It has been shown by Berryman (1980, 1981) that the speed of the
slow wave [*i.e.*, the second compressional wave predicted by Biot
(1956a)] can be written as

(28) |

(29) |

That is a measure of the tortuosity has also been shown using
a very different argument by Brown (1980). He shows that is
related to the electric formation factor for a porous system.
In particular , where is the electrical
formation factor [which should not be confused with the dynamic
viscosity factor to be introduced later]
defined by , with *g*_{f} being the
electrical conductivity of the pore fluid and *g* being the effective
overall conductivity of the system when the solid is nonconducting.
The formation factor and the tortuosity are both equal to unity when
. For some systems, it is known both from Archie's law and
from theory too that is often a reasonable estimate
for pore systems. Thus, . Both this
expression and (27) have the same repesentation as when is large, showing that the two approaches
using electrical tortuosity and the induced mass do in fact give similar
results in this limit, even though it might seem hard to understand
physically just exactly why this should be true.

7/8/2003