Biomedical Engineering Reference
In-Depth Information
The dispersion coefficient may be written as,
D
eff
¼ a
d
Q
A
cr
D
R
(18.55)
where a
d
is a constant, varies only with the flow conditions. For turbulent flows in a pipe,
a
d
¼ 310
7
Re
2:1
þ1:35 Re
0:125
(18.56)
D
R
r
Q
m
v
A
cr
¼
Q
pm
v
D
R
>
4
r
which is valid for
Re ¼
m
v
is the viscosity of the liquidmedium.
For a tube of constant diameter of D
R
and length L,
Eqn (18.51)
is reduced to
2000. Here
1
!
p
1þ4a
d
D
R
L
1
k
d
s
pð
s
Þ¼exp
L
(18.57)
2a
d
D
R
The probability of the entire population in one reactor-full process fluid of volume V not
vanishing from the heat treatment is
1
!
p
1þ4a
d
D
R
L
1
k
d
s
C
X
0
Vexp
L
2a
d
D
R
P
1
ð
s
Þ¼1P
0
ð
s
Þ¼1½1pð
s
Þ
C
X
0
V
z
1
!
p
1þ4a
d
D
R
L
1
1þ
C
X
0
V
1
2
k
d
s
exp
L
2a
d
D
R
(18.58)
which corresponds to the dimensionless sterilization time of
p
1þ4a
d
D
R
L
1
k
d
s
1
t
S
¼
L lnðC
X
0
VÞ
(18.59)
2a
d
D
R
Example 18-2. Holding time and tube length requirement for a continuous sterilizer.
Medium at a flow rate of 3.6 m
3
/h is to be sterilized by heat exchange with steam in a contin-
uous sterilizer. The liquid contains bacterial spores at a concentration of 2
10
12
m
3
. The ster-
ilization temperature is to be conducted at 121
C, at which the death rate of the bacterial
spores is k
d
¼
400 h
1
. The sterilizer tube has an inner diameter of 0.1 m; the density of the
medium is 1000 kg/m
3
and the viscosity is 0.001 Pa s. How long of the tube is needed to ster-
ilize the medium for a risk of 0.001 for fermentation of each sterilizer full of medium?
4rQ
pm
v
D
R
¼
4
1000
0
:
001
p0:0010:1
¼ 12732 > 2000
3.6 m
3
/h
0.001 m
3
/s;
Re ¼
Solution: Q
¼
¼
a
d
¼ 310
7
Re
2:1
þ1:35 Re
0:125
¼ 0:486
V ¼
4
D
10
12
; P
1
(
R
C
X0
¼
2
s
)
0.001;
L
;
s
¼
V/Q. Solving
Eqn (18.55)
with Excel,
1
!
p
1þ4a
d
D
R
L
1
k
d
s
C
X
0
Vexp
L
2a
d
D
R
1
!
P
1
ð
s
Þ
z
p
1þ4a
d
D
R
L
1
1þ
C
X
0
V
1
2
k
d
s
exp
L
2a
d
D
R
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