Fluids in porous media: A morphometric approach

A set of four morphological measures, so-called Minkowski functionals, was defined which allows to quantitatively characterize the shape of spatial structures, to optimally reconstruct porous media, and to accurately predict material properties. The method is based on integral geometry and Kac's theorem which relates the spectrum of the Laplace operator to the four Minkoski functionals. The integral geometric measures, i.e., Minkowski functionals of the spatial structure proved to be structural quantities which are important for many physical properties of heterogeneous materials. It was shown that completely porous media exhibit very similar conductivities and elastic moduli as long as the structures have the same Minkowski functionals.