Numerical Simulations

The governing equations describing our systems of interest are usually a set of coupled nonlinear partial differential equations and algebraic equations. Therefore, numerical solutions are commonly required. In most of our studies, we solve a set of mass transfer equations (usually using the Nernst-Planck equation), an equation describing electrostatic interactions (either the electroneutrality condition or the Poisson equation), and expressions describing the chemical reactions that occur (either homogeneous or redox). To solve this complex set of nonlinear equations, we usually use COMSOL Multiphysics®. The solutions of such models can provide valuable information, including local pH values and the characteristics of local boundary layers.

Further reading:

• Calculation of local pH in an electrosorption cell:
  • Shocron et al., PNAS, 2021, link: https://doi.org/10.1073/pnas.2108240118
  • Shocron et al., Chem. Eng. J., 2023, link: https://doi.org/10.1016/j.cej.2023.142722
• Analysis of boundary layers develop in an electrodialysis stack: Shocron et al., J. Membr. Sci., 2025, link: https://doi.org/10.1016/j.memsci.2024.123668