Biomedical Engineering Reference
In-Depth Information
18.7.2.3. Thermal Sterilization in a Laminar Flow Tubular Reactor
In practice, the strictly PFR does not exist. There is always backmixing due to flow-
induced dispersion and/or velocity distribution (other than a flat plug profile). Let us first
look at the sterilization in a laminar flow tubular reactor. Assume the flow is fully developed
and the velocity profile on the cross-section of the tube is given by
2
u ¼ 2Uð1 r
Þ
(18.45)
Q
A cr
1
4 p
D R being the cross-sectional area of
the tube available to the process fluid, and r is the dimensionless radial distance (radial
distance divided by the tube radius) from tube center. If we neglect the transverse diffu-
sion/dispersion, the cells would follow the streamline. The cells in the center of the tube
will spend less time in the sterilization zone than those near the tube wall. Therefore, the
overall probability of a cell surviving the sterilization is
where U is the average velocity, U
¼
with A cr
¼
Þexp
d
Z
1
Z
1
2r u
U
C X
C X 0
k d s
2 ð1 r
2
s Þ¼
d
r ¼
4r ð1 r
r
2
Þ
0
0
(18.46)
2 Z N
k
s
2ð1r
d
e y
y
Þ 1
2 ðk d s Þ
2
¼¼¼¼
d
y
3
k
2
d
where
is the space time and defined by Eqn (18.42) . Since k d s
is greater than 2 for meaning-
s
ful sterilization operations, integration of Eqn (18.46) leads to
13y 1
y n
N
2 e y
2y
/ þð1Þ n ðnþ 2 Þ !
2
þ12y 2
s Þ¼ðk d s Þ
3
k d s
2
exp
2 Z N
(18.47)
e y
y nþ1 d
ð1Þ n ðnþ 3 Þ 4 ðk d s Þ
4ðk d s þ2Þ
k d s ðk d s þ8Þ
k d s
2
y z
k
2
d
Comparing Eqn (18.47) with Eqn (18.41) , one can infer that sterilization in laminar flow
reactor is less effective than that in a PFR of the same space time. However, it is much
more effective than in a CSTR as described by Eqn (18.36) . The probability of the entire pop-
ulation in one reactor-full process fluid of volume V not vanishing from the laminar flow heat
treatment is
exp
4ðk d s þ2Þ
k d s ðk d s þ8Þ
1
2 k d s
C X 0 V
P 1 ð s Þ¼1P 0 ð s Þ¼1½1pð s Þ C X 0 V z
exp
(18.48)
2 ðC X 0 V 1 Þðk d s þ 2 Þ
k d s ðk d s þ8Þ
1
2 k d s
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