Application of the Force Balance Model and Fractal Scaling Analysis for Size Estimation of the Complex-Agglomerates in a Conical Fluidized Bed

Document Type : Research Article


Chemical Engineering Department, Hamedan University of Technology, P. O. Box 65155 Hamedan, I.R. IRAN



The size estimating of fluidized Titania agglomerates in a conical fluidized bed was studied by force balance model and fractal scaling analysis. The primary size of Titania Nano Particles (NPs) was 21 nm, while for complex agglomerates was in the size range of several hundred micrometers. The formation mechanism of simple-agglomerate and complex-agglomerate structures was studied experimentally. The size distribution and morphology of agglomerates were determined by advanced laser dynamic imaging and scanning electron microscopy. The AFM-nanoindentation test was used to determine the elastic modulus of agglomerates with porous structures. The size distribution of Titania NP agglomerates was estimated by the fractal analysis through the relationship between the number of particles and gyration diameter. The fractal exponent obtained from the power-law scaling of agglomerates and the complex agglomerate sizes were determined experimentally and theoretically. A simple theoretical model was applied to estimate the complex agglomerates' size based on the equilibrium of the separation and cohesion forces. The proposed model showed satisfactory results compared with the experimental data. The results of the present study can help to determine the critical gas velocity in achieving the desired agglomerate size of Titania NPs.


Main Subjects

[1] Nam C.H., Pfeffer R., Dave R.N., Sundaresan S., Aerated Vibrofluidization of Silica Nanoparticles, AIChE J. 50(8): 1776-1785 (2004).
[2] Yao W., Guangsheng G., Fei W., Jun W., Fluidization and agglomerate structure of SiO2 nanoparticles, Powder Technol. 124(1-2): 152-159 (2002).
[3] Hotze E.M., Phenrat T., Lowry G.V., Nanoparticle Aggregation: Challenges to understanding transport and reactivity in the Environment, J. Environ. Qual. 39(6): 1909-1924 (2010).
[4] Bashiri H., Mostoufi N., Sotudeh-Gharebagh R., Chaouki J., Effect of Bed Diameter on the Hydrodynamics of Gas-Solid Fluidized Beds, Iran. J. Chem. Chem. Eng. (IJCCE), 29(3): 27-36 (2010).
[5] Fotovat F., Ansart R., Hemati M., Simonin O., Chaouki J., Sand-Assisted Fluidization of Large Cylindrical and Spherical Biomass Particles: Experiments and Simulation, Chem. Eng. Sci. 126(1): 543-559 (2015).
[6] Sun G., Grace R., Effect of Particle Size Distribution in Different Fluidization Regimes, AIChE J. 38(5): 716-722 (1992).
[7] Geldart D., Types of Gas Fluidization. Powder Technol. 7(5): 285-292 (1973).
[8] Jing S., Hu, Q., Wang J., Jin Y., Fluidization of Coarse Particles in Gas-Solid Conical Beds, Chem. Eng. Process. 39(4): 379-387 (2000).
[9] Castellanos A., Valverde J.M., Quintanilla M.A.S. Physics of Compaction of Fine Cohesive Particles, Phys. Rev. Lett. 94(7): 075501 (2005).
[10] de Martin L., Sanchez-Prieto J., Hernandez-Jimenez F., van Ommen J., A Settling Tube to Determine the Terminal Velocity and Size Distribution of Fuidized Nanoparticle Agglomerates, J. Nanopart. Res. 16(1): 1-9 (2013).
[11] Wang XS, Palero VSoria J, Rhodes MJ., Laser-Based Planar Imaging of Nano-Particle Fluidization: Part i: Determination of Aggregate Size and Shape, Chem. Eng. Sci. 61(16): 5476-5486 (2006).
[12] To D., Dave R., Yin X., Sundaresan S., Deagglomeration of Nanoparticle Aggregates Via Rapid Expansion of Supercritical or High-Pressure Suspensions, AIChE J. 55(11): 2807-2826 (2009).
[13] Van Ommen R., Valverde, J.M., Pfeffer R., Fluidization of Nanopowders: A Review, J. Nanopart. Res., 14(3) :737-766 (2012).
[14] Hakim L.F., Portman J.L., Casper M.D., Aggregation Behavior of Nanoparticles in Fluidized Beds, Powder Technol. 160(3): 149-160 (2005).
[15] Laube J, Salameh S, Kappl M, Madler L, Ciacchi LC., Contact Forces between TiO2 Nanoparticles Governed by Interplay of Adsorbed Water Layers and Roughness, Langmuir 31(41): 11288-11296 (2015).
[16] Pimpang P., Zoolfakar A.S., Wongratanaphisan D., Gardchareon A., Nguyen E.P., Zhuiykov S., Choopun S., Kalantar-Zadeh K., Atomic Force Microscopy Adhesion Mapping: Revealing Assembly Process in Inorganic Systems, J. Phys. Chem. C, 117(39): 19984-19990 (2013).
[17] Jiang Q., Logan B.E., Fractal Dimensions of Aggregates Determined From Steady-State Size Distributions, Environ Sci. Technol. 25(12): 2031-2038 (1991).
[18] de Martin L., Fabre A., van Ommen J.R., The Fractal Scaling of fluidized Nanoparticle Agglomerates, Chem. Eng. Sci. 112: 79-86 (2014).
[19] Fabre A, Salameh S, Colombi Ciacchi L, Kreutzer M.T., van Ommen J.R. Contact Mechanics of Highly Porous Oxide Nanoparticle AgglomeratesJ. Nanopart. Res. 18(1): 1-13 (2016).
[20] Fabre A., Steur T., Bouwman W.G., Kreutzer M.T., van Ommen J.R., Characterization of the Stratified Morphology of Nanoparticle Agglomerates, J. Phys. Chem. C 120(36): 20446-20453 (2016).
[21] Valverde J.M., Castellanos A., Fluidization of nanoparticles: A Modified Richardson-Zaki Law, AIChE J., 52(2): 838-842 (2006).
[22] Ehrl L., Soos M., Lattuada M., Generation and Geometrical Analysis of Dense Clusters with Variable Fractal Dimension, J. Phys. Chem. B, 113(31): 10587-10599 (2009).
[23] Quintanilla M.A.S., Valverde J.M., Castellanos A., Lepek D., Pfeffer R., Dave R.N., Nanofluidization as Affected by Vibration and Electrostatic Fields, Chem. Eng. Sci. 63(22): 5559-5569 (2008).
[24] Sorensen C.M., Roberts G.C., The Prefactor of Fractal Aggregates, J Colloid Interf. Sci. 186(1): 447-456 (1997).
[25] Jiang Q., Logan B.E., Fractal Dimensions of Aggregates Determined from Steady-State Size Distributions, Environ. Sci. Technol. 25(12):2031-2038 (1991).
[26] Nakamura H., Watano S., Fundamental Particle fluidization Behavior and Handling of  Nano-Particles in a Rotating Fluidized Bed, Powder Technol., 183(3): 324-332 (2008).
[27] Zhou T., Li H.Z., Force Balance Modelling for Agglomerating Fluidization of Cohesive Particles, Powder Technol., 111(1-2): 60-65 (2000).
[28] van Ommen J.R., Mudde R.F., Measuring the Gas-Solids Distribution in Fluidized Beds-A Review. Int. J. Chem. React. Eng. (IJCRE), 6(1): 1-29 (2008).
[29] Rong W., Pelling A.E., Ryan A., Gimzewski J.K., Friedlander S.K., Complementary TEM and AFM Force Spectroscopy to Characterize the Nanomechanical Properties of Nanoparticle Chain Aggregates, Nano Lett. 4(11): 2287-2292 (2004).
[30] Bahramian A., Kalbasi M., CFD Modeling of TiO2 Nano-Agglomerates Hydrodynamics in a Conical Fluidized Bed Unit with Experimental Validation, Iran. J. Chem. Chem. Eng., (IJCCE), 29(2): 105-120 (2010).
[31] Bahramian A., Grace J.R., Fluidization of Ttitania Nanoparticle Agglomerates in a Bench-Scale Conical Vessel, Powder Technol. 310(1): 46-59 (2017).
[32] Brasil A.M., Farias T.L., Carvalho M.G., A Recipe for Image Characterization of Fractal-Like Aggregates, J. Aerosol Sci. 30(10): 1379-1389 (1999).
[33] Tamadondar M.R., Zarghami R. Boutou K., Tahmasebpoor M., Mostoufi N.Size Of Nanoparticle Agglomerates in Fluidization, Can. J. Chem. Eng. 94(3): 476-484 (2016).
[34] Zhang W., Noda R., Horio M., Evaluation of lubrication Force on Colliding Particles for DEM Simulation of Fluidized Beds, Powder Technol., 158(1-3): 92-101 (2005).
[35] Bushell G., Yan Y., Woodfield D., Raper J., Amal R., On Techniques for the Measurement of the Mass Fractal Dimension of Aggregates, Adv. Colloid Interface Sci. 95(1): 1-50 (2002).
[36] Bergstrom L., Hamaker Constants of Inorganic Materials, Adv. Colloid Interface Sci. 70(1): 125-169 (1997).
[37] Ergun S., Fluid Flow Through Packed Columns, Chem. Eng. Prog. 48(2): 89-94 (1952).
[38] Masoodiyeh F., Karimi Sabet J. Mozdianfard M., Population Balance Modelling of Zirconia Nanoparticles in Supercritical Water Hydrothermal Synthesis, Iran. J. Chem. Eng. (IAChE), 38(4): 1-9 (2019).
[39] Ghorbani H., Sotudeh-Gharebagh R., Abbasi M., Zarghami R., Mostoufi N., Modeling of Vibration of a Fluidized Bed Cylindrical Shell, Iran. J. Chem. Eng. (IAChE), 10(2): 67-80 (2013).
[40] Kendall K., Alford N.M., Birchall J.D., Elasticity of Particle Assemblies as a Measure of the Surface Energy of Solids, Proceedings of the Royal Society of London A: Mathematical. Phys. Eng. Sci. 412(1843): 269-283 (1987).
[41] Shabanian J., Jafari R., Chaouki J., Fluidization of Ultrafine Powders, Int. Rev. Chem. Eng. (I.RE.CH.E.), 4(1): 16-50 (2012).