An improved model for estimating fractal structure of silica nano-agglomerates in a vibro-fluidized bed

A Esmailpour, N Mostoufi, R Zarghami


A study has been conducted to determine the effects of operating conditions such as vibration frequency, vibration amplitude on the fractal structure of silica (SiO2) nanoparticle agglomerate in a vibro-fluidized bed. An improved model was proposed by assimilation of fractal theory, Richardson-Zaki equation and mass balance. This model has been developed to predict the properties of nanoparticle agglomerate, such as fractal dimension and its size. It has been found out the vibration intensity increase leads to a slight reduction in fractal dimension of agglomerate. This Paper is also indicated that the size of agglomerate has the same behavior as fractal dimension with respect to vibration intensity changes. This study demonstrated that the fractal dimension of Silica nanoparticle agglomerate is in the range of 2.61 to 2.69 and the number of primary particles in the agglomerate is in the order of 1010. The vibration frequency is more impressive than its amplitude on agglomerate size reduction. Calculated Minimum fluidization velocity by applying predicted agglomerate sizes and experimental data are acceptable fitted.

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Hakim, L. F., Portman, J. L., Casper, M. D. and Weimer, A. W., Aggregation behavior of nanoparticles in fluidized beds, Powder Technology, 2005, 160, 149–160. CrossRef

Seville, J. P. K., Willett, C. D. and Knight, P. C., Interparticle forces in fluidization: a review, Powder Technology, 2000, 113, 261–268. CrossRef

Chaouki, J., Chavarie, C. and Klvana, D., Effect of Interparticle forces on the hydrodynamic behavior of fluidized aerogels, Powder Technology, 1985, 43, 117–125. CrossRef

Zhou, T. and Li, H., Estimation of agglomerate size for cohesive particles during fluidization., Powder Technology, 1999, 101, 57–62. CrossRef

Morooka, S., Kusakabe, K., Kobata, A. and Kato, Y., Fluidization state of ultrafine powders, Journal of Chemical Engineering of Japan, 1988, 21, 41–46. CrossRef

Zhu, C., Yu, Q., Dave, R. N. and Pfeffer, R., Gas fluidization characteristics of nanoparticle agglomerates, AIChE Journal, 2005, 51, 426–439. CrossRef

Matsuda, S., Hatano, H., Muramoto, T. and Tsutsumi, A., Modeling for size reduction of agglomerates in nanoparticle fluidization, AIChE Journal, 2004, 50, 2763–2771. CrossRef

Vaidya, T. S., Fluidization behavior of alumina nano-particles, Applied Mechanics and Materials, 2012, 110, 1833–1840.

Valverde, J. M. and Castellanos, A., Fluidization of nanoparticles: A simple equation for estimating the size of agglomerates, Chemical Engineering Journal, 2008, 140, 296–304. CrossRef

Yao, W., Guangsheng, G., Fei, W. and Jun, W., Fluidization and agglomerate structure of SiO2 nanoparticles, Powder Technology, 2002, 124, 152–159. CrossRef

Valverde, J. M. and Castellanos, A., Fluidization, bubbling and jamming of nanoparticle agglomerates, Chemical Engineering Science, 2007, 62, 6947–6956. CrossRef

Richardson, J. F. and Zaki, W. N., Sedimentation and fluidization: Part I, Chemical Engineering Research and Design, 1977, 75, S82–S100. CrossRef

Nam, C. H., Pfeffer, R., Dave, R. N. and Sundaresan, S., Aerated vibrofluidization of silica nanoparticles, AIChE Journal, 2004, 50, 1776–1785. CrossRef

Valverde, J. M. and Castellanos, A., Fluidization of nanoparticles: A modified Richardson-Zaki law, AIChE Journal, 2006, 52, 838–842. CrossRef

Yang, J., Zhou, T. and Song, L., Agglomerating vibro-fluidization behavior of nanoparticles, Advanced Powder Technology, 2009, 20, 158–163. CrossRef

Kaliyaperumal, S., Barghi, S., Briens, L., Rohani, S. and Zhu, J., Fluidization of nano and sub-micron powders using mechanical vibration, Particuology, 2011, 9, 279–287. CrossRef

Liang, X., Duan, H., Zhou, T. and Kong, J., Fluidization behavior of binary mixtures of nanoparticles in vibro-fluidized bed, Advanced Powder Technology, 2014, 25, 236–243. CrossRef

Ammendola, P., Chirone, R. and Raganati, F., Fluidization of binary mixtures of nanoparticles under the effect of acoustic fields, Advanced Powder Technology, 2011, 22, 174–183. CrossRef

Ammendola, P., Chirone, R. and Raganati, F., Effect of mixture composition, nanoparticle density and sound intensity on mixing quality of nanopowders, Chemical Engineering and Processing: Process Intensification, 2011, 50, 885–891. CrossRef

Deng, X., Scicolone, J. V. and Dave, R. N., Discrete element method simulation of cohesive particles mixing under magnetically assisted impaction, Powder Technology, 2013, 243, 96–109. CrossRef

Quevedo, J. A., Pfeffer, R., Shen, Y., Dave, R. N., Nakamura, H. and Watano, S., Fluidization of nanoagglomerates in a rotating fluidized bed, AIChE Journal, 2006, 52, 2401–2412. CrossRef

Xu, C. and Zhu, J., Experimental and theoretical study on the agglomeration arising from fluidization of cohesive particles-effects of mechanical vibration, Chemical Engineering Science, 2005, 60, 6529–6541. CrossRef

Mandelbrot, B. B., The Fractal Geometry of Nature, WH Freeman and Co., New York, 1983.

van Ommen, J. R., Valverde, J. M. and Pfeffer, R., Fluidization of nanopowders: a review, Journal of Nanoparticle Research, 2012, 14, 1–29.

Castellanos, A., Valverde, J. M. and Quintanilla, M. A. S., Aggregation and sedimentation in gas-fluidized beds of cohesive powders, Physical Review E, 2001, 64, 043104.

Mawatari, Y., Ikegami, T., Tatemoto, Y. and Noda, K., Prediction of agglomerate size for fine particles in avibro-fluidized bed, Journal of Chemical Engineering of Japan, 2003, 36, 277–283. CrossRef

Filippov, A.V., Zurita, M. and Rosner, D. E., Fractal-like aggregates: Relation between morphology and physical properties, Journal of Colloid and Interface Science, 2000, 229, 261–273. CrossRef

Xiong, C. and Friedlander, S. K., Morphological properties of atmospheric aerosol aggregates, Proceedings of the National Academy of Sciences, 2001, 98, 11851–11856. CrossRef

Forrest, S. R. and Witten Jr., T. A., Long-range correlations in smoke-particle aggregates, Journal of

Sorensen, C. M. and Roberts, G. C., The prefactor of fractal aggregates, Journal of Colloid and Interface Science, 1997, 186, 447–452. CrossRef

Brasil, A. M., Farias, T. L. and Carvalho, M. G., Evaluation of the fractal properties of cluster-cluster aggregates, Aerosol Science & Technology, 2000, 33, 440–454. CrossRef

Wu, M. and Freidlander, S. K., Note on the power-law equation for fractal-like aerosol agglomerates, Journal of Colloid and Interface Science, 1993, 159, 246–248. CrossRef

Wang, H., Zhou, T., Yang, J. S., Wang, J. J., Kage, H. and Mawatari, Y., Model for calculation of agglomerate sizes of nanoparticles in a vibro-fluidized bed, Chemical Engineering & Technology, 2010, 33, 388–394. CrossRef

Rogak, S. N. and Flagan, R. C., Stokes drag on self-similar clusters of spheres, Journal of Colloid and Interface Science, 1990, 137, 206–218.

Gmachowski, L., Calculation of the fractal dimension of aggregates, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2002, 211, 197–203. CrossRef

Zhou, L., Wang, H., Zhou, T., Li, K., Kage, H. and Mawatari, Y., Model of estimating nano-particle agglomerate sizes in a vibro-fluidized bed, Advanced Powder Technology, 2013, 24, 311–316. CrossRef

Garside, J. and Al-Dibouni, M. R., Velocity-voidage relationships for fluidization and sedimentation in solid-liquid systems, Industrial & Engineering Chemistry Process Design and Development, 1977, 16, 206–214. CrossRef

Kunii, D. and Levenspiel, O., Fluidization Engineering, 2nd edn., Butterworth-Heinemann, Boston, 1991.


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