CHEMICAL ENGINEERING

MASS TRANSFER 255

At depth of 0.1 mmD 10 ^4 m:

√

1

6

k 2

D

yD 93. 8

and:

{(

CAs

CA

) 1 / 2

 1

}

D 93. 8 C

C 1 / 2

As D^18.^8

(

CAs

CA

) 1 / 2

D 19. 8

CAD

0. 04

19. 82

D 0 .00010 kmol/m^3.

(ii) The molar transfer rate at surface is:

NAD

dCA

dy

D

√

2

3

k 2

D

C^3 As/^2 D

.

D

√

2 k 2 D

3

C^3 As/^2

D

√

2

3

ð 9. 5 ð 103 ð 1. 8 ð 10 ^9  0. 04

3 /^2

D 3. 38 ð 10 ^3 ð 0. 008 D 2. 70 ð 10 ^5 kmol/m^2 s.

(iii) The molar transfer rate at depth of 0.1 mm is:

NAD

√

2 k 2 D

3

C

3 / 2

A

D 3. 38 ð 10 ^3 ð 0. 00010

3 /^2 D 3. 38 ð 10 ^9 kmol/m^2 s

PROBLEM 10.32

In calculating the mass transfer rate from thepenetration theory, two models for the
age distribution of the surface elements are commonly used — those due to Higbie and
to Danckwerts. Explain the difference between the two models and give examples of
situations in which each of them would be appropriate.

(a) In the Danckwerts model, it is assumed that elements of the surface have an age
distribution ranging from zero to infinity. Obtain the age distribution function for this
model and apply it to obtain the average mass transfer coefficient at the surface, given
that from the penetration theory the mass transfer coefficient for surface of agep tis
[D/t
], whereDis the diffusivity.
(b) If for unit area of surface the surface renewal rate iss, by how much will the mass
transfer coefficient be changed if no surface has an age exceeding 2/s?
(c) If the probability of surface renewal is linearly related to age, as opposed to being
constant, obtain the corresponding form of the age distribution function.