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 transported 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 surfaces 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. Using this procedure, we evaluate constitutive material parameters of the continuum model, which include: 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 configurations: silica nanofibers, and a complex internal structure consisting of randomly placed nanospheres and nanofibers. This new approach, consisting of microstructural model, numerical homogenization and continuum model, offer a new platform for modeling diffusion within complex media, capable of connecting micro and macro scales.