Handbook of Solvents - George Wypych - ChemTech - Ventech!

372 Semyon Levitsky, Zinoviy Shulman
closely connected with the effect of a strong increase in local stresses in a polymer solution
flow when the longitudinal velocity gradient reaches the value of reciprocal relaxation
time. 3
7.2.2 THERMAL GROWTH OF BUBBLES IN SUPERHEATED SOLUTIONS OF
POLYMERS
Growth of vapor bubbles in a superheated liquid is the central phenomenon in boiling processes.
When the bulk superheat is induced by a decrease in pressure, then the initial stage
of vapor bubble growth is governed by inertia of the surrounding liquid. During this stage
the rheological properties of liquid play important role, discussed in the previous section.
The basic features, characterizing this stage, are pressure changes within bubbles and their
pulsations. After leveling of pressure in the phases, the process turns into the thermal stage
when the cavity growth rate is controlled by ability of the liquid to supply the heat necessary
for phase transitions. Expansion of vapor bubble in the thermal regime was examined 46 for
the case of liquid representing a binary solution. Similar problem was treated 47 under additional
assumption that the convective heat and mass transfer in the two-component liquid
phase is insignificant. More recent works on dynamics of vapor bubbles in binary systems
are reviewed elsewhere. 48-50
The features, peculiar to vapor bubbles evolution in polymeric solutions at the thermal
stage, owe mainly to the following. First, only the low-molecular solvent takes part in phase
transitions at the interface because of a large difference in molecular masses of the solvent
and polymer. The second, polymeric solutions, as a rule, are essentially non-ideal and,
therefore, saturated vapor pressure of the volatile component deviates from the Raul’s law.
Finally, the diffusion coefficient in solution is highly concentration dependent that can
greatly influence the rate of the solvent transport toward the interface. The role of the listed
factors increases at boiling of systems that possess a lower critical solution temperature
(LCST) and thus are subjected to phase separation in the temperature rangeTTs(k0,pf0), assuming that both pressure
and temperature in the vapor phase are constant
p v =p f0, T v =T s(p f0, k R)=T fR, k R= k(R, t), T fR =T f(R, t) [7.2.44]
Parameters k 0,T f0 characterize the state of solution far from the bubble (at r = ∞). Unlike a
one-component liquid, the temperature T fR here is unknown. It is related to the surface concentration
of solvent, k R, by the equation of phase equilibrium at the interface.
Equations for heat transfer and diffusion in the solution have the form
∂T
∂
v
∂t
∂
R
2 T
f
f
+ fR = r
2
r r
∂k
∂
v
∂t
∂
R
2
k
+ fR = r
2
r r
∂
∂r
ar
⎛
⎜ f
⎝
−2
2
∂
∂r
Dr
⎛
⎜
⎝
−2
2
∂k
⎞
⎟
∂r
⎠
∂Tf
⎞
⎟
∂r
⎠
[7.2.45]
[7.2.46]