Numerical analysis on optimization of porosity distribution in a reaction-diffusion system

Reaction-diffusion systems in porous media are widely seen in chemical and electrochemical engineering, e.g. fuel cells and batteries. The reason that porous media are typically used in electrochemical devices is because of their capability to enhance the catalytic surface area. Topology optimization of a spatial distribution of porosity in porous media is one of the promising approaches for maximizing overall reaction in the system. However, the solution obtained from this approach is just based on mathematical foundation.  In this study, a numerical investigation based on adjoint methods was carried out to examine an optimized porosity distribution in reaction-diffusion systems. 0D, 1D and 2D optimization results were compared. Nonequilibrium thermodynamics was then applied to investigate for the entropy generation in the system. The results from this study provide a basic foundation of how to improve performance of electrochemical devices using a tuning of a spatial distribution of porosity in porous media.