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The behavior of the Attiogbe equation (t) for
voids of zero radius suggests a relationship to the mean free path
(
)
between
air voids. As stated previously, the mean free path is numerically equivalent
to the average paste chord lengths in a paste-air system. This quantity
has been studied for some time, and is known to an acceptable level of
accuracy[15]:
If the center of the air voids remain fixed, as the radii of the air voids decreases to zero, the mean free path diverges toward infinity, like the Attiogbe equation for t.
This similarity is more than coincidental. In fact, the Attiogbe equation
for t is directly proportional to
. Expressing the Attiogbe equation for t as
A
can be simplified using
Eqs. (1) and (3):
Therefore, at low air contents the Attiogbe equation t is approximately equal to one half the mean free path between air voids in a paste-air system.