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
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 gf 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.