Design principle for topography-optimized porous reactors: entropy generation minimization and equipartition of entropy production

In this study, we explore the connection between topography-optimized porous structures and theoretical frameworks like entropy generation minimization and equipartition of entropy production within a porous reaction-diffusion system. Using topography optimization (TO) with diverse objective functions—maximizing reaction rates, minimizing inlet concentration, reducing global total entropy generation, and enhancing uniformity in entropy generation—we analyze how optimized structures respond across Damköhler numbers ranging from 0.1 to 50. Our findings show that, despite the variation in objectives (except for enhancing uniformity in entropy generation), the optimized porous structures exhibit a root-like morphology that facilitates both mass transport and reaction, adapting to different conditions to balance reaction and diffusion processes. The results reveal that the entropy generation in these optimized structures becomes more uniform and approaches similar values across all objective functions, aligning with the principles of entropy generation minimization. In contrast, the optimized porous structure obtained for the case of enhancing uniformity in entropy generation exhibits a simple distribution, with higher porosity near the inlet and lower porosity at the farthest end. This uniformity in entropy generation indicates that structural evolution converges towards an efficient balance between reaction and transport requirements. These findings establish a foundational link between TO-derived porous structures and thermodynamic optimization principles, suggesting that design processes can leverage these principles directly to achieve high-efficiency structures.