Electrodialysis has become a relevant technology in promoting sustainability within the food industry. Bipolar membrane electrodialysis offers an efficient and eco-friendly alternative for skim milk acidification, eliminating the need for added acids that affect milk composition and properties. For the first time, this study presents a comprehensive 2-D computational model to investigate the multi-ionic transport and dynamics of skim milk electro-acidification using bipolar membrane electrodialysis. The model is based on conservation equations for mass-charge transport, coupled with the description of water-splitting through the second Wien effect. The primary focus of the analysis was on the skim milk pH evolution and the concentration profiles of the major ions. The results showed that ion concentration values varied due to concentration polarization and differences in ion mobilities. The simulations were compared with experimental data, showing reasonable agreement, particularly for Ca²⁺ ion concentration. Despite excluding organic components in its analysis, this model offers a novel and valuable approach to the study of skim milk electro-acidification using bipolar membrane electrodialysis, providing essential insights for process understanding and optimization.