Original Research PaperModel of estimating nano-particle agglomerate sizes in a vibro-fluidized bed
Graphical abstract
Comparison of the estimated agglomerate sizes and experimental data for SiO2 nano-particles.
Highlights
► The effects of operating conditions on agglomerate sizes are studied in VFB. ► Agglomerate sizes were decreased due to introduction of vibration energy. ► A model to predict agglomerate sizes is developed on the basis of energy balance. ► Average agglomerate sizes predicted by this model are in well agreement with data.
Introduction
Nano-particles, due to their high cohesion, and therefore, agglomeration, have limited industrial application. Vibro-fluidization is a technique successfully used to disperse and enhance the fluidization behavior of cohesive powders classified by the Geldart’s group as C classification in industry. The technique provides good mixing, large gas–solid contact area, and very high rates of heat and mass transfer. Previous studies [1], [2], [3] showed that the mechanism of vibration energy transfer in a vibro-fluidized bed (VFB) is based on vibration wave propagation, and vibration energy could not be restricted by particle physical properties. So, the VFB would have the potential to maximize utilization of dispersibility of nano-particles in the manufacture of drugs, cosmetics, foods, plastics, catalysts, energetic, and biomaterials. Several authors [4], [5], [6], [7], [8], [9] have proved that mechanical vibration is an effective method to improve fluidization quality of nano-particles.
Agglomerate size is one of the key variables in gas-fluidized beds of nano-particles, and significantly influences the fluidization quality in VFB. Several authors [4], [5], [7], [9] determined the agglomerate size and the agglomerate size distribution as affected by parameters such as: properties of primary particles, fluidization conditions, and auxiliary facilities including mechanical vibration, auxiliary magnetic field, and ultrasound field. Mawatari et al. [2] reported that agglomerate size depended on the balance between cohesive force (van der Waals force) and separation force (gravity, vibration and shear force by a gas flow), and proposed a force balance model to estimate agglomerate size of micro-sized glass beads and white alumina particles in a vibro-fluidized bed. Xu and Zhu [3] studied the fluidization behavior of Talc (4.1 μm) and CaCO3 (5.5 μm) powders, and examined effects of gas velocity, fluidization time and mechanical vibration on the self-agglomeration during fluidization of cohesive particles experimentally and theoretically. However, the effect of energy generated by fluid shear on agglomerate size was ignored in their model, and moreover the powders used in their experiments were micro-sized particles. Nam and Pfeffer [4] proposed combination of a fractal analysis with a modified Richardson–Zaki approach to predict the agglomerate sizes of 12 nm SiO2 nano-particles and voidage in a vibro-fluidized bed, and SiO2 nano-particles could be easily and smoothly fluidized in the form of stable, very porous agglomerates with negligible elutriation in the aid of vibration and aeration.
Many influencing factors were contributory to agglomerate due to different size and preparation methods of particles. The work reported in the literature thus far includes experimental and theoretical modeling of SiO2, TiO2, ZnO nano-particle agglomerate sizes in a conventional fluidization bed (CFB) and VFB. In this paper, a model to predict the agglomerate sizes is developed based on energy balance between the agglomerate collision energy, the effective energy arising from vibration wave, energy generated by laminar shear and cohesive energy.
Section snippets
Theoretical analysis
Two different studies [5], [10] showed that nano-particles could be fluidized in the form of agglomerates (agglomerate particulate fluidization, APF) in VFB, and the nano-particle agglomerates in a fluidized bed was characterized by a dynamic process consisting of agglomerate growing and agglomerate disrupting [3], [11]. To simplify the analysis, the following assumptions are made:
- (1)
The agglomerates are assumed as non-porous spheres.
- (2)
The size of agglomerates is represented by a mean diameter of da.
Experimental setup
Schematic diagram of the fluidized bed for nano-particles can be found in our previous article [5]. The fluidized agglomerates were taken out from the different axial and radial locations of a bed with a self-made sampling ladle as shown in Fig. 1. The average agglomerate size is determined as following: Agglomerate number percentage size distributions can be obtained based on agglomerate sizes measured by positive position metallographic microscope. Agglomerate number median diameter, dnm, is
Agglomerate sizes in a conventional fluidized bed
SiO2 and TiO2 nano-particles were difficult to be fluidized in a conventional fluidization bed (CFB), and there existed three stages: slugging, channeling and partial agglomerate fluidization. Visual observation revealed that nano-particles of the top-bed gradually fluidized in the form of smaller agglomerates with increasing gas velocity albeit the larger agglomerates occurred at the bottom of the fixed bed with maximum size around 2 mm. Contrasted with the two above-mentioned nano-particles,
Conclusion
The effect of vibration on the agglomeration in vibro-fluidized beds of nano-particles depended on the vibration frequency corresponding to a minimum agglomerate size. It can help to suppress formation of agglomerates due to the additional vibration energy, and it can also favor the coalescence of the agglomerates due to the enhanced contacting probability between particles and/or agglomerates. However, the overall trend of agglomerate sizes decreased with increasing vibration amplitude. The
Acknowledgements
The authors acknowledge with gratitude the financial support of the National Natural Science Foundation of China (Contract No. 21176266), The Research Fund for the Doctoral program of Higher Education from the Ministry of Education of China (No. 20070533121), the NSFC-JSPS cooperation program and The Research Fund for the Postgraduate Dissertation Innovation Project of Central South University (Contract No. 2009ssxt034).
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