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