Page 210 - Percolation Models for Transport in Porous Media With

208 CHAPTER 12. ACOUSTIC WAVES AND PERMEABILITY

2. Directly at the unloading stage of the traveling wave, for the given Po
and Pa, cavitation in the fluid cannot develop, either. This follows clearly from
the relationship (12.15), which shows that after the value Pa is substituted for p
in this expression, the sum (Pa + Po) never becomes negative, and cavitation is
therefore impossible in principle. In [92] an interval Po± l:l.ph of pressures, called
the metastable zone, was established experimentally. Supposedly, outgassing and
cavitation take place for low intensity of the acoustic field, if the difference between
the reservoir pressure Po and the saturation pressure of the fluid with the gas lies
in the mentioned interval. However the presented data, concerning the change
of the velocity of sound in the saturated medium and the volume of the released
gas, do not permit to make any definite conclusions on the physical picture of
the processes that take place here (in particular, the development of cavitation),
let alone the quantitative parameters of these phenomena. Therefore there is no
reason to think that at the given amplitude and intensity of the acoustic action
and such high reservoir pressure cavitation may develop in the pore space filled
with the fluid.

12.4 Dissipation of Acoustic Energy Due to Ther-
mal Slide

It was established in §12.1 that when there is no integral flow in a chain, the
mechanism of the acoustic energy dissipation due to thermal slide is possible. The
characteristic feature of this mechanism is the vanishing of the total flow of the
fluid, even within a single capillary.
Since the capillary length is assumed to be much greater than the radius, a
capillary can be considered having infinite length, so that boundary effects on
the capillary junctions can be neglected. Consider the fluid movement in a cap-
illary under the outlined condition and under the action of a pressure wave with
amplitude Pa and frequency vo
p = Pa cos[21r(vot- xf -\)] (12.18)

where -\ is the wavelength, whose correlation with the frequency is expressed by
the well-known formula AVo= Cm (Cm is the velocity of sound in the medium). In
writing out the relationship (12.18), it was supposed that the wave propagates in
the direction of the x-axis, which coincides with the axis of the capillary. For such
relative location of the wave vector k and the capillary axis, the action upon the
fluid of a longitudinal simple harmonic wave in the capillary is maximal. The closer
(k, x) to zero, the less the components of pressure and the corresponding velocity
of the movement along the capillary, and therefore the less the considered effect.
The point is that the velocity of thermal slide is proportional to the gradient of