Metal Foams: A Design Guide

Electrical properties of metal foams 191
density, normalized by the conductivity of the fully dense alloy. The conductivity
varies in a non-linear way with relative density. Additional data for
nickel foams can be found in patents referenced as Babjak et al. (1990), at
the end of this chapter.
14.3 Electrical conductivity and relative density
Figure 14.3 shows an idealization of a low-density open cell foam. The cell
edges have length ℓ and cross-section t ð t, meeting at nodes of volume t 3 .
The relative density of an open-cell foam is related to the dimensions of the
cells (omitting terms of order ⊲t/ℓ⊳ 4 )by
Potential
gradient
s
³ 3t2
ℓ 2
t
t
⊲14.4⊳
Figure 14.3 An idealized open-cell foam consisting of cell edges of length ℓ
and cross-section t 2 , meeting at nodes of volume t 3 . In real foams the nodes
are larger (‘Plateau borders’) and the edges thinner at their mid-points,
because of the effects of surface tension
The dependence of electrical conductivity on relative density can be understood
in the following way. The cell edges form a three-dimensional network.
If a potential gradient is applied parallel to one set of cell edges, the edges
which lie parallel to the gradient contribute to conduction but those which
lie normal to it do not, because there is no potential difference between their
ends. The network is linked at nodes, and the nodes belong to the conducting
path. At low relative densities the volume of the nodes is negligible compared