Structural Characterization of Porous and Granular Materials

摘要

The morphological details of permeable porous materials impact significantly their macro-scale properties and in particular transport properties (e.g. permeability). A programme to derive macroscopic behaviour and responses from pore-scale information is a holy grail in the field. We report here progress on, and tests of, a recently proposed such a programme. The main steps of the programme are as follows. The solid phase of a porous material is first skeletonised into a framework of nodes and edges. Then the local structure is quantified by means of structure tensors, which describe the shape of novel volume elements called quadrons. Next, the local tensor description is used in an entropy-based statistical formalism to compute macroscopic structural characteristics as expectation values over a certain partition function. From the structural characteristics, physical properties can be evaluated. The 'thickened' structure is taken account of with an additional partition function, giving more accurate evaluation of structural and physical properties. Here we present tests for the initial stages of the programme. The tests are carried out on numerically generated two-dimensional granular aggregates. Specifically, we describe results on the statistics of the quadrons and the structural tensors.