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
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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