Page 120 - Percolation Models for Transport in Porous Media With

6.2 ELECTRIC POROMETRY 113

.
. .

Figure 41: Principal scheme of measurements in the electric porometry method

electrolyte, then the concentration of such chains on an elementary cross-section
is Nb = K-1- 2 • Bonds of each chain are connected successively, and therefore the

1
conductivity of a vertical chain is ui = ( ~ n;) - (R; is the resistance of the j-th
)=1
bond of the i-th chain, N 1 = z- 1 is the number of bonds in a chain).
Estimate the contribution made by each of the subsystems to the value of
Ui· We shall take into account the following facts: characteristic radius of sites
is r 6 = l/4 and bonds are cylinders with characteristic radii Tb ¢:: 1 and lengths
~ l/2.
In this case, for the resistances of the bonds in the chains we have ~ "'
u-; 1 (1/r~), Rs "' u-; 1 1- 1 , and their ratio Rs/ Rb "' (rb/1) 2 ¢:: 1. This implies
Nl/2 )-1
(
ui = ~ (Rb); "' uer~, from which we obtain the following estimate for the
J=1
specific electric conductivity of the material,
Nh
U(O) "'LUi ,..., Ue(Tb/1) 2 (6.15)
i=1
The relationship (6.15) shows that the specific electric conductivity of a spec-
imen made up of the site pore and the bond pore subsystems of different scale
depends only on the bond resistances. Therefore it is possible within the proposed
electric porometry method (EPM) to pass from the network model (NM) with
solid sites to an NM with point sites, where the volumes, electric and fluid flow
resistances of the sites vanish. The properties of such network (from the point
of view of the EPM) are determined by the radius probability density function
(PDF) of the bond pores. Hence radii of different bonds in capillary chains of any
orientation are of the same order (unlike the chains with sites, where capillaries of
different scale Tb > r 8 ,..., l connect at each period of the network). This permits to
establish the actual correlation between capillaries of variable radii and cylindrical