Handbook of Solvents - George Wypych - ChemTech - Ventech!

7.2 Bubbles dynamics and boiling 363
Martin equation is usually valid in the range of reduced concentrations, ~ c ≤ 10. For
evaluation of [η], the Mark-Houwink relationship 21 is recommended
[] η =KM a
[7.2.33]
where K and a are constants for a given polymer-solvent pair at a given temperature over a
certain range of the molecular mass variation. The parameter a (the Mark-Houwink exponent)
lies in the range 0.5 to 0.6 for solutions of flexible chains polymers in thermodynamically
bad solvents and in the range 0.7- 0.8 for good solvents. For the former ones the
constant K ≈ 10 -2 (if the intrinsic viscosity [η] is measured in cm 3 /g), while for the latter
K≈10 -3 .
Thus, the spectral functions, F1(λ), are comprehensively studied both experimentally
and theoretically. The behavior of relaxation functions, G2(t) and G3(t), is still much less
known. The properties of the function, G2(t), were mainly studied in experiments with longitudinal
ultrasound waves. 22-24 It has been found that relaxation mechanisms manifested in
shear and bulk deformations are of a similar nature. In particular, polymeric solutions are
characterized by close values of the temperature-shift factors and similar relaxation behavior
of both shear and bulk viscosity. The data on the function, F3(λ), indicate that relaxation
behavior of isotropic deformation at thermal expansion can be neglected for temperatures
well above the glass-transition temperature. 22
7.2.1.2 Dynamic interaction of bubbles with polymeric liquid
Behavior of bubbles in liquid at varying external pressure or temperature is governed by cooperative
action of a number of physical mechanisms, which are briefly discussed below.
Sufficiently small bubbles execute radial motions (growth, collapse, pulsations) retaining
their spherical shape and exchanging heat, mass and momentum with environment. Heat
transfer between phases at free oscillations of gas bubbles is caused by gas heating during
compression and its cooling when expanding. Due to the difference in thermal resistance of
liquid and gas, the total heat flux from gas to liquid is positive for the oscillation period. This
unbalanced heat exchange is the source of so-called heat dissipation. The magnitude of the
latter depends on the relation between the natural time of the bubble (the Rayleigh time)
t0=R0(ρf0/pf0) 1/2 , governed by the liquid inertia, and the time of temperature leveling in gas
2
(characteristic time of heat transfer in a gas phase), tT =R0/ag, that is from the thermal
Peklet number, PeT =tT/t0, where:
R radius of the bubble
ag thermal diffusivity of gas, ag=kg/(pg0cgp) kg heat conductivity of gas
cgp specific heat capacity of gas at constant pressure
0 index, referring to equilibrium state
f index, referring to liquid
g index, referring to gas
In the limiting cases PeT >> 1 and PeT > 1
and ω PeT