The suspension characteristics of ultrafine powder slurry in the stirred vessel were simulated by using computational fluid dynamics. The results show that the Rushton disk turbine impeller is more conducive to maintaining suspended homogeneity and circulation of slurry compared with the pitch blade turbine pumping up impeller and the pitch blade turbine pumping down impeller. And the increase in stirring speed enhances turbulent fluctuation and anisotropic velocity of the fluid at the cost of more power consumption, which improves dispersibility and suspensibility of the particles. Meanwhile, the change of impeller clearance has a weak influence on the flow pattern, and the impeller clearance of 0.32T (T is the diameter of the bottom of the reactor) can achieve better dispersivity and suspensibility of the particles with lower power consumption and larger axial velocity. The experiments of surface coating modification of ultrafine titanium dioxide (TiO2) were carried out under the same conditions for those of the simulation system. The surface film morphology and photocatalytic properties of the modified TiO2 were analyzed, and the obtained data are well consistent with the simulation results.
Mechanically stirred vessels with solid–liquid suspension system have been widely used in chemical and biological reaction processes, such as polymerization, chemical deposition, catalysis and crystallization [1,2,3,4]. In order to obtain the desired products, it is necessary to create a fine dispersibility and maintain the dispersion stability of the suspension during the reaction process. The changes in impeller type, internal structure of the vessel, operating conditions and material properties have nonnegligible effects on the interactions between solid and liquid phases [5,6,7]. Therefore, sedimentation and aggregation of solid particles as well as formation of “dead zone” may occur under certain circumstances, which will influence the dispersibility of the particles and eventually affect the power consumption, yield and performance of products [8,9,10].
Computational fluid dynamics (CFD) can provide an accurate and effective understanding of the flow field inside the stirred vessel, which is helpful to explain the theory and experimental phenomena. Gu et al.  simulated the suspensibility of glass beads with particle sizes of 80, 120 and 160 μm in the liquid phase and pointed out that the blade structure has influence on the homogeneity of solid–liquid suspension. Li et al.  adopted CFD to simulate the suspension property of low-density polypropylene beads with particle sizes of 0.25–2.00 mm in the stirred tank and obtained the flow pattern, power consumption and distribution of solid phase particles; moreover, other researcher’s experiment was compared to illustrate the accuracy of the simulation results. Xie and Luo  employed a three-dimensional (3D) CFD-KTGF model to investigate the influence of interaction between particles with an average particle size of 231 μm on the suspension quality for dense solid–liquid systems. The obtained simulation results can benefit the optimization and scale-up of the particle suspension apparatus. It is reported by Qiao et al.  that geometrical design and physical property had effects on the mixing quality of floating solids with particle sizes of 0.5–4.0 mm in stirred tanks under an up-pumping pitched blade turbine.
The above researches focus on achieving the uniform suspension of large-size solid particles in the liquid phase, but the suspensibility and dispersibility of ultrafine particles are rarely studied. Ultrafine powder refers to a series of powder materials ranging from micron to nanometer level ; in order to broaden the application value and prospect of ultrafine powder, surface modification is usually carried out [16,17,18,19]. As a rule, various physical or chemical methods are adopted to make particles be single particle dispersed and suspended in liquid phase before surface modification of ultrafine powders [20,21,22,23]. However, due to the small particle size and high surface energy of ultrafine particles, it is still challenged to avoid spontaneous agglomeration and sedimentation of ultrafine particles in the subsequent surface modification process even if they have already been single particle dispersed and suspended through previous dispersion processes. Therefore, it is of great significance to study how to maintain the single-particle dispersed and suspended state of ultrafine powder in the subsequent surface modification process.
Based on the background of surface modification of coating-grade titanium dioxide (TiO2) to shield photocatalytic performance [24,25,26,27,28], the suspension characteristics of single-particle dispersed and suspended ultrafine TiO2 slurry in the stirred reactor were studied by CFD simulation and experiments in this paper. The effects of impeller type, stirring speed and impeller clearance on flow field distribution and power consumption were investigated. In addition, the surface modification of ultrafine TiO2 particles was carried out under the experimental conditions which were completely consistent with the simulation system. The accuracy of the simulation results was analyzed by observing the coating morphology and comparing the photocatalytic properties of coated TiO2 particles. At the same time, the obtained results provide a favorable reference for the structure optimization of stirred vessel and the engineering scale-up of TiO2 coating modification.
As shown in Fig. 1a, a cylindrical flat-bottomed stirred vessel was adopted in the present study. The bottom diameter of the vessel was set as T = 140 mm, and the liquid level was set as H = T. Four full baffles with width of W = 0.11T and thickness of a = T/35 were evenly distributed on the inner wall of the tank. The structure of impellers used in simulation, as shown in Fig. 1b, included a 45° pitch blade turbine pumping down (PBTD) impeller, a 45° pitch blade turbine pumping up (PBTU) impeller and a Rushton disk turbine (DT) impeller. The blade diameter, width and thickness of the impellers were set as D = T/2, b = T/7 and d = 2 mm, respectively. And the impeller clearance was C = 0.25T, 0.32T or 0.50T.
In order to improve the weatherability of coating-grade TiO2, an inert film is needed to coat on the surface of all single particles to shield its photocatalysis. Therefore, it is necessary to study how to maintain single-particle dispersibility and suspensibility of TiO2 particles in well-dispersed slurry  and avoid TiO2 particles settling to the bottom of the tank in the process of coating modification. Ultrafine TiO2 slurry with an average particle size of 139 nm and a TiO2 content of 20 wt% was selected as the simulation material. The slurry viscosity is 0.0116 Pa·s, and the density is 1152.53 kg·m−3. According to the mathematical model theory of flow field proposed by Zhang , the ultrafine TiO2 slurry in the stirring vessel can be regarded as a homogeneous single-phase flow.
ANSYS mesh software was used to generate grids. In order to employ the “multiple reference frame (MRF)” method to simulate flow field, the whole computational domain was divided into two parts, i.e., the moving region of rotating impeller and the other stationary region. The unstructured tetrahedral meshes with stronger structural adaptability were employed in the whole computational domain, and the meshes were refined at blades, baffles, agitator shafts and interfaces between the two regions. At the same time, in order to ensure the accuracy of the simulation results and avoid the waste of computing resources, grid independence was tested before simulation computation. The torque value was selected as the basis of grid independence , and the results are shown in Fig. 2. When the grid number is greater than 290,000, the variation range of torque value is within 0.5%. Finally, 290,000 meshes were used in this paper. And the specific grid division of stirred vessel is shown in Fig. 3.
The standard k–ε turbulence model was adopted in the simulation because it is economical, rapid and can provide a reasonable agreement with the realistic experimental data [1, 12]. A “moving reference frame” boundary condition was set for the moving region with the rotational speeds were 200, 400 or 600 r·min−1, and a “stationary reference frame” was set for stationary region. As shown in Fig. 3, the surfaces between rotating impeller region and the other stationary region were set as “interface” boundary condition. The blade and the agitator shaft in the moving region were set as rotational wall. The agitator shaft in the stationary region was set as moving wall. The free liquid surface was treated as symmetry boundary condition. Based on the pressure-based solver, the SIMPLE algorithm was used for coupling the pressure and velocity field. All terms used in the governing equations were discredited by the second-order upwind scheme method with numerical under-relaxation. In addition, the calculations were considered to be converged when the residuals of all equations were below 1 × 10−4.
The ultrafine TiO2 slurry with single-particle dispersibility was prepared by mechanical wet grinding. Then the TiO2 slurry was transferred into the cylindrical flat-bottomed stirred vessel and heated to 80 °C. The aqueous solution of Na2SiO3·9H2O (1 mol·L−1) was added into the slurry with the ratio of SiO2 to TiO2 at 5%. The TiO2 slurry was adjusted to a pH value of 9.0 by adding H2SO4 (1 mol·L−1) aqueous solution. After addition, the slurry was aged at 80 °C for 2 h. And after coating SiO2 film, aqueous solution of NaAlO2 (1 mol·L−1) was added into the SiO2-coated TiO2 slurry with the ratio of Al2O3 to TiO2 at 3%. The slurry was adjusted to a pH value of 5.0 by dropping H2SO4 (1 mol·L−1) aqueous solution and then aged at 80 °C for 2 h. The precipitate was filtered and washed with deionized water until there were no sulfate ions. During the reaction, stirring was always maintained. The impeller type, stirring speed and impeller clearance were determined according to the conditions of simulation.
The degradation of rhodamine-B (RhB) in the TiO2 suspension under ultraviolet (UV) irradiation was used to evaluate the weather durability of the TiO2 particles. The naked or film-coated TiO2 particles (400 mg) were dispersed in 100 ml RhB solution with a concentration of 4 mg·L−1 under magnetic stirring. A sufficient dark absorption was applied before ultraviolet–visible (UV) irradiation for 30 min. Then the suspension was irradiated using UV light for 6 h. The suspension was sampled and centrifuged. The characteristic absorption of the supernatant at 554 nm was measured using a UV–visible spectrophotometer (UV-2102, UNICO). In addition, the morphology and structure of the naked and film-coated TiO2 particles were examined with a transmission electron microscope (TEM, JEM-1400/2100, JEOL).
Results and discussion
Verification of modeling
At the same stirring speed, the unit volume stirring power (Pv) is an important index to characterize the stirring effect . And the Pv can be expressed as follows:
where N is the stirring speed (r·s−1); M is the torque of the impeller (N·m); V is the total volume of the stirred reactor (m3); and V is 0.00216 m3 in this experiment.
The numerical simulation and experimental data were compared to verify the accuracy of the calculation method. Table 1 compares the simulated and experimental values of specific volume power under DT impeller. It can be seen that the average relative error of specific volume power is only 6.12% between simulated results and experimental data, and the both variation trends are completely consistent, which proves that the simulation model used and parameter setting are accurate and reliable.
Effect of impeller type
Maintaining the good dispersibility and suspensibility of TiO2 particles and suspended homogeneity of slurry plays very important roles in achieving no settlement of TiO2 particles and modification of single-particle surface coating during the subsequent surface modification process. As the types of impellers seriously have affected the suspension characteristics of fluid [32, 33], the effects of PBTD, PBTU and DT impellers on the suspension quality of slurry were evaluated, respectively, by CFD. In this process, the stirring speed was maintained at 400 r·min−1 and the impeller clearance was 0.32T.
The flow condition of fluid in the stirred vessel is closely related to the flow pattern. As shown in Fig. 4, the maximum velocity of three kinds of impellers all appears in the tip of blade. For PBTD impeller, a jet zone is formed in the 45° direction below the blade, and a main vortex zone is formed above the moving zone. A secondary vortex is formed under the moving zone, and the velocity of the secondary vortex is significantly reduced, resulting in the weaken interaction between fluid and the bottom of the stirring vessel, which is extremely disadvantageous for the suspension of the settled particles. For PBTU impeller, a jet zone is formed in the 45° direction above the blade, and the main vortex zone is located in the lower part of the vessel. At the same time, its velocity is significantly larger in the bottom region of the vessel compared with the PBTD impeller. For the DT impeller, a high-speed horizontal jet zone is formed in the middle portion between the vessel wall and the blade tip. After the fluid hits the vessel wall, two mainstream zones of circulating flow are formed on the upper and lower sides of the impeller, respectively. And near the bottom of the vessel, its velocity is also significantly higher than that of the PBTD impeller. The flow pattern and distribution of the three flow fields are well consistent with the simulation results of the predecessors [34,35,36].
For the ultrafine powder suspension studied in this paper, even if single-particle dispersion has been achieved, some suspended particles may still settle to the bottom of the vessel in the stirring process. Therefore, the axial velocity of the fluid in the vessel, especially the axial velocity of the fluid near the bottom of the vessel, plays an important role in achieving the resuspension of sedimentation particles and maintaining the uniformity of suspension. The results given in Fig. 5 reflect the distribution curves of dimensionless axial velocity of the fluid along the axial direction at r = 0.45R, 0.65R and 0.90R under the three types of impellers, where Vz represents the axial velocity and Vtip represents the linear velocity at the blade tip. Meanwhile, the upward and downward motions of the fluid are represented by positive and negative, respectively. It can be seen that in the region near the bottom of the vessel where h/H < 0.18, the absolute values of the fluid’s axial velocities under DT and PBTU impellers are significantly larger than that of PBTD impeller at three different investigation locations. It is demonstrated that both DT and PBTU impellers have greater effects on the circulation of fluid near the bottom of the vessel than PBTD impeller, which is favorable for maintaining the suspension of the fluid and upward movement of sedimentation particles. In the region of upper part of the vessel where h/H > 0.46, the absolute values of the fluid’s axial velocities under the DT and PBTD impellers are larger than that of the PBTU impeller, which is conducive to the circular flow of fluid in the upper part of the vessel. In the region of 0.18 < h/H < 0.46, the axial velocities of the fluid under PBTD and PBTU impellers present an antisymmetric distribution, and at the observation position where r = 0.45R, the axial velocities of the fluid under DT impeller are slightly smaller than that of PBT impellers. This can be attributed a hindrance to the speed transfer by a disk of DT impeller along the agitating shaft at this position.
During the agitation process, the fluid will be subjected to the force of turbulent vortices. Therefore, the strength of turbulent fluctuation will affect the suspension of fluid. Generally, turbulent kinetic energy is used to characterize the strength of turbulent fluctuation [31, 33]. As shown in Fig. 6, the turbulent kinetic energy of PBTD and PBTU impellers is mainly distributed in the area above and below the impeller, respectively, while the turbulent kinetic energy in other regions is very weak. The turbulent kinetic energy under the DT impeller is widely distributed throughout the stirred tank, and in most areas, the turbulent kinetic energy of the DT impeller is larger than that of PBT impellers to varying degrees, which not only is favorable to the upward movement of the bottom fluid, but also effectively promotes the axial circulation of the fluid.
According to the analysis of flow pattern, axial velocity and turbulent kinetic energy, in order to keep the dispersibility and suspensibility of the particles in slurry and avoid the formation “dead zones” with no motion or weak motion at the bottom region of the tank, the flow field distribution near the bottom of the stirred tank plays the most important role in the suspension quality. Meanwhile, to ensure better circulation of fluid, the DT impeller produces the best results, which is superior to the PBTU and PBTD impeller in turn.
The unit volume stirring power of three different impellers is shown in Table 2. It can be seen that the power consumption of PBTU and PBTD impellers is basically equal at the same speed, while the power consumption of DT impeller is about three times as that of PBT impellers. As a result, although DT impeller is more beneficial for maintaining a single-particle suspension state of fluid in the whole stirred tank, its power consumption is also higher.
Effect of stirring speed
In the stirred system, the rotational speed is a major operating parameter that affects the intensity of turbulent fluctuation and magnitude of velocity . In this paper, the effects of stirring speed on the suspension characteristic of TiO2 slurry were further studied by using DT impeller and impeller clearance of 0.32T. The turbulent kinetic energy and velocity changes of the fluid at speeds of 200, 400 and 600 r·min−1 were investigated, respectively.
The results shown in Fig. 7 reflect the radial distribution curve of turbulent kinetic energy at the lower (h = 0.18H) and upper (h = 0.46H) positions of impeller when the stirring speeds of DT impeller are 200, 400 and 600 r·min−1, respectively. The turbulent kinetic energy at all radial positions increases obviously with the increase in stirring speed, and the increase value is larger in the region where the turbulent kinetic energy is relatively large. This phenomenon indicates that increasing the agitation speed can fully enhance the fluid circulation and provide stronger turbulence intensity, so that the particle suspensibility in the stirred tank can also be improved. However, the increase in agitation speed will inevitably lead to the higher power consumption. Therefore, it is necessary to select a suitable rotational speed during the stirring process to ensure the mixing and suspension quality and avoid the waste of power consumption.
The results given in Figs. 8, 9 reflect the normalized axial and radial velocity curves of the fluid as a function of stirring speed at two sample positions, respectively. It can be seen that both axial and radial velocities of the fluid are in positive correlation of the stirring speed, which indicates that the increase in stirring speed can fully improve the axial and radial circulation of the fluid, thus achieving better suspension homogeneity as well as single-particle dispersibility and suspensibility. At the same time, a higher stirring speed can provide a greater shear strain rate, that is, a greater shear force, which is conducive to the redispersion of reagglomerated particles during agitation process. As a result, single-particle suspensibility of the slurry and the final coating completeness are improved.
Effect of impeller clearance
Because the impeller clearance is one of the important factors affecting the suspension characteristic of the fluid in vessel, the impeller clearance of DT impeller was further studied. Under the stirring speed of 400 r·min−1, the velocity distribution and power consumption of the fluid in the vessel were investigated with an impeller clearance of 0.25T, 0.32T and 0.50T, respectively.
The distribution curve of dimensionless axial velocity of fluid along the axial direction as a function of impeller clearance at three different observation positions are shown in Fig. 10. With a change of impeller clearance, the line shape of the axial velocity distribution curve shows no change. It means that the change of impeller clearance has little influence on the flow pattern. When the impeller clearance increases from 0.25T to 0.32T, the variation of velocity is relatively small. In the region near the bottom of the tank, the axial velocity generated by 0.32T is greater than 0.25T at r = 0.45R, and the axial velocity generated by 0.32T is basically the same as that generated by 0.25T at r = 0.65R and 0.90R. In the region near the upper part of the tank, the axial velocity generated by 0.32T is all larger than that generated by 0.25T at three different observation positions. Therefore, 0.32T produces better results than 0.25T. When the impeller clearance increases to 0.50T, in the region near the bottom of the tank, the axial velocity generated by 0.32T is larger than that by 0.50T at r = 0.45R and 0.90R, while their axial velocities are basically the same at r = 0.60R. Since the impeller is relatively far from the bottom when impeller clearance is 0.50T, the velocity is also higher in the region near the top of the tank. It is inferred that the impeller clearance of 0.32T can better guarantee the fluid movement at the bottom of the stirred tank and the fluid circulation in the tank.
The unit volume power consumption under different impeller clearances is listed in Table 3. When the impeller clearance increases from 0.25T to 0.32T and 0.50T, the power consumptions increase by 4.82% and 16.87%, respectively. Combined with the axial velocity analysis, the impeller clearance of 0.32T can achieve a better single-particle suspension state of the slurry with lower power consumption and larger axial velocity.
The surface coating modification of TiO2 particles was carried out under the conditions that were completely consistent with the simulation systems. The surface film morphology and photocatalytic performance of the coated TiO2 were characterized to assess the stirring effect.
Effect of impeller type and stirring speed
As shown in Fig. 11, the surface of naked TiO2 is smooth. The TEM images of Al2O3-/SiO2-coated TiO2 at different stirring speeds under three types of impellers are shown in Fig. 12, and the stirring speeds are 200, 400 and 600 r·min−1 from left to right. At a low stirring speed of 200 r·min−1, some aggregated TiO2 particles are coated with common Al2O3/SiO2 film under PBT impellers, which will result in that certain TiO2 particles are not completely coated. And under DT impeller, the SiO2 or Al2O3 aggregates obviously distribute among TiO2 particles. At a stirring speed of 400 r·min−1, SiO2 or Al2O3 aggregates still exist among TiO2 particles under PBT impellers, especially under PBTD impeller. However, the particles show a better dispersibility in comparison with that at the speed of 200 r·min−1, and many TiO2 particles have achieved single-particle coating under DT impeller. At the stirring speed of 600 r·min−1, all of the TiO2 particles have basically achieved single-particle coating under three types of impellers, and almost no aggregations of SiO2 or Al2O3 are observed.
Experimental result revealed that the degradation rate of RhB was 70.3% by the naked TiO2 following UV light irradiation for 6 h. And under UV light irradiation for 6 h, the degradation rates of RhB by coated TiO2 corresponding to samples in Fig. 12 are shown in Fig. 13. When the stirring speed increases from 200 to 600 r·min−1, the degradation rates of RhB by TiO2 under PBTD, PBTU and DT impellers decrease from 34.5%, 30.6% and 21.0% to 14.0%, 13.9% and 13.7%, respectively. In other words, RhB degradation rate decreases with the increase in stirring speed for the three types of impellers. On the other hand, at stirring speeds of 200 and 400 r·min−1, the degradation rate of RhB by coated TiO2 under DT impeller is less than that of PBTU impeller, and both of them are less than that of the PBTD impeller. When the stirring speed is 600 r·min−1, the degradation rates of RhB are basically the same under three types of impellers. These phenomena are well consistent with the TEM analysis and CFD simulation results. Therefore, we can conclude that the single-particle suspension state of the slurry and the coating quality of TiO2 are the best under DT impeller, and successively better than those of PBTU and PBTD impellers. And the higher the stirring speed of impeller is, the better the effect produced is. Considering power consumption, speed of 400 r·min−1 is a suitable coating condition for DT impeller.
Effect of impeller clearance
The influence of impeller clearance on the single-particle suspension state of the slurry and the coating quality of TiO2 particles were further studied by DT impeller. As shown in Fig. 14, TiO2 particles mostly achieve the single-particle surface coating when the impeller clearance is 0.25T or 0.32T, and the particle dispersibility is better at 0.32T. At the clearance of 0.50T, some SiO2 or Al2O3 aggregates among TiO2 particles will break the density and completeness of the film.
Under different impeller clearances, the degradation rates of RhB by coated TiO2 for 6 h are shown in Fig. 15. The degradation rates of RhB are 20.0%, 16.5% and 24.4% at the impeller clearances of 0.25T, 0.32T and 0.50T, respectively. These phenomena are well consistent with the TEM analysis and CFD simulation results. It means that the single-particle suspension state of the slurry and the coating quality of TiO2 are the best at impeller clearance of 0.32T.
CFD simulation and surface coating experiments were used to conduct numerical calculation and experimental analysis on the suspension characteristics of ultrafine powder slurry in stirred reactor, respectively. The DT impeller can better maintain suspended homogeneity and circulation of slurry and avoid the formation of a “dead zone.” The single-particle dispersibility and suspensibility under DT impeller are better than those of PBTU and PBTD impellers, but the power consumption of the DT impeller is the largest. The increase in stirring speed leads to the increase in turbulent fluctuation and shear force at the expense of more power consumption, which is beneficial to the redispersion of the reagglomerated particles and can improve the suspension quality. The change of impeller clearance has a weak influence on the flow pattern, and the impeller clearance of 0.32T can achieve better dispersion and suspension of particles with lower power consumption and larger axial velocity.
The coating quality and photocatalytic shielding performance of TiO2 particles are the best under DT impeller, and the higher the stirring speed is, the better the coating and photocatalytic shielding effect will be. For the DT impeller, a good effect has been achieved at the stirring speed of 400 r·min−1. At the impeller clearance of 0.32T, the coating and photocatalytic shielding effect are better than 0.25T and 0.50T, respectively. The experimental results are in good agreement with the simulation data.
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This work was financially supported by the National Natural Science Foundation of China (Nos. 21838003, 91834301 and 21878092), the Shanghai Scientific and Technological Innovation Project (No. 18JC1410600), the Social Development Program of Shanghai (Nos. 17DZ1200900 and 18DZ2252400), the Innovation Program of Shanghai Municipal Education Commission and the Fundamental Research Funds for the Central Universities (No. 222201718002).
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Wu, W., Cui, J., Jiang, H. et al. Computational fluid dynamics simulation and experimental analysis of ultrafine powder suspension. Rare Met. 39, 850–860 (2020). https://doi.org/10.1007/s12598-019-01323-1
- Computational fluid dynamics simulation
- Ultrafine powder slurry
- Suspension quality
- Impeller type
- Stirring speed
- Impeller clearance