CHEMICAL ENGINEERING

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