Characterising the Morphology of Disordered Materials

Abstract

Abstract. We introduce Minkowski functionals to characterise, reconstruct and discriminate different complex material microstructures, for instance, experimental data sets generated from X-ray computer tomography imaging; samples include a suite of Fontainebleau sandstone, and a heterogeneous cross-bedded sandstone. Three distinct classes of digitised complex microstructure are considered: particle based Boolean models, structures generated by level-cuts through Gaussian fields, and models based on a Voronoi tesselation of space. One can define a set of measures for random composite media from a single image at any phase fraction φ which allows one to accurately reconstruct the medium for all other phase fractions and to predict, for instance, the percolation threshold pc. The evolution of the Minkowski functions during erosion and dilation operations on non-convex morphologies leads to a very accurate discrimination of morphologybetter than commonly used techniques such as structure functions or chord length distributions. Spatial Structures: Experimental Data and Stochastic ModelsThe structure of a disordered material -an oil bearing rock, a piece of paper, or a polymer composite -is a remarkably incoherent concept. Despite this, scientists and engineers are asked to predict the properties of a disordered material based on the "structure" of its constituent components. A major shortcoming in the understanding of processes involving complex materials has been an inability to accurately characterize microstructure. The specification of "structure" requires topological as well as geometric descriptors to characterize the connectivity and the shape of the spatial configuration. In oil recovery from petroleum reservoir rocks, an area of particular interest to the authors, recovery depends crucially on the topology of the pore space and on the mean curvature of the surfaces where immiscible phases meet at a contact angle. To determine accurate flow models and to devise intelligent recovery strategies requires an accurate characterization of reservoir rocks in terms of topology and geometry.To date, the main toolkit used to quantify complex structures has been primarily that of the statistical physicist and not the advanced techniques developed in spatial statistics [11,59]

Design of acoustic trim based on geometric modeling and flow simulation for non-woven

“…granular porous media or foams. Boolean models can be fitted to sandstone samples [3], open foams can be described using the edge system of random tessellations [15], concrete by random packings of spheres [4], sinter structures as random tessellations. In most cases the suitable models can not be described using few parameters and model fitting is restricted to "trial and error".…”

“…Order of convergence 1.5 is proven for arbitrary located interface, and second order convergence is proven for the case when the interface coincides with a grid node. Furthermore, following the ideas from [3], modifi ed HA discretization are suggested for particular cases. The velocity and the stress are approximated with second order on the interface in this case.…”

Minkowski Functionals of Connected Soil Porosity as Indicators of Soil Tillage and Depth

“…Among these, Minkowski functionals (Arns et al, 2002;Lehmann et al, 2006) are specially interesting. They provide four fundamental geometrical properties of 3D objects, like soil porosity, embedded in three-dimensional space.…”

“…Mecke (2002) and Vogel et al (2005) studied the variation of Minkowski funcionals based on the morphological effect of the dilation and erosion operations. This technique was also used by Arns et al (2002Arns et al ( , 2004 to characterize 3D images of Fontainebleau sandstone. Furthermore, Renard and Allard (2013) used the Euler numbers variation subject to erosion and dilation to describe connectivity as a means for characterizing heterogeneous aquifers with 2D models.…”

Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

“…Erosion of the pore space is dilation of the soil 219 matrix, and erosion of the soil matrix is dilation of 220 pore space. For an object K , the erosion by a ball of 221 radius r is defined as (ARNS et al, 2002).…”