Handbook of Solvents - George Wypych - ChemTech - Ventech!

7.3 Drying of coated film 389
down the coating surface. Thus the heat and mass are transferred simultaneously through
the surface of coating.
Assuming that the heat is supplied only by convection of hot air and the substrate is
impermeable. Further if we neglect the internal resistance of solvent transport to the coating
surface, the heat and mass balance consist a lumped parameter system.
A schematic diagram of the modeled system is shown in Figure 7.3.3. The corresponding
mass and heat balance of the systems are as follows 28
where:
R b ( )
dz i
sat
mass, i i C kmCi Ci
dt
= = − ∞
ρ [7.3.1]
∞ ( )
k
ρfbC f Pf ρizbC i C Pi
δ
i
dT
k
⎛
⎞
⎜ + ∑ ⎟ = h T −T −∑R − H
⎝
= 1 ⎠ dt
i = 1
Rmass,i evaporation rate of component i
zi volume fraction of component i
ρi density of pure component i
b thickness
sat
Ci saturated solvent concentration of component i
∞
Ci solvent concentration of component i in the bulk air
km mass transfer coefficient
h heat transfer coefficient
T temperature of coated film
T∞ temperature of drying air
,( )
mass i evap
i
[7.3.2]
δH latent heat of solvent
Cp heat capacity
Subscript f and C mean the substrate and coating layer respectively. Equation 7.3.1 and
7.3.2 apply to the each component of coating.
7.3.2.2 Liquid-vapor equilibrium
The equilibrium saturated solvent concentration is related to the concentration of solvent at
the coating surface by thermodynamic equilibrium relations, such as Henry’s law, Raoult’s
law and the Flory-Huggins equation. 8 The Raoult’s law is
C z P
sat
sat
i
i =γ i i
[7.3.3]
RT
where:
γi activity coefficient of component i
sat
Pi saturated vapor pressure of component i
R gas constant
The saturated vapor pressure is calculated from the Antoine equation at the specific
temperature.
sat B
log10 P = A−
T + C
[7.3.4]