Biomedical Engineering Reference
In-Depth Information
which is a fast convergent series for the cases we are interested in, i.e. long enough time to
sterilize the system. For fast estimation, one can approximate the probability of unsuccessful
fermentation P
1
(t)by
N
0
e
k
d
t
1þ
N
0
1
2
P
1
ðtÞ
z
(18.24)
e
k
d
t
Therefore, for the same level of sterilization, the time and/or temperature requirement is
different for different size of reactors. The dimensionless sterilization time that can be
employed to examine the sterilization of any given reactor can be estimated by
t
S
¼ k
d
t lnN
0
(18.25)
Specific death rate dependence on temperature is given by Arrhenius equation:
k
d
¼ k
d
0
expðE
ad
=RTÞ
(18.26)
where E
ad
is the activation energy for the death of the organism and k
d0
is the pre-exponential
specific death rate constant. Values of E
ad
range from 250 to 650 kJ/mol. Bacterial spores are
typically more thermal resistant than vegetative forms of bacteria or yeast. At 121
C, for
example, the specific death rate k
d
for vegetative cells may range up to 10
10
/min, while k
d
for spores is 0.5
e
5.0 min
1
. Mold spores are 2
e
10 times more resistant to vegetative forms
of bacteria, viruses and bacteriophage are 1
e
5 times more resistant. Therefore, sterilization
design is usually based on destruction of bacterial spores.
For typical spores of B. stearothermophilus, k
d0
¼
10
37
min
1
and E
ad
¼
8.236
283 kJ/mol,
530 kJ/mol. Typically sterilizations occur at 121
C. For most spores,
k
d
falls very rapidly with temperatures. There is a 10-fold decrease of death rate at T
while for E. coli, E
ad
z
110
C
rather than 121
C. The sterilization is accomplished by increase the temperature to a set
temperature, commonly 121
C, for a period of time and then cool down to working temper-
ature (
Fig. 18.9
). For each heat sterilization, the dimensionless sterilization time can be
computed by
¼
t
S
¼ k
d
0
Z
t
0
e
E
ad
RT
d
t lnN
0
(18.27)
130
110
90
70
50
30
0
20
40
60
80
100
120
t
, minutes
FIGURE 18.9
Typical sterilization temperature profile.
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