Handbook of Solvents - George Wypych - ChemTech - Ventech!

7.3 Drying of coated film 395
Figure 7.3.9. Concentration and temperature dependence of the binary
diffusion coefficient of a polystyrene-toluene solution according
to the free volume theory of Vrentas and Duda. [After
References 17].
coating solution. In CDRP, as
shown in the figures the slope of
solvent content loss with time
(drying rate) and the coating temperature
are nearly constant.
These drying rate curves were obtained
by measuring weight
changes of coating in an oven with
blowing hot air above the coating
samples - see Section 7.3.3.1.
However, as the solvent content
decreases the drying rate of
coating also decreases gradually
as shown in Figure 7.3.8. In this
falling rate regime, mass transfer
within the coating becomes the
limiting factor, and with constant
heat input the temperature of coating
rises and drying rate de-
creases. The solvent is transported to the exposed coating surface by diffusion and
convection, where the solvent evaporates to the bulk air in a polymeric coating system. In
most drying processes of thin film coatings the convection of solvent within the coating is
negligible, thus the diffusion of solvent is the only method for solvent to reach the coating
surface. The diffusivity of solvent in a polymeric solution falls dramatically when the solvent
content is low as shown in Figure 7.3.9. Therefore the diffusion process of solvent
within the coating controls the rate of drying in FDRP.
To understand and improve the drying process during the FDRP, it is important to estimate
diffusion coefficient of solvent within the coating. Vrentas and Duda predicted the binary
diffusion coefficient by using free volume theory. 17 Figure 7.3.9 shows the binary
diffusion coefficient of toluene in the polystyrene-toluene solution that was found by applying
free volume theory. The diffusion coefficient falls by a number of magnitudes in the low
solvent concentration range, and it increases with increasing temperature. By the way the
concentration dependency of diffusion coefficient at the low solvent concentration range
declines at a high temperature. For example, at the temperature of 100 o C the diffusion coefficient
of toluene falls 5 orders of magnitude (about 10 -5 ) from its highest value, but at the
temperature of 180 o C it falls only one order of magnitude. This shows us that it is highly required
to eliminate residual solvent of coating at the low solvent concentration range the
temperature of oven should be high enough. Therefore the temperatures of final zones keep
high enough to achieve complete dryness in a multiple zone dryer. Normally the temperature
of oven is restricted by the onset of deformation of substrate such as wrinkles and it is
also restricted by the properties of coated material, such as melting point of binders.
The parameters for the free volume theory of binary solution systems can be found in
the literatures, 17,53-55,60 and they have been effectively used in modeling drying process. 1,2,6-8
But there are many difficulties in estimating diffusion coefficient for the ternary systems.
Until now, almost all the empirical and theoretical correlations are restricted to the binary
solution systems.