VAPOUR TRANSFER PROBLEMS
In equation [l], thickness
is proportional to the square root of the time, that
the constant o: is determined from
2 DMA};
—
a_2 = —_
RT
_
[21
where M = molecular weight of water
'
…
R = gas constant
_
T
=
absolute temperature
p
=
ice density.
Vapour Pressure Differences
'
‘
The vapour pressure difference Ap between the moving interface and the surface of the
dry layer
5
may be derived by equating the submati0n rate to the migration rate of vapour
di‘using from the surface of the product to the condenser, and to the condensation rate;
Thus
_
’
_
AP = ps — P + (P ——Pc— Gs/al)e‘»G-‘”’
[3]
where ps
=
sublimation vapour pressure
_
_
-
])c
=
condensation vapour pressure
_
.
,
P
=
vacuum pressure
-
»
,
GS = sublimation rate.
’
»
The constant al depends on the condensation of vapour ; b is also a constant, and is
equal to DOMP/l RT, where B., is the diusion coeicient for water vapour in air and 1 is
the distance between product and condenser.
_
,
,
Drying Rates
The drying rate G or mass ow rate per unit drying surface area is given by Fick’s equation.
The vapour pressure gradient is taken as positive in the same direction as the distance.
Thus
.
A dt
RT
ôx
,
_
,
where A = surface area
‘
m
=
mass of ice sublimed.
,
_
Dierentiating equation [1] with respect to x and substituting from
above equation
gives :
.
-
,
DM Àp »
_
-
_
,
,
:
__
.
4
G"
'RT0LÈ
-
'
»
[,]