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

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.