Mathematical Analysis

Mathematical analysis of the equations describing different processes can be a powerful tool. One can estimate the typical timescales or lengthscales of the different processes, assess the conditions that lead to different regimes, and, in some cases, even obtain a complete analytical solution, from which optimization can be performed very easily. However, such analyses usually require simplifications that are not always valid. Therefore, in our lab, we perform such analyses when possible. Examples include deriving an analytical expression for the system’s impedance (as illustrated in the figure), simplifying expressions of boundary conditions, and assessing the constraints under which widely adopted models are valid.

Further reading:

• An analytical expression for the impedance of an electrode: Alfisi et al., ACS Sustainable Chem. Eng. A, 2022, link: https://doi.org/10.1021/acssuschemeng.2c02169
• Simplifying the boundary conditions used to describe an electrosorption cell: Guyes et al., Desalination, 2017, link: http://dx.doi.org/10.1016/j.desal.2017.03.013
• Find the conditions for which the volume averaging approach can be used to describe an electrosorption cell: Shocron and Suss, EPL, 2020, link: http://doi.org/10.1209/0295-5075/130/34003