ω_i represent the coefficient of rolling friction, the distance of the contact point from the center of mass and the unit angular velocity vector of the object at the contact point, respectively.

3. Simulation Conditions

The main purpose of the simulations was to study the particle flow and mixing behavior in the high speed shear mixer (HSSM) and compare simulation results of the HSSM with that of the traditional cylinder mixer (CM). Figure 1 shows the schematic diagram of HSSM used in the simulations, where the HSSM with four stirring blades was taken as an example. The HSSM equipment consists of a cylinder and several stirring blades. The blade includes two parts, a blade tip and a material distribution part, as shown in Fig. 2. The blade tip was designed as a solid triangular structure. The material distribution part was designed as curved surfaces and it was inclined at an angle of 55° to the horizontal plane. The axial distance between the blades was shown in Table 1. The distance between the blades and cylinder wall was 0.5 mm, which can help the blades to scrape off the adhered material on the cylinder wall. The purpose of this design was that the inclined area of the material distribution part can drive the mixture and throw it to a suitable height and range when the stirring blades impacting with the particles. Then, the particles were intensive mixed in the axial and radial directions.

Fig. 1.

Schematic diagram of the high speed shear mixer. (Online version in color.)

Fig. 2.

Parameters of the designed stirring blade (mm).

Table 1. Facility parameters of the high speed shear mixer used in the simulations.

Number of blades	Distance between blades (mm)	Interval of Angle (°)	Rotational speed (rpm)
3	275.0	120	100
4	183.3	90	25, 50, 75, 100, 125
5	137.5	72	100

In high speed shear mixing machines, the design of the stirring blades directly affects the mixing of the particles. To study the effect of the number of blades on particle motion and mixing efficiency, the number of blades at 3, 4 and 5 were selected. Besides, different rotational speed at 25, 50, 75, 100 and 125 rpm were set to investigate their effect on particle mixing, and the related parameters were listed in Table 1. The simulated raw material conditions of these different number of blades and rotational speeds were the same, therefore, comparison with each other was reasonable.

In order to compare the mixing efficiency of the HSSM and the cylinder mixer, the same size of the HSSM and the cylinder mixer was employed, both of them were 500 mm in length and 400 mm in diameter. The equipment schematic diagram of cylinder mixer was shown in Fig. 3, and the rotational speed of cylinder mixer was 22 rpm.

Fig. 3.

Schematic diagram of the cylinder mixer. (Online version in color.)

In this study, the materials proportion was set according to the actual mixing and granulation process. The main raw materials were iron ore, fuel and flux. The filling degree of HSSM and CM was 12%, and the total mass of iron ore powder, fuel and flux was 8.21 kg. The material properties and particle contact parameters were given in Table 2.³³⁾

Table 2. The material properties of raw materials used in simulation.

	Iron ore	Fuel	Flux	Steel (blade materials)
Poisson ratio (-)	0.3	0.25	0.29	0.3
Shear modulus (Pa)	6.77×107	1.12×108	1.26×109	7.00×1010
Density (kg*m−3)	2900	450	2500	7800
Particle radius (mm)	2, 4, 6, 9, 10	1	1	–
Mass ratio (%)	87	4.2	8.8	–
Number of particles (-)	41401	180375	66110	–
Coefficient of restitution (-)	0.2	0.3	0.3	0.5
Static friction coefficient (-)	0.5	0.6	0.5	0.5
Rolling friction coefficient (-)	0.02	0.05	0.05	0.05

In the simulation process, the total simulation time was set to 21.5 s. Simulation process was divided into four steps, as shown in Fig. 4. The particles were generated and fallen by the order of iron ore powder, fuel and flux, and the generation rate of the particles was 2 kg/s. When the time was 4.16 s, all the particles were fallen on the bottom of the cylinder and static settlement for a period of time. The blades or drum starts to rotate at 5 s, indicating that the mixing process starts. Particle mixing process was end in the 20 s and static settlement for a period of time. Then, the simulation results were analyzed and the data was visualized by the post-processing module of EDEM software.

Fig. 4.

Flow sheet of simulation. (Online version in color.)

4. Results and Discussion

4.1. Model Validation

DEM has been widely used in the simulation of bulk particles and has good reliability. In this work, limited by the experimental conditions, it is difficult to capture the dynamic data in the experiment. Thus, the velocity vector of particles in the cylinder mixer from DEM simulation is compared with the experimental results. Figure 5(a) shows the velocity vector of particles in the simulation. It can be found that the motion of particles consist of two components: slipping and slumping. As the drum rotates counterclockwise, the particles gradually climb along the cylinder wall under the action of the lifting plates and friction force. Hence, the velocity vector direction of particles close to the wall is upward along the wall. The velocity vector direction of surface particles is towards the bottom of the mixer. This is because the stacking angle of the particles on the side wall exceeds the largest angle of repose with the rotation of the mixer. Particularly, some particles continue to climb to the top of the cylinder under the action of the lifting plate, and finally fall to the bottom under the action of gravity.

Fig. 5.

Comparison of particles flow pattern between the simulation and experiment. (Online version in color.)

Figure 5(b) is the snapshot of particles flow pattern in the experiment. It can be seen that the flow pattern of particles shows a trend of slipping and slumping. Moreover, the rising height of slipping part at the right of mixer in the experiment is about 200 mm. A similar phenomenon also can be observed from the simulation results. Thus, the comparison of the experimental and the simulation results verified the capability of the DEM model for the simulation of the mixing process in the cylinder mixer.

4.2. Particle Motion Behavior

Figure 6 presents the particles flow pattern in the cylinder mixer and HSSM. For cylinder mixer, particle motion consists of two components: slipping and slumping, as described in section 4.1. For HSSM, the movement of particles mainly consists of two parts: rolling and cascading. The particles at the bottom of the mixer roll up under the action of the rotational blades, reaching the highest position for free-falling movement, and some particles climb to a higher position under the effect of the mixing blades.

Fig. 6.

Particle flow pattern in the cylinder mixer and high speed shear mixer. (Online version in color.)

To quantitatively describe the intensity of particle movement, an intensity coefficient A is proposed, as shown in Eq. (14). A is the ratio of S_p to S_m, which can evaluate the intensity of particle movement in the mixing devices. S_p represents the moving area of particles projected to the side direction when the particles are moving in the mixer. The side direction is the X axis direction which is shown in Fig. 1. S_m is cylindrical area in the axis direction.   

$$A=\frac{S_p}{S_m}\times 100\%$$(14)

The particles movement area for the eight different patterns can be calculated according to the simulation results. The side views of each mixing machine are taken at 5, 10, 15, 20 and 21.5 s. Moving particles are colored, so the change in color can be used to obtain the moving area of the particles. Then the particle movement intensity coefficient can be calculated based on the Eq. (14).

Figure 7 shows the distribution of intensity coefficient in different mixing time and operating parameters. It can be found that the intensity coefficient of the cylinder mixer is always smaller than that of HSSM, indicating that the movement of the particles in HSSM is more intense. For HSSM cases with four blades, the intensity coefficient increase as rotational speed increases. Besides, the intensity coefficient is about 30% when the rotational speed is 25 rpm, and it reaches 80% when the rotational speed is 125 rpm. This shows that the particle movement is more intense with the increase of the rotational speed under the condition of a certain number of stirring blades. In addition, for all the cases with the blades rotational speed of 100 rpm, increasing the number of stirring blades has little effect on the intensity coefficient.

Fig. 7.

Intensity coefficient of particle movement in different operating conditions. (Online version in color.)

4.3. Mixture Homogeneity Analysis

In order to compare the mixing efficiency, named homogeneity, the mixers were divided into 4 average parts with different colors in order to visualize the mixing of particles along the axial direction, as shown in Fig. 8. The four pictures are the top view of the cylinder mixer (CM) and HSSM at 5 s and 21.5 s, respectively. It is observed that there is a phenomenon of stratification in CM after mixing, and the particles are unevenly distributed in the axial direction of each fraction. This is because the particles in the cylinder are mainly driven by gravity and the baffle in the radial direction, and lack of the driving force in the axial direction. For HSSM, the agitator blades push up or roll away the particles. Some particles flow to the blades, while particles in the flow collided with each other or with the vessel wall and with the rotating blades. It means that the stirring of the blades promotes the uniform mixing of the particles in the radial and axial directions. Furthermore, the particle motion became more intense with the increasing of rotational speed, because the high rotational speed leads to larger collision frequency. By comparing the mixing effect of CM and HSSM in the radial and axial directions, it can be concluded that the particles are better mixed in HSSM and the particles are evenly distributed.

Fig. 8.

Mixture analysis of cylinder mixer and high speed shear mixer. (Online version in color.)

4.4. Evaluation on Variation Coefficient of Homogeneity

The variation coefficient of homogeneity is a statistic index that indicates the composition distribution. It is an absolute value representing the degree of composition dispersion. The variation coefficient of homogeneity describes that the relationship of standard deviation and average value. The variation coefficient of homogeneity (CV) is calculated by the following equation:   

$$CV=\frac{S}{\overline{x}}\times 100\%$$(15)

Where CV is the variation coefficient of homogeneity, S is the standard deviation and $\overline{x}$ is the average value.

In granulation production, quasi-particles are supposed to have the appropriate composition ratio and particle size. The composition of the particles after mixing reaches or approaches the desired value, meaning well mixing. A large value of variation coefficient means that significant composition segregation and worse mixing effect. On the contrary, a small value means better mixing effect.

The simulation analysis selects the data of the three materials (iron ore, flux and fuel) at 5 s and 21.5 s to calculate the CV. The impeller starts to rotate from 5 s and stops at 20 s. Therefore, 5 s and 21.5 s are the start and end states of mixing, respectively. By comparing the CV value before and after mixing, the mixing effect under different equipment and operating parameters can be obtained. In order to calculate the CV, the mixer is divided into 1000 small cubes along its external contour, the location distribution is 10×10×10 in X, Y and Z axis, as shown in Fig. 9. Each cube in the mesh is represented by its integer coordinate (x, y, z). Due to the particles at the bottom, the coordinate is from (1, 5, 1) to (10, 5, 1) and (1, 6, 1) to (10, 6, 1).

Fig. 9.

The division of the simulated area. (Online version in color.)

The selected 20 cube are marked as No. 1 to No. 20. The amount of iron ore, flux and fuel particles in each cube are $n_i^{iron}$, $n_i^{flux}$ and $n_i^{fuel}$. The individual particle mass of the three material are M_iron, M_flux and M_fuel. Total mass of iron ore particles in each cube is $M_i^{iron}$ (Flux is $M_i^{flux}$, Fuel is $M_i^{fuel}$). Taking iron ore particles as an example, the mass of particles in each cube is calculated by the following equation:   

$$M_i^{iron}=n_i^{iron}\cdot M_{iron}$$(16)

Total mass of three material in each cube $M_i^{tot}$ is given as follows:   

$$M_i^{tot}=M_i^{iron}+M_i^{flux}+M_i^{fuel}$$(17)

The mass fraction of iron ore $X_i^{iron}$ (Flux is $X_i^{flux}$, Fuel is $X_i^{fuel}$) in each cube is given as follows:   

$$X_i^{iron}=\frac{M_i^{iron}}{M_i^{tot}}$$(18)

The theoretical mass fractions of three materials in each cube are ${\overline{X}}^{iron}$, ${\overline{X}}^{flux}$ and ${\overline{X}}^{fuel}$ (Iron ore is 87%, Flux is 8.8% and Fuel is 4.2%). The ratio of the mass fraction of iron ore to the theoretical mass fraction is given (Iron ore is $x_i^{iron}$, Flux is $x_i^{flux}$ and Fuel is $x_i^{fuel}$) as follows:   

$$x_i^{iron}=\frac{X_i^{iron}}{{\overline{X}}^{iron}}$$(19)

The average deviations within 20 cubes are ${\overline{x}}^{iron}$, ${\overline{x}}^{flux}$ and ${\overline{x}}^{fuel}$.   

$${\overline{x}}^{iron}=\frac{{\sum }_1^{20}{x}_i^{iron}}{20}$$(20)

The mass fraction standard deviation of iron ore particle is $S_X^{iron}$ (Flux is $S_X^{flux}$, Fuel is $S_X^{fuel}$) as follows:   

$$S_X^{iron}=\sqrt{\frac{{\sum }_1^n{\left(x_i^{iron}-{\overline{x}}^{iron}\right)}^2}{n-1}}$$(21)

The coefficient of variation CV of three material particles is calculated by the following equation (Iron ore is taken as an example):   

$$C{V}_{iron}=\frac{S_X^{iron}}{{\overline{x}}^{iron}}\times 100\%$$(22)

Figure 10 shows the variation coefficient of homogeneity for three materials in the CM and HSSM at 5 seconds. It is known that the mixer starts to rotate from 5 s. Therefore, the variation coefficient of the material is influenced by the material preparation. Due to the layering of the material, a number of flux particles in the divided small cube is zero. The variation coefficient of homogeneity is also zero. It reflects the initial state of the material.

Fig. 10.

The initial variation coefficient of homogeneity. (Online version in color.)

Figure 11 investigates the mixing result at 21.5 s. For HSSM case with four blades, the variation coefficient of homogeneity reduces as rotational speed increases. It indicates that HSSM devices are with the good mixing effect. In addition, HSSM with rotational speed of 125 rpm has the best particle mixing effect. The rotational blades push up or sweep away the particles. Some particles flow to the blades, while particles in the flow collided with each other or with the vessel wall and with the rotating blades. Thus, the movement range and height of the particles in the mixers become larger with the increasing of rotational speed. For HSSM with rotational speed of 100 rpm and the blades number of 3, 4 and 5, the variation coefficients of the particles of the three mixers are similar, indicating that the number of blades has little effect on the CV. This shows that the number of blades has little effect on the movement of particles. Comparison of the CM and the HSSM, the variation coefficient of the HSSM reduce the most. It means that the mixing effect of HSSM is better than the CM.

Fig. 11.

The final variation coefficient of homogeneity. (Online version in color.)

5. Conclusions

In this paper, the particle motion in HSSM and CM were simulated by discrete element method (DEM). The number of rotational blades and their agitation speed in the HSSM are associated with the particle motion and the mixing effect. The main findings can be summarized as:

(1) For the CM, the particles are mainly subject to gravity and sliding friction, thus the particle movement consist of slipping and slumping. For the HSSM, the particles roll up under the action of the rotational blades and reach the highest position for free-falling movement, the movement of particles mainly consists of rolling and cascading.

(2) The particle movement intensity coefficient in the CM is smaller than that in the HSSM, indicating that the movement of the particles in HSSM is more intense. Besides, the particle movement intensity coefficient increases as rotational speed increases. However, the number of rotational blades has little effect on the particle movement intensity coefficient.

(3) For the HSSM case with four blades, the variation coefficient of homogeneity reduces as rotational speed increases, and the best particle mixing effect could be obtained when the rotational speed is 125 rpm. The number of blades has little effect on the variation coefficient. Comparison of the CM and the HSSM, the variation coefficient of the HSSM reduce the most. It means that the mixing effect of HSSM is better than the CM.

Acknowledgements

This work was supported by the National Key R&D Program of China (2018YFC1900500), the National Natural Science Foundation of China (52004046), China Postdoctoral Science Foundation (2020M673131) and the Postdoctoral Science Foundation of Chongqing (cstc2020jcyj-bshX0030).

References

• 1)   M.  Gan,  X. H.  Fan,  Z. Y.  Ji,  X. L.  Chen,  L.  Yin,  T.  Jiang,  Z. Y.  Yu and  Y. S.  Huang: Ironmaking Steelmaking, 42 (2015), 351.
• 2)   T.  Umadevi,  A. V.  Deodar,  P. C.  Mahapatra,  M.  Prabhu and  M.  Ranjan: Steel Res. Int., 80 (2009), 686.
• 3)   J.  Pan,  D.  Zhu,  P.  Hamilton,  X.  Zhou and  L.  Wang: ISIJ Int., 53 (2013), 2013.
• 4)   X.  Lv,  C.  Bai,  G.  Qiu,  S.  Zhang and  M.  Hu: ISIJ Int., 50 (2010), 695.
• 5)   V.  de Morais Oliveira,  A. L. A.  Domingues,  M. C.  Bagatini and  V. G.  de Resende: ISIJ Int., 60 (2020), 2376.
• 6)   T.  Umadevi,  U. K.  Bandopadhyay,  P. C.  Mahapatra,  M.  Prabhu and  M.  Ranjan: Steel Res. Int., 81 (2010), 419.
• 7)   S.  Wu and  G.  Zhang: Steel Res. Int., 86 (2015), 1014.
• 8)   C.  Yang,  D.  Zhu,  J.  Pan and  L.  Lu: ISIJ Int., 58 (2018), 1427.
• 9)   M. M. H. D.  Arntz,  H. H.  Beeftink,  W. K.  den Otter,  W. J.  Briels and  R. M.  Boom: AlChE J., 60 (2014), 50.
• 10)   A.  Di Renzo and  F. P.  Di Maio: Chem. Eng. Sci., 59 (2004), 525.
• 11)   J. L.  Turner and  M.  Nakagawa: Powder Technol., 113 (2000), 119.
• 12)   J.  Khosa and  J.  Manuel: ISIJ Int., 47 (2007), 965.
• 13)   Y.  Yamaguchi,  C.  Kamijo,  M.  Matsumura and  T.  Kawaguchi: ISIJ Int., 53 (2013), 1538.
• 14)   R.  Soda,  A.  Sato,  J.  Kano,  E.  Kasai,  F.  Saito,  M.  Hara and  T.  Kawaguchi: ISIJ Int., 49 (2009), 645.
• 15)   J.  Zhu,  S.  Wu,  J.  Fan,  G.  Zhang and  Z.  Que: ISIJ Int., 53 (2013), 1529.
• 16)   Z.  Que,  S.  Wu,  X.  Zhai and  K.  Li: Ironmaking Steelmaking, 46 (2019), 246.
• 17)   M.  Marigo,  D. L.  Cairns,  M.  Davies,  A.  Ingram and  E. H.  Stitt: Powder Technol., 217 (2012), 540.
• 18)   D.  Li,  G.  Liu,  H.  Lu,  Q.  Zhang,  Q.  Wang and  H.  Yu: Powder Technol., 291 (2016), 86.
• 19)   X.  Xiao,  Y.  Tan,  H.  Zhang,  R.  Deng and  S.  Jiang: Powder Technol., 314 (2017), 182.
• 20)   A.  Realpe and  C.  Velázquez: Chem. Eng. Sci., 63 (2008), 1602.
• 21)   A.  Kumar,  K. V.  Gernaey,  T.  De Beer and  I.  Nopens: Eur. J. Pharm. Biopharm., 85 (2013), 814.
• 22)   K.  Terashita,  T.  Nishimura,  S.  Natsuyama and  M.  Satoh: J. Jpn. Soc. Powder Powder Metall., 49 (2002), 638.
• 23)   H.  Leuenberger,  M.  Puchkov,  E.  Krausbauer and  G.  Betz: Powder Technol., 189 (2009), 141.
• 24)   M.  Cavinato,  M.  Bresciani,  M.  Machin,  G.  Bellazzi,  P.  Canu and  A. C.  Santomaso: Int. J. Pharm., 387 (2010), 48.
• 25)   Z.  Mirza,  J.  Liu,  Y.  Glocheux,  A. B.  Albadarin,  G. M.  Walker and  C.  Mangwandi: Particuology, 23 (2015), 31.
• 26)   A. M.  Nilpawar,  G. K.  Reynolds,  A. D.  Salman and  M. J.  Hounslow: Chem. Eng. Sci., 61 (2006), 4172.
• 27)   A.  Darelius,  E.  Lennartsson,  A.  Rasmuson,  I. N.  Björn and  S.  Folestad: Chem. Eng. Sci., 62 (2007), 2366.
• 28)   J. A.  Gantt,  I. T.  Cameron,  J. D.  Litster and  E. P.  Gatzke: Powder Technol., 170 (2006), 53.
• 29)   H.  Nakamura,  H.  Fujii and  S.  Watano: Powder Technol., 236 (2013), 149.
• 30)   N.  Rahmanian,  A.  Naji and  M.  Ghadiri: Chem. Eng. Res. Des., 89 (2011), 512.
• 31)   Y.  Sato,  H.  Nakamura and  S.  Watano: Powder Technol., 186 (2008), 130.
• 32)   E. L.  Chan,  K.  Washino,  H.  Ahmadian,  A.  Bayly,  Z.  Alam,  M. J.  Hounslow and  A. D.  Salman: Powder Technol., 270 (2015), 561.
• 33)   H.  Zhou,  Z. G.  Luo,  T.  Zhang,  Y.  You,  Z. S.  Zou and  Y. S.  Shen: ISIJ Int., 56 (2016), 245.