### Random geometric graphs for modelling the pore system in fibre-based materials

Schmidt, V *(Ulm)*

Wednesday 31 March 2010, 16:00-17:00

Seminar Room 2, Newton Institute Gatehouse

#### 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.