Page 208 - Percolation Models for Transport in Porous Media With

206 CHAPTER 12. ACOUSTIC WAVES AND PERMEABILITY

-z

-4

-6
Figure 74: Relation between the pressure in the fluid around the bubble and
the extent of its growth {plotted according to the data of L. K. Zaremba and
V. A. Krasilnikov) Code of the curves - ao, m

As the pressure around the bubble drops, its radius increases by Ea times.
Suppose that the expansion of the bubble is isothermal and that the mass of gas
inside the bubble does not change. In this case the external compensating pressure
is
{12.14)

Use {12.14) to estimate the maximal negative pressure that can be endured by
a fluid with identical bubbles of initial radius ao. Consider the derivative dp0 fdE 11 •
Rupture of the fluid takes place only when the curve p0 (e-a) has an extremum,
since after the curve passes its extremum, the expansion of bubbles continues with
the pressure going up. Typical p0 (Ea) curves are represented in fig. 74 for two
different values of the parameter ao. After setting the derivative dp0 jdEa to zero,
we obtain the following from {12.14) for the critical value of the variable,

E* = ~ ao (Po+ 2x)
a
2 X ao
The minimal size of the cavitating germ can be estimated from the condition of
the fluid rupture. This condition implies that the total pressure must be negative
and must exceed in absolute value the critical pressure Poe, which corresponds to

{2x/ao) 3 {12.15)
3{Po + 2xfao)
For the value p"' -1 GPa when Po "' 10MPa, IP/Pol » 1, and the equation
{12.15) can be rewritten in the form
7p Po(ao/2x) = 1- 7p (aof2x) 2
2
3
2