446
Chapter 10
(Note: This is valid only for £ ^
RP
)
The mass flux of A expressed by Fick’s law at £ =
Rp
and that expressed using the mass transfer coefficient
must be equal,
le.
ki icA
,s
- 0) =
- D a
(6)
With the derivative of Eq. 5 inserted we get
R p
кі°А;
= ^
-
R p
0)
or
k ld b
o A
(
8
)
This result, i.e.
Sh
=
2,
is probably one of the best
remembered pieces of knowledge by chemical
engineering students. However, it must be kept in mind that it applies only for steady-state mass transfer
from a single sphere into a stagnant medium.____________________________________________________
Table 10.7. Some reported correlations for the Sherwood number
Correlation
Conditions
Remarks
Source
Sh =
і
і
2 + 0.55
Re* Sc*
2 < R e<
1300
Immobile gas-liquid
interface
Froesshng, 1938
Sh =
і
і
0.82
Re* Sc3
200
< Re <
4000
Immobile gas-liquid
interface
Rowe
et al,
1965
Sh =
(
l \ i
4 + 1.2U V
L
J
Re<
1
Pe <
104
Immobile gas-liquid
interface
Brian and Hales, 1969
Sh =
і
t
0.42Gr3S c2
і
Free convection
Mobile interface, large
bubbles
Calderbank and Moo-
Young, 1964
Sh =
0.65
P e2
1
Re<
1
Mobile gps-liquid
interface
Blanch and Clark, 1997
Sh =
0.65^1 + y j 2iV
1
<
Re
< 10
Mobile gas-liquid
interface
Blanch and Clark, 1997
Sh
=
1
1.13
P e2
R e »
1
Mobile gas-liquid
interface
Blanch and Clark. 1997
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