Applying Mode Analysis for Morphology Dependent Evaluation of Particle Scale Averaged Diffusion-Reaction in Porous Media

In applications such as heterogeneous catalysis and drying, intraparticle transport resistances can be rate limiting. Transport phenomena in porous media have shown to be elusive to describe accurately on the macro-scale, albeit research on this topic has been conducted for more than a century. The major challenge of this multiscale problem is the intricate influence of pore-scale phenomena on the macroscopic-level transport. To evaluate the applicability of common averaged porous media models, an evaluation method was developed which investigates the decay of Fourier modes within a given porous medium. In addition, a 3D resolved model of diffusion and first order reaction within a spherical porous particle was developed using a Finite-Volume approach, applying a second order implicit immersed boundary method for geometry insertion. This numerical model was used to monitor transient concentration fields at a variety of characteristic length scales and particle Thiele moduli. As complementary analysis, the effective transient flux at the particle boundary was computed. The gathered results were then subjected to the developed mode decay analysis and compared with the ideal averaged solutions. The insight generated on the emergence of effective macroscopic-scale behavior from the pore-scale phenomena will be discussed.