CHEMICAL ENGINEERING

MASS TRANSFER 279

Thus: CADCT 0. 25  0
D 0. 25 CT

CBmD

1  0. 75

ln 0.^175

CTD 0. 869 CT

CT

CBm

D 1. 150

and the mass transfer rate:

ANA 0 D 0. 25 CT

17. 9 ð 10 ^6

L

1. 150 AD 5. 15 ð 10 ^6

ACT

L

kmol/sD 0 .090 kmol/s

PROBLEM 10.45

What is the penetration theory for mass transfer across a phase boundary? Give details
of the underlying assumptions.
From the penetration theory, the mass transfer rate per unit areaNAis given in terms of
the concentration differenceCAbetween the interface and the bulk fluid, the molecular
diffusivityDand the agetof the surface element by:

NAD

√

D

t

CA kmol/m^2 s (in SI units)

What is the mean rate of transfer if all elements of the surface are exposed for the same
timetebefore being remixed with the bulk?
Danckwerts assumed a random surface renewal process in which the probability of
surface renewal is independent of its age. Ifsis the fraction of the total surface renewed
per unit time, obtain the age distribution function for the surface and show that the mean
mass transfer rateNAover the whole surface is:

NAD

p

DsCA kmol/m^2 s, in SI units

In a particular application, it is found that the older surface is renewed more rapidly than
the recently formed surface, and that after a times^1 , the surface renewal rate doubles,
that is it increases fromsto 2s. Obtain the new age distribution function.

Solution

Assuming the age spread of the surface ranges fortD0, totD1, consider the mass
transfer per unit area in each age group isttotCdtandsoon.
Then the mass transfer to surface in age groupttotCdtis:

D

√

D



CAt^1 /^2 dt

Thus the total mass transfer per unit area is:

√

D



CA

∫te

0

t^1 /^2 dtD

√

D



CA

[

t^1 /^2

1

2

]te

0

D 2

√

D



CAte^1 /^2