A foam can be modeled as a homogeneous random tessellation with convex cells. In the case 
sata ie of an open foam, see Figure 1(a), the solid component forms a parallel set (i.e. a dilated set) of 
ade the cell edges of the underlying tessellation. Thus an important geometric characteristic of an 
vr open foam is the length density Ly of the edges, also called the total length of edges per unit 
. volume or the specific edge length. For La we get the estimate Ly ~ My /m(1 — Vy). Notice 
- that form Ly one can compute a lot of further characteristics, e.g. the mean cell volume Vv 
or the expectation of the mean cell diameter b. Assuming a Poisson-Voronoi tessellation we 
#0 forma get the relationships V = 13.702 Ly ? and b = 3.284 LY ? In the case when all cells form 
N ; pentagonal dodecahedrons of constant size we have V =11.423 Ly 2. 
Mo In the case of the copper sinter material, Figure 1(b) the number of sinter necks can be 
banal estimated from Kvy. Let a be the copper component and a, the component a morphologically 
vl ve eroded with a ball of radius r where r is chosen such that all necks are opened up, but non 
oe = of the copper particles is removed form the image during this opening operation. Then 
Ky (a,)/4n is the particle density, (Kv (a,) — Kv(a))/4n is the density of sinter necks, and 
ii = 2(Kv (ar) — Kv(a))/Ky(a,) is the mean number of sinter necks per copper particle. 
JPET 0DSicts 
Hons’ in the 
¢ ‘Integration 
onfigurations 
assigned an 
je generation 
od version of (a i(b) 
rmulae, and 250 jum 500 um 
ige about the zz A 
we The neigh- Figure 1: XCT images of an open nickel foam (a) and of a porous copper sinter material 
re is of (b). The images show 2d visualizations of the 3d images represented as 3d voxel matrices. 
rae For the nickel foam we obtain a mean cell volume V = 3.47 - 10% um? (i.e. b = 221 um) 
i rol assuming a Poisson-Voronoi tessellation and V = 2.89 - 108 pm? assuming that the cells 
le 0 hen form pentagonal dodecahedra of uniform size. Since both assumptions mark marginal cases 
netions which for the models of the foam structure, the two values can be considered as the upper resp. 
lower bound of the mean cell volume. From the 3d image (b) we obtain for the mean 
number of sinter necks per particle n = 3.76. 
i dha 4 Discussion 
wor used VEIY 
era Iter The boundary of a can be modeled as a smooth spatial surface which separates the set of 
‚oc. Fyamnles lattice points covered by a from the complementary set of lattice points. Modeling such 
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