Biomedical Engineering Reference
In-Depth Information
TABLE 17.1
Diffusivity in Gaseous Phase, Liquid Phase, and Solid Phase
Order of
magnitude, m
2
/s
Phase
Temperature (and pressure) dependence
T
T
0
1:75
10
5
P
P
D
AB
ðT; PÞ¼D
AB
ðT
0
; P
0
Þ
Gas: bulk
T
T
0
2
10
6
Gas: in fine capillaries
(Knudsen diffusion)
D
A
ðTÞ¼D
A
ðT
0
Þ
B
D
T
0
þ C
D
T
T
0
exp
B
D
T þ C
D
10
9
Liquid
D
AB
ðTÞ¼D
AB
ðT
0
Þ
E
D
RT
0
E
D
RT
10
13
Solid
D
AB
ðTÞ¼D
AB
ðT
0
Þexp
Forced convection can generate much stronger fluid motion and thus induced mixing. To
account for the flow-induced diffusion or dispersion, one usually resorts to mass transfer
coefficient. That is,
N
A
¼ k
c
ðC
A
1
C
A
2
Þ
(17.2)
where
N
A
is the mass transfer flux in the direction from
C
A1
to
C
A2
. Mass transfer coefficient
k
c
is a function of flow, geometry, fluid, and mass transfer species.
Dwidevi PN and Upadhyay SN (
Ind. Eng. Chem. Process Des. Dev
. 1977, 16: 157) reviewed
a number of mass transfer correlations for both fixed and fluidized beds and arrived at the
following correlation for packed beds when
Re
1:
ε
Sh ¼ 0:4548Sc
1=3
Re
0:5931
>
(17.3)
where
is the voidage or volume fraction/ratio of nonparticles in the bed,
Sh
is Sherwood
number,
Re
is the Reynolds number,
Sc
is the Schmidt number. The dimensionless numbers
are defined by
ε
k
c
d
p
D
AB
Sh ¼
(17.4a)
m
f
r
f
D
AB
Sc ¼
(17.4b)
d
p
r
f
U
m
f
Re ¼
(17.4c)
TABLE 17.2
Mass Transfer Coefficient in Gaseous and Liquid Phases,
to or from Particles of Diameter d
p
Temperature (and pressure)
dependence
Phase
U
0:5931
T
0:777
ðd
p
PÞ
0:4069
Gas
k
C
f
U
0:5931
T
2=3
d
0:4069
p
Liquid
k
C
f
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