MASS TRANSFER 239
Putting dCA/dyDq:
d^2 CA
dy^2
D
dq
dy
D
dq
dCA
dCA
dy
Dq
dq
dCA
Thus: Dq
dq
dCA
kC^2 AD 0
qdqDk/D
C^2 AdCA
q^2 / 2
Dk/D
C^3 A/ 3 Cconst.
In an infinite system atyD1,CAD0anddCA/dyD0 and hence the constantD0.
∴
(
dCA
dy
) 2
D
2
3
k
D
C^3 Aand
dCA
dy
D
√
2 k
3 D
C^3 A/^2
noting the negative sign sincedCA/dy
is negative for all values ofCA.
Thus: 2 CA^1 /^2 D
√
2 k
3 D
yCconstant
At the free surface,yD0andCADCAiDconstant.
∴ constantD 2 CAi^1 /^2
and: 2
(
CA^1 /^2 CAi^1 /^2
)
D
p
2 k/ 3 D
y
or: CA^1 /^2 CAi^1 /^2 D
p
k/ 6 D
y
WhenyDy 1 ,CADCAi/2, and:
CAi/ 2
^1 /^2 CAi^1 /^2 D
√
k/ 6 D
y 1
Wheny 1 D 10 ^3 , substituting gives:CAi^1 /^2 D 2. 42 ð 10 ^3
p
k/ 6 D
∴ C
1 / 2
Ai ^2.^42 ð^10
3 pk/ 6 D
Dpk/ 6 D
y
The mass transfer rate at the interface, whereyD0, is:
NA (^) tDD
(
dCA
dy
)
yD 0
D
√
2 kD
3
C^3 Ai/^2
D
√
2 kD
3
ð
(
1
2. 42 ð 10 ^3
p
k/ 6 D
) 3
D 8. 47 ð 108 D^2 /k
WhenDD 1 ð 10 ^8 m^2 /sandNAD 4 ð 10 ^6 kmol/m^2 s:
kD 8. 47 ð 108
ð 1 ð 10 ^8
2 / 4 ð 10 ^6 D212 m^3 /kmol s
PROBLEM 10.21
Experiments have been carried out on the mass transfer of acetone between air and a
laminar water jet. Assuming that desorption produces random surface renewal with a