(中南大学 冶金与环境学院，长沙 410083)
摘 要: 采用分形维理论对经典的流固反应收缩核模型进行分析，推导了新的流固反应分形收缩核模型，包括界面反应控制模型、外扩散控制模型及内扩散控制模型，体现了固体颗粒表面不规则性对流固反应的影响。通过废弃电路板多金属富集粉末低温碱性熔炼产物的水浸出过程，对比经典模型和分形模型的拟合效果。结果表明：两模型对此浸出过程控制步骤判断一致，为内扩散控制。而分形模型较经典模型与实验数据的符合程度更高、物理意义更清晰，因而具有更强的适用性。
关键字: 分形几何；收缩核模型；废弃电路板；水浸出
（School of Metallurgy and Environment, Central South University, Changsha 410083, China）
Abstract:The concept of fractal was applied to analyze the classical shrinking core models of fluid-solid reactions, the novel fractal shrinking core models, including interface reaction model, boundary diffusion model and intraparticle diffusion model of fluid-solid reactions are obtained based on fractal geometry. The effect of the surface irregularity of the solid particles on the reaction was investigated. Fitting effects of classical models and fractal models were compared by water leaching experiments of low-temperature alkaline smelting product with metal enrichment from waste printed circuit boards. The results show that the leaching processes of both models are controlled by intraparticle diffusion, whereas, the fractal models agree better with the experimental data, and have clearer physical understanding. So, the fractal kinetic models are more suitable than the classical models.
Key words: fractal geometry; shrinking core models; waste printed circuit board; water leaching
