Handbook of Solvents - George Wypych - ChemTech - Ventech!

376 Semyon Levitsky, Zinoviy Shulman
m 2 s -1 ; for1-4:α= 0; for 2�, 2��: α = 1, -1; for 1, 3: χ = 0.1; for 2, 4: χ = 0.4. Here
-1
α=kR( dD/dk)
,k=k/k
k=k R.
0
It is seen that the Δ� T* value decreases with reduction of k0 and/or increasing the
non-linearity factor, α. Raising the value of the Flory-Huggins constant, χ, causes the Δ� T*
value to increase and extends the range k* ≤ k0 ≤ 1. The ΔT ∧
* value essentially depends on
the rate of the diffusion mass transfer; reduction of the latter lowers the limiting superheat,
that is the value of ΔT*, below which the bubble grows in a polymeric liquid as though it
were a pure solvent. For polymer solutions in volatile organic solvents, the limiting superheat
is lower than for aqueous solutions of the same concentrations. Note that for low molecular
binary solutions the term “limiting superheat” in the current sense is meaningless in
view of pronounced dependence Ts =Ts(k0) in the entire range of the k0 variation. The scale
of the effect under consideration is closely connected with the deviation of the solution behavior
from the ideal one: the larger is deviation the less is the effect. This can be easily understood,
since in the case of a very large difference between molecular masses of the
solvent and solved substance, typical for a polymer solution, the graph Ts=Ts(k0), plotted in
accordance with the Raul law, nearly coincides with the coordinate axes. 20 For this reason,
the bubble growth rate in a polymer solution that obeys the Flory-Huggings law, is always
lower than in a similar ideal solution.
The reduction of the diffusion mass transfer rate (G ~ (Le) 1/2 ) at a fixed superheat, ΔT*,
leads to a substantial decrease in the effective Jackob’s number, Ja. The growth of the content
of a polymer in a solution leads to the same result. This follows from Figure 7.2.11
where curves 1-5correspond to k0 = 0.99, 0.95, 0.7, 0.5, 0.3; 2� -2���: k0= 0.95; 3� -3��:
k0=0.7; 4�� ��:k0= 0.5, 0.3;1-5:α=0;2�-3�:α= - 0.5; 2��: α = 0.8; 2���,3��,4�,5�:α= 2. For all
graphs, ΔT*= 15 K, χ = 0.1, Kρ = 0.7.
The influence of non-linearity of diffusional transport is higher for diluted solutions.
This is explained by a decrease in the deviation of the surface concentration, kR, from the
bulk k0 with lowering k0. This takes place due to simultaneous increase in |∂Ts/∂k| that is
characteristic of polymeric liquids. The presence of a nearly horizontal domain on the curve
Ja = Ja(G) at k0≥0.95 is explained by the existence
of the limiting superheat dependent on
the Lewis number.
The role of diffusion-induced retardation
increases with the bulk superheat. This reveals
itself in reduction of the number Sn with a
growth in ΔT* (Figure 7.2.12). For solutions of
polymers in volatile organic liquids, such as
solvents, the effect is higher than in aqueous
solutions. For concentrated solutions the difference
between the effective ΔT and bulk ΔT*
superheats makes it practically impossible to
increase substantially the rate of vapor bubble
Figure 7.2.12. Effect of the solution bulk superheat growth by increasing the bulk superheat.
on the Scriven and Jacob numbers. (−) - solution of Curves 5 and 5� clearly demonstrate this. They
polymer in toluene, (- - -) - aqueous solution. [Re-
are calculated for solution of polystyrene in toprinted
from Z.P. Shulman, and S.P. Levitsky, Int. J.
Heat Mass Transfer, 39, 631, Copyright 1996, the luene at k0 = 0.3, therewith for the curve 5 the
reference 52, with permission from Elsevier Science]
dependence of the diffusion coefficient from