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Institut für Wasserbau - IWS

Selected Topics and International Network Lectures

16:00 Uhr
Herr Mecke, Max-Planck-Institut Stuttgart

Fluids in porous media - a morphometric approach

The structure of a disordered material - an oil bearing rock, a piece of paper, a polymer composite - is a remarkably incoherent concept. Despite this, scientists and engineers are asked to relate its properties to the structure of its constituent components. For instance, the fluid flow in sandstones depend crucially on the shape and distributiuon of the pores. Integral geometry furnishes a suitable family of morphological descriptors, known as Minkowski functionals, which are related to curvature integrals and do not only characterize connectivity (topology) but also size and shape (geometry) of spatial structures. Applying the Minkowski functionals to parallel surfaces of distance (r) to a structure one can define a family of morphological functions to characterize and reconstruct complex materials at porosity. Based on the morphological functions one can derive accurate expressions for percolation thresholds, transport properties and phase equilibria in porous media.

We illustrate this for the conductivity and elasticity of complex model systems and experimental sandstone samples. In particular, for Boolean models the morphological functions are uniquely determined by its value at r=0 at any porosity. Thus a single image of a porous media is sufficient to estimate and to predict physical properties such as permeabilities and elastic moduli.

C. H. Arns, M. A. Knackstedt, and K. Mecke, Reconstructing complex materials via effective grain shapes, Phys. Rev. Lett. 91, 215506 (2003).

Mecke, K. R. and D. Stoyan, Morphology of Condensed Matter - Physics and Geometry of Spatially Complex Systems, Lecture Notes in Physics, Vol. 600, Springer 2002.