Ziemus A., Numerical modeling of diffusion in complex media with surface interaction effects

Abstract: Diffusion in natural, technological and biological systems is very common and most important process. Within these systems, which contain complex media, diffusion may depend not only on internal geometry, but also on the chemical interactions between solid phase and trans-ported particles. Modeling remains a challenge due to this complexity. Here we first present a new hierarchical multiscale microstructural model for diffusion within complex media that incorporates both the internal geometry of complex media and the interaction between diffusing particles and sur-faces of microstructures. Hierarchical modeling approach, which was introduced in [1], is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. Us-ing this procedure, we evaluate constitutive material parameters of the continuum model, which in-clude: equivalent bulk diffusion coefficients and the equivalent distances from the solid surface. Here, we examined diffusion of glucose through water using the following two geometrical/material confi-gurations: silica nanofibers, and a complex internal structure consisting of randomly placed nanos-pheres and nanofibers. This new approach, consisting of microstructural model, numerical homogeni-zation and continuum model, offer a new platform for modeling diffusion within complex media, ca