Prediction of agglomerate size distributions during nanoparticle fluidization using a mechanistically grounded gas shear breakage kernel function in population balance model

Nanoparticles always fluidize as agglomerates in fluidized bed reactors, the agglomerate size distribution evolution due to breakage and agglomeration affects the fluidization quality and reaction efficiency. Regarding this, the present study proposes a mechanistically grounded gas shear breakage kernel function based on the outer layer stripping breakage mechanism experimentally suggested by numerous researchers, and incorporates the agglomeration kernel function considering gas shear and perikinetic motion, to obtain dynamic agglomerate size distributions by solving population balance equations. Then the dynamic agglomerate sizes are used to modify the kinetic theory of cohesive particle flow and the gas-agglomerate interphase momentum exchange, to simulate agglomerate behaviors of 25 nm SiO₂ nanoparticles at superficial gas velocities of 1.58 ∼ 2.50 times the minimum fluidization velocity. Furthermore, the experiments under conditions corresponding to the simulations are conducted. Experimental validation for simulations is performed using splash-zone particle image velocimetry data, although the inherent limitations exist in the resolution for agglomerate identification of experimental measurement and image processing within the splash zone. The simulated results show that the bed expansions, volume fractions, and size distributions of agglomerates agree well with experimental data. Comparative analysis with literature kernels reveals improved predictive accuracy of the proposed kernel. Particularly, the prediction error for agglomerate sizes is approximately 4 %. A local sensitivity analysis confirms the prediction error change remains below 0.88 %. This indicates the outer layer stripping breakage mechanism is crucial in reflecting nanoparticle agglomerate breakage and the proposed breakage kernel function can be used to effectively predict agglomerate size distributions during nanoparticle fluidization.