Results of Granulometry & Porosimetry
As the Granulometry tries to place spheres of discrete sizes into the pores, the size of a pore can only be determined within a small frame, which corresponds to the Bin Size.
Enter the Bin Size in units of voxels. The equivalent in metric length units is shown on the right. The bin size determines the range of diameters that belong to one class of pore sizes.
All bins have equal bin size. Beginning with the largest possible diameter that is divisible by the bin size the diameter is reduced by the bin size in each step. Every voxel is then assigned the diameter of the largest possible sphere that can be fitted in the pore and contains this voxel. Thus, each bin contains pore voxels with an assigned diameter in the range comprised between and , where is the bin number.
For example, when analyzing a porous structure with a voxel size of 1 µm, you can set the bin size to 2 or to 4 (voxels) which would come to classify the pores by their diameter in ranges of 2 µm or 4 µm, and would result in the following bins:
Bin number () |
Pore diameter between |
|
|---|---|---|
Bin Size 2 µm |
Bin Size 4 µm |
|
1 |
0 µm - 2 µm |
0 µm - 4 µm |
2 |
2 µm - 4 µm |
4 µm - 8 µm |
3 |
4 µm - 6 µm |
8 µm - 12 µm |
.. |
... |
... |
When choosing the bin size, be aware that the underlying algorithm to compute the Euclidean distance operates directly on the voxel grid. Thus, the smallest possible distance between two grid points is 1 voxel, which corresponds to a pore radius of 1 voxel. This means the smallest pore diameter that the algorithm will find is 2 voxels. In general, the error made when computing the pore size distribution is of the same order of magnitude as the discretization error of the structure, i.e. 1 voxel.
In the result viewer, for each bin the Minimal Diameter, which is the diameter of the smaller sphere, and the Maximal Diameter, which is the diameter of the larger sphere, are given. This means all pore voxels in that bin have a diameter that is larger or equal than the minimal diameter and smaller than the maximal diameter.
The Volume Fraction of the pore voxels in each bin and the Cumulative Volume Fraction (starting with the smallest pore diameters) based on the total pore volume of the structure are shown. For each bin, the Pore Volume in m3 is computed as the summarized volume of the voxels that belong to this bin.
The Differential Pore Volume for each bin is computed, where both the common logarithm () and the natural logarithm () are shown. The differential pore volume distribution is then computed as:
with the pore diameter of the -th bin, the cumulative volume fractions, and the mass of the pores. The latter is computed using the densities of the constituent materials of the sample entered in the Material Densities tab. This normalization ensures that the value of the differential pore volume is independent of the domain size.
