Finite-size effects on heat and mass transfer in porous electrodes

In thin electrode applications, as the ratio of the obstacle size with respect to the system size increases, issues such as finite-size effects become more influential in the transport of heat and mass within a porous structure. This study presents a numerical approach to evaluate the finite-size effects on the heat and mass transfer in porous electrodes. In particular, numerical simulations based on the lattice Boltzmann method (LBM) are employed to analyze the pore-scale transport phenomena. Analyzing the results at both the electrode level and the pore level shows that the mass transfer performance is more influenced by the finite-size effects compared to the transfer of heat. The numerical simulations show that as the parameter m being the ratio of the electrode thickness to the particle diameter is halved, the effective diffusivity increases by 20% while the effective conductivity remains unchanged. We propose a novel analytical tortuosity-porosity (tau - phi) correlation as tau = [1-(1-phi)(m+1)]//phi where the finite-size effects are taken into account via the parameter m. Besides, particles of small size provide more uniform distributions of temperature and concentration within the porous structure with standard deviations of approximately half of the values obtained from the case made up of large particles. Our findings at the electrode level are compared with the commonly used macroscopic porosity-dependent correlations found in the literature. At the end, by performing a systematic assessment, we provide guidelines for efficient design of porous electrodes.