SCS

Abstract

A stochastic network model is developed which describes the 3D morphology of the pore system in fibre-based materials. Such materials are used e.g. for the so-called gas diffusion layer (GDL) in polymeric fuel cells. In the pore space of GDL essential transport processes take place, like the diffusion of oxygen and hydrogen, respectively, towards the electrochemically active sites,or the drainage of produced water. Recently, various models for the solid phase of GDL, in particular for the fibre system itself, have been developed where the pore space is considered as complementary set. However, this indirect description of pore space often leads to very complex geometric structures, i.e., it is described by huge sets of voxels, which make numerical simulations of transport processes quite complicated and computer time consuming, especially for large domains. In the present talk, a mathematical model for random geometric graphs is developed, representing the pore space directly. It can be applied e.g. to investigate transport processes in GDL on a large scale. We first model the vertex set of the graph by a stack of 2D point processes, which can physically be interpreted as pore centres. Each pore centre is then marked by its pore size. In the second step, the edge set of the graph is constructed, where the vertices are connected using tools from graph theory and MCMC simulation. The model parameters are statistically fitted to real 3D data gained by means of synchrotron tomography. Finally, the stochastic network model is validated by considering physical characteristics of GDL like their tortuosity, i.e., the distribution of shortest path lengths through the material relative to its thickness. The talk is based on joint research with W. Lehnert, I. Manke and R. Thiedmann.