CAVTAT 2006

1
Application of Micro Computer Tomography to
Identification of Pore Structure Parameters of
Porous Materials Mieczyslaw Cieszko, Zbigniew
Szczepanski Institute of Environmental Mechanics
and Applied Computer Science Kazimierz Wielki
University, Bydgoszcz, Poland cieszko_at_ukw.edu.pl
zszczep_at_ukw.edu.pl
1. Introduction
Determination of the pore space structure
parameters of porous materials is very important
for applications. Porous materials are commonly
present in nature (e.g. the rocks, soils, wood),
biology (e.g. bone tissue, lung, membranes) and
technology (e.g. sintered metals, ceramics,
aerogels and concretes). Their pore structure
plays important role in many physical and
chemical processes occurring in such materials
in transport of mass, momentum and energy, in
wave propagation or chemical reactions. It also
strongly influences mechanical properties of the
skeleton. There are many different methods used
for identification of pore structure parameters
optical, dynamical (e.g. ultrasonic and vibration
methods) and static (e.g. permeametry, gas
picnometry, electric spectroscopy and mercury
porosimetry). To the static methods belongs also
the Micro Computer Tomography (µCT). It is very
modern method of identification of microscopic
structure of inhomogeneous materials.
This allows to determinate their stochastic
characteristics, macroscopic parameters of
structure and also material constants. The
purpose of this paper is to apply the scans of
microscopic geometry of human bones obtained by
µCT method to identification of their macroscopic
pore structure parameters volume porosity,
permeability and tortuosity of pores and
skeleton. These parameters, except the volume
porosity, have been determined by simulations of
microscopic processes of viscous fluid flow and
electrical current passage through samples of
bones. The simulations were performed using the
COMSOL Multiphysics environment assigned for
solution of boundary value problems described by
partial differential equations, by use of the
finite element method.
2. Identification of microscopic geometry of pore
space
Scaning (pixel size17mm)
a)
c)
a)
b)
Fig.2. 3D Microcomputer Tomography scans of human
bone (a) and its selected parts of size
500x500x100 (b) and 200x200x100 (c) (pixel
size17mm)
Fig.1. Microcomputer thomograph of SkyScan
,
Reduction of recognition. Weighting method

Sample size 120x120x8 Voxel size 34mm Binary
file size S 17 MB
Sample size 60x60x4 Voxel size 68mm Binary file
size S 7 MB
Sample size 240x240x16 Voxel size 17mm Binary
file size S 40 MB


Fig.5.
Fig.4.
Fig.3.
3. Determination of macroscopic parameters of
pore space structure
Volume porosity. Influence of sample size.
a)
b)
Fig.6. Dependence of volume porosity on the size
of one-layer sample (a) and on the size of the
sample (b)
Macroscopic description
Measurement of tortuosity and surface porosity
Tortuosity of pores
Ohms law for current passage
is a measure of mean length of paths of inviscid
fluid particle flow in the pore space between two
parallel planes to distance between these planes.
For anisotropic pore space.
where
Theoretical basis for conductometric measurements
I current density
E current intensity
Pore level Analogy of inviscid fluid flow
and current passage through the conductor
filling nonconductive skeleton.
?0 specific resistivity of conductor ?
specific resistivity of sample
R resistivity tensor
C conductivity tensor
MA metric tensor of pore space
M metric tensor of physical space
Tortuosity (d) and surface porosity (?)
For isotropic pore space
For direction n they take form
Vf,Ve potentials of fluid velocity and
electrical field.
where