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11.3 MODIFICATION OF PERMEABILITY 197
Suppose that the relationships {11.40) and {11.47) hold, i.e., we neglect the
outlined variations of Hand Z. In this case, according to {11.34), e(o) ~ 2.5, and
the condition {11.42) holds for a/ao > 1.5. It follows accordingly that
HB*
2
3
w* ~ -A ~ 1.8 · 10 t {11.56)
Xo
This implies that a/ao "' 10 when t"' 10 seconds.
If, however, we suppose that the capillary is shut off for a"' r = 8 ·10 5 m, then
t ~ 0.8 hours.
{11.56) implies that
Therefore
and the left side of ( 11.36) is of the order of
2
11
8
w*w~ + 3/2(w:) ~ -{4 · 10 + 2 · 10 )
The term in the right side of the equation is of the order of
It follows that for the given characteristic parameters, the dynamic terms in the
Rayleigh-Lamb equation may indeed be neglected. Thus this equation assumes
the form {11.40), and the dynamics of the bubble growth is taken into account in
the equation {11.35).
Thus the following stages of the reversible change of the permeability for a mi-
cro heterogeneous medium as the electric current passes through it can be outlined,
based on the theoretical analysis and the obtained experimental data.
1. Increase of the electric conductivity and the permeability of the medium
caused by the destruction of the bounded fluid on the surface of capillaries
and by the decrease of its viscosity. At the same stage, the migration of
bubbles of fluid towards the thin capillaries of the medium, which are heat
sources, takes place.
2. Termination of the growth of the electric conductivity and the permeability
and the formation of a "platform" in I<(t) and E{t) coordinates. At this
stage, the growth of bubbles of vapor takes place at a temperature less than
the boiling point. These bubbles shut off the capillaries and make up for the
increase of the electric conductivity and the permeability of the fluid caused
by the increase of the capillary cross-sections.