Resolving Multiscale Diffusion in a Nanoparticle Fluidized Bed Atomic Layer Deposition Reactor by an Extended Two-Fluid–Population Balance Model

Fluidized bed atomic layer deposition (FB-ALD) has emerged as a scalable technique for surface coating on nanoparticles with subnanometer precision. Nevertheless, nanoparticles, due to strong cohesive forces, tend to form polydisperse agglomerates during fluidization, complicating mass transfer and reaction processes. In this study, a two-stage diffusion-reaction model for nanoparticle agglomerates is developed and coupled with a two-fluid model–population balance model (TFM-PBM), which effectively simulates fluidized bed reactors while considering fragmentation and reassembly of agglomerates during fluidization. The effects of particle cohesion and fluidizing gas velocity on ALD of nanoparticles in a fluidized bed reactor are investigated. The diffusion-reaction model can capture diffusion resistances at two scales: primary and complex agglomerates of nanoparticles and describe how the diffusion resistance increases with agglomerate size. The main factors affecting precursor conversion are the average size of complex agglomerates and the precursor residence time. The smaller the agglomerate size, the smaller the diffusion resistance; the longer the precursor residence time, the more sufficient contact with substrate particles. The precursor utilization is optimal when the agglomerate size is small and the gas velocity is just sufficient for fluidization.