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Mechanical size reduction is a critical pretreatment for hydrometallurgical recovery of valuable metals in electronic waste. The particle size resulting from milling ranges from a few micrometers to a few millimeters, presenting challenges of achieving sufficient leaching percolation in portions occupied by fine particles. This work investigates the hydrodynamics of percolation through micrometer-sized fine particle beds by using many-body dissipative particle dynamics flow simulations. The results show that higher effective pore size resulting from high aspect-ratio particle packing contributes to higher permeability than spherical particle packing. Increasing surface wettability enhances maximum saturation rates but reduces permeability. Moreover, increasing tortuosity negatively impacts permeability and the degree of reduction in permeability caused by increased surface wettability decreases with increasing tortuosity. These findings imply possible complex relationships between tortuosity, pore size, and surface wettability that collectively impact percolation in loosely packed fine particle beds and can be used to guide improvement in pretreatment. 

An extended population balance model (PBM) and a deep learning-based enhanced deep neural operator (DNO+) model are introduced for predicting particle size distribution (PSD) of comminuted biomass through a large knife mill. Experimental tests using corn stalks with varied moisture contents, mill blade speeds, and discharge screen sizes are conducted to support model development. A novel mechanism in the extended PBM allows for including additional input parameters such as moisture content, which is not possible in the original PBM. The DNO+ model can include influencing factors of different data types such as moisture content and discharge screen size, which significantly extends the engineering applicability of the standard DNO model that only admits feed PSD and outcome PSD. Test results show that both models are remarkably accurate in the calibration or training parameter space and can be used as surrogate models to provide effective guidance for biomass preprocessing design.