Numerical analysis of sodium diffusion in aluminum electrolysis cathode carbon blocks based on a microstructure multi-factor corrected model

Current researches on sodium penetration in electrolytic aluminum cathode carbon blocks primarily measure cathode expansion curves, showing mostly macroscopic characteristics. However, the microscopic structure is often underexplored. As a porous medium, the diffusion performance of cathode carbon blocks is closely tied to their internal pore structure. Viewing the cathode carbon block as a multiphase composite material, this study examines the sodium diffusion process from a microstructural perspective. A prediction model for sodium diffusion, considering factors like porosity, temperature, binding effects, current density, and molecular ratio, was developed. A random aggregate model was implemented in Python and imported into finite element software to simulate sodium diffusion using Fick's second law. Results indicate that increased porosity, higher temperatures, reduced binding effects, increased current density, and higher molecular ratios enhance sodium infiltration, reducing diffusion resistance and increasing the diffusion coefficient. The simulation aligns well with experimental results, confirming its accuracy and reliability.