An approach in analyzing the kinetics of reacting metallurgical system enhanced by applied electrical potential difference has been proposed. The approach accounted the electrochemical mechanism by combining Fick’s first law and Nernst–Planck equation, building upon the approach by Kim et al. and extending it to simultaneously solve the key kinetics parameters of boron diffusivity in slag (D_(B)) and potential difference (\({\Delta \phi }_{s}\)) across the slag phase. The approach was utilized to examine the kinetics of enhanced boron removal from silicon with CaO-SiO₂ and CaO-SiO₂-Al₂O₃ slags, in the context of silicon recycling and refining. The model was used to describe the mobility of boron in the molten silicon and slag phases, i.e., boron mass transfer coefficient in liquid silicon (k_m), in the slag (k_s), and the diffusivity of boron in slag phase (D_(B)). The results demonstrated that the new kinetics model fit well with the experimental data with an average coefficient of determination (R² value) of 0.91. The k_s and D_(B) were calculated to be in the range of 0.9 to 1.3 × 10^–6 and 1.1 to 29.2 × 10^–9 m² s⁻¹, respectively. The application of external voltage was observed to reduce B final concentration in the silicon phase by 18 pct from approximately 120 to 100 ppmw in all samples. The addition of Al₂O₃ in the slag phase consistently reduced the mobility of boron in the slag phase by approximately 50 pct.

提出了一种分析由外加电势差增强的反应冶金系统动力学的方法。该方法以 Kim等人的方法为基础，通过结合菲克第一定律和能斯特-普朗克方程来解释电化学机制。并将其扩展以同时求解渣中硼扩散率 ( D _{( B )} ) 和渣相电位差 ( \({\Delta \phi }_{s}\) )的关键动力学参数。该方法用于检查使用 CaO-SiO ₂和 CaO-SiO ₂ -Al ₂ O _{3从硅中去除硼的强化动力学}炉渣，在硅回收和精炼的背景下。该模型用于描述硼在熔融硅和渣相中的流动性，即硼在液态硅中的传质系数（k _m）、在渣中的传质系数（k _s）和硼在渣相中的扩散系数（D _（乙））。结果表明，新的动力学模型与实验数据吻合良好，平均决定系数（R ²值）为0.91。k _s和D _{( B )}的计算范围为 0.9 至 1.3 × 10 ^–6和 1.1 至 29.2 × 10 ^–9 m ²  s ⁻¹，分别。观察到外部电压的应用使所有样品中硅相中的 B 最终浓度降低了 18 pct，从大约 120 到 100 ppmw。_{Al 2} O ₃在渣相中的添加始终如一地减少了硼在渣相中的流动性大约 50 pct。