Page 190 - Percolation Models for Transport in Porous Media With

188 CHAPTER 11 GAS COLMATATION IN ELECTRIC ACTION

where Lp is the specific heat of liquid evaporation, we obtain

R dTs 1- pp(pp)fPJ(Pp)
pPp dpp = "fpL*(pp) (11.24)

L • _ Lp(Pp) ,._ _ c: _ c: (11.25)
- ' IP- p - p
"fpRpTs(Pp) Cv Cp- Rp
After substituting (11.24) in (11.22) and (11.19) and taking into account (11.23),
we obtain the correlation between Q~ and the change of pressure

3
q~ = ( 4/3)1!'a (r:;- )dppf dt (11.26)
1
r. = ("'p -1)£*(1- PpfPJ)-1
Since along the vapor isentrope (the entropy of the vapor is Sp =canst)

and along the saturation line of the vapor, according to (11.24), (11.25),

it follows that the quantity r. shows how close to isentropic is the behavior of the
vapor, since
r _ (arp) /(arp)

• - opp sp opp s
When r. > 1 and dppfdt < 0, it follows from (11.26) that q~ > 0 and from
(11.20} that 8Qp > 0. This means that the vapor is receiving heat, while the pres-
sure in the bubble grows. At the same time, the temperature gradient oTpfor < 0,
and therefore the temperature is higher in the center of the bubble than on its
surface. The latter fact demonstrates the stability of the bubble growth.
If we differentiate the mass conservation equation for the bubble

and take into account the relationship

where e12 is the mass flow of the bubble due to the phase transition in the boundary
layer through a unit surface area, we obtain

(11.27}