82
‘
'
FREEZE-‘DRYING
Thevapourpressure- di"erehæ Ap is obtained from equation [3], but the value of (is/a1
is found/co. «be» small compared With P, and can therefore be neglected. Accordingly ::
_“ _ f
“j
_'
,
“
A? =Ps—[P + (P —pc)e—G”b [
'
Ù
‘
ï
HH
‘
All the quantities ps, P, Ïpc, Gs can be evaluated by measurement, either directly
Ï
‘
Examples of data relating to hydrodynamic
and di‘usive vapour transfer in the course
of freeze drying orange juice
3 and coled
meat are given in Table 1. This table shows,
in particular. the "application of the moving boundary analysis to the calculation of vapour
pressure
and
iœ- Sublimed.
.
,
The results show that values of the mass of ice sublimed can be calculated to
and 9 % by using the moving boundary theory. Calculated' and observed vapoùr pressure
di‘erenœsare fairly close…
!
‘
-
-
.
«
Flash Flow
‘
‘
‘
“
Assume that With‘ea‘eh ash of vapour in a cyclic variation of vacuum pressure the following
,
,_
conditions apply : —
,
,
-
‘,
…
a. The vapour pressure inside the product is greater than that outside, and lags behind it;
17. The vapour has a high exit velocity and signicant
energy.
«
f
c.
The vapeur is acCelerated along the pores of the dry product.
,
,
_
d. Work done on the vapeur as it ows
porous product is
viscous
drag.
.
-
_
,
‘
-.
::
‘
,
The conditions satisfy Bernouilli’s law for uid motion, which states that the rate of
work equals the rate of change of kinetic energy plus the rate of change of viscous energy.
“
Cancelling velocity in each energy term leads to & differential equation for ‘hydrodynamic’
_
‘
relaxation :
—‘
_
,,
dv
dv
.
1 :
"
AA
=
——
A1 ——
-
12
.
‘
}?
dr
[]
_
'
whefeV =vapour‘velocity
‘
“
…
-
A1 = internal surface areaof the pores
r;
", =equlvalentpore rad1us
>
f
‘
Sepamüngthemakamequaü°[121therelaxauonümeœnstm 18 obtamed
dragt0theümeïaŒ°f0hageofm0menæmthlsraü°fdaüngehmo tota1quanüüe8
’
'1h&s‘S,—m °abeusedlne@uaüons[121and[131mstead°fthemdeærmmaæsmasssubhmed
‘
"P‘ËI ‘Cÿclc;
‘
,
—
than A1 obtained from permeabltyandporosltymeasurements ,i_.forîr the
‘
j ,
‘
'
FREEZE-‘DRYING
Thevapourpressure- di"erehæ Ap is obtained from equation [3], but the value of (is/a1
is found/co. «be» small compared With P, and can therefore be neglected. Accordingly ::
_“ _ f
“j
_'
,
“
A? =Ps—[P + (P —pc)e—G”b [
'
Ù
‘
ï
HH
‘
All the quantities ps, P, Ïpc, Gs can be evaluated by measurement, either directly
Ï
‘
Examples of data relating to hydrodynamic
and di‘usive vapour transfer in the course
of freeze drying orange juice
3 and coled
meat are given in Table 1. This table shows,
in particular. the "application of the moving boundary analysis to the calculation of vapour
pressure
and
iœ- Sublimed.
.
,
The results show that values of the mass of ice sublimed can be calculated to
and 9 % by using the moving boundary theory. Calculated' and observed vapoùr pressure
di‘erenœsare fairly close…
!
‘
-
-
.
«
Flash Flow
‘
‘
‘
“
Assume that With‘ea‘eh ash of vapour in a cyclic variation of vacuum pressure the following
,
,_
conditions apply : —
,
,
-
‘,
…
a. The vapour pressure inside the product is greater than that outside, and lags behind it;
17. The vapour has a high exit velocity and signicant
energy.
«
f
c.
The vapeur is acCelerated along the pores of the dry product.
,
,
_
d. Work done on the vapeur as it ows
porous product is
viscous
drag.
.
-
_
,
‘
-.
::
‘
,
The conditions satisfy Bernouilli’s law for uid motion, which states that the rate of
work equals the rate of change of kinetic energy plus the rate of change of viscous energy.
“
Cancelling velocity in each energy term leads to & differential equation for ‘hydrodynamic’
_
‘
relaxation :
—‘
_
,,
dv
dv
.
1 :
"
AA
=
——
A1 ——
-
12
.
‘
}?
dr
[]
_
'
whefeV =vapour‘velocity
‘
“
…
-
A1 = internal surface areaof the pores
r;
", =equlvalentpore rad1us
>
f
‘
Sepamüngthemakamequaü°[121therelaxauonümeœnstm 18 obtamed
dragt0theümeïaŒ°f0hageofm0menæmthlsraü°fdaüngehmo tota1quanüüe8
’
'1h&s‘S,—m °abeusedlne@uaüons[121and[131mstead°fthemdeærmmaæsmasssubhmed
‘
"P‘ËI ‘Cÿclc;
‘
,
—
than A1 obtained from permeabltyandporosltymeasurements ,i_.forîr the
‘
j ,