VAPOUR TRANSFER
81
Where_Ï is the
mean thickness
of the dry layer, tl is the drying time to produce a thickness
of 2_L.
K rs the permeabity_ceeîcient
of water vapeur in the porous product and is
_obtamed
from the corresponding permeability coefcient Ko using nitrogen, since water
vapeur would be ready adsorbed by a freeze-dried product. Since K varies inversely
With the square root of the molecular weight of the gas, we have :
’
‘
K
(îf)
'
Ko values at the appropriate pressure can beread from a graph of K,, against Î’, and
,
1.75
_
can be corrected for temperature by multiplying by (%)
From equation [3], the vapeur pressure difference for the casenew under consideration,
where e”Gs/b approaches unity, and Gs/a1 is not negligible, becomes :
AP : Ps —Pc _ Gs/a1
[8]
The term (is/a1 may be evaluated by using Knudsen’s equation for condensation of vapeur,
namely :
_
.
,
,
_
= Gc = alApc
[9]
where al
=
a1(M/2nR)—ë
_
-
“
j
_
oc1
=
condensation ceeîciet‘(æl :1)
'
GC = condensation rate
_
_‘
'
Tc = mean temperature-of condensation
Apc = vapeur pressure difference
for condensation, which has to be determined
experimentally. - '
”
‘
-
,
|
'
Diffusive Flow
It has been shown that di‘usive ow occurs during the falling—rate period, and equations [4]
and [5] give respectively the drying rate and the mass sublimed, the derived constant a
_
_
2 DM Ap
"
being gwen by oc2 =
_p_RΗ
,
Values of the diusion
D for water vapeur
products must be
corrected for the operating vacuum,pressure and_temperatuæ. _The_ coefcients _vary directly
temperature to the
pressure, and are derived
from
_
the self—diusion coeîcient for Water vapeur in
(Do = 0.250 cmz/sec at 760 torr and
20 °C).
.
.
Fer water vapeur trau8fçr in,, ??
by a factor Whmh 15 the
ratio of the potd;èirÿî to“t1ië tortu031tyfætorPOTOSËYSC‘1UE‘15
the volm
Of the VÔÏdS
divided by the wholevolumeohôpmd‘mT°”“051tyfacœr (Le/92 °.quals
the square
of the ratio of theactualowpathmthepoïcsLï““° Êhe dry laY‘îf thl‘îknf’ss
L—
…
Thus, correcting Ï)
the full relationship 13
769
T)1‘75
'
'
'
«.
‘
'
’
”
[ ]
81
Where_Ï is the
mean thickness
of the dry layer, tl is the drying time to produce a thickness
of 2_L.
K rs the permeabity_ceeîcient
of water vapeur in the porous product and is
_obtamed
from the corresponding permeability coefcient Ko using nitrogen, since water
vapeur would be ready adsorbed by a freeze-dried product. Since K varies inversely
With the square root of the molecular weight of the gas, we have :
’
‘
K
(îf)
'
Ko values at the appropriate pressure can beread from a graph of K,, against Î’, and
,
1.75
_
can be corrected for temperature by multiplying by (%)
From equation [3], the vapeur pressure difference for the casenew under consideration,
where e”Gs/b approaches unity, and Gs/a1 is not negligible, becomes :
AP : Ps —Pc _ Gs/a1
[8]
The term (is/a1 may be evaluated by using Knudsen’s equation for condensation of vapeur,
namely :
_
.
,
,
_
= Gc = alApc
[9]
where al
=
a1(M/2nR)—ë
_
-
“
j
_
oc1
=
condensation ceeîciet‘(æl :1)
'
GC = condensation rate
_
_‘
'
Tc = mean temperature-of condensation
Apc = vapeur pressure difference
for condensation, which has to be determined
experimentally. - '
”
‘
-
,
|
'
Diffusive Flow
It has been shown that di‘usive ow occurs during the falling—rate period, and equations [4]
and [5] give respectively the drying rate and the mass sublimed, the derived constant a
_
_
2 DM Ap
"
being gwen by oc2 =
_p_RΗ
,
Values of the diusion
D for water vapeur
products must be
corrected for the operating vacuum,pressure and_temperatuæ. _The_ coefcients _vary directly
temperature to the
pressure, and are derived
from
_
the self—diusion coeîcient for Water vapeur in
(Do = 0.250 cmz/sec at 760 torr and
20 °C).
.
.
Fer water vapeur trau8fçr in,, ??
by a factor Whmh 15 the
ratio of the potd;èirÿî to“t1ië tortu031tyfætorPOTOSËYSC‘1UE‘15
the volm
Of the VÔÏdS
divided by the wholevolumeohôpmd‘mT°”“051tyfacœr (Le/92 °.quals
the square
of the ratio of theactualowpathmthepoïcsLï““° Êhe dry laY‘îf thl‘îknf’ss
L—
…
Thus, correcting Ï)
the full relationship 13
769
T)1‘75
'
'
'
«.
‘
'
’
”
[ ]