NUMERICAL HOMOGENIZATION AS A METHOD FOR MODELING CONSTRAINED DIFFUSION

Material transport by diffusion is present in nature, as well as in living organisms as a vital process. The basic and generally used is a phenomenologically established law, named Fick’s law, It states that the material flux is proportional to the concentration gradient and that the material flows from the higher to lower concentration. However, if the diffusion occurs in nano space, the interaction of the transported molecules produces deviation from Fick’s law leading to a so-called restrained, or retarded diffusion. Using the Molecular Dynamics (MD) methodology, we have calculated the effects of the molecule-solid interaction by introducing the scale functions and used them in our finite element code PAK to find the equivalent bulk diffusivity and equivalent distance from the solid surface. This computational procedure is called numerical homogenization, where the equivalent diffusion parameters are evaluated from the mass release curves. Verification of our multiscale modeling of the retarded diffusion is demonstrated on glucose transport through a device with nanochannels (NDS). Our methodology is illustrated by two examples – one to show the effects of the molecular interaction within a space with solid spheres and several porosities, and another where the equivalent diffusion coefficients are computed using images of pancreatic tumor tissue.