CHEMICAL ENGINEERING

MASS TRANSFER 271

Concentration of solute in dropDKt^1 e/^2 d^0 ^1

∴ C 2 DK

{

H

kd^02 ^34 d^2

} 1 / 2

d^0 ^1

Given that:C 2 /C 1 D 0 .9, then:

K

{

H

kd^02 ^34 d^2

} 1 / 2

d0^1

K

√

2 H

k

d^2

D 0. 9

Squaring gives:

d0^2

d^02 ^34 d^2

D 1. 62 d^4

WritingRD

d^0

d

, then:

1

R^4 ^34 R^2

D 1. 62

R^4 ^34 R^2  0. 6173 D 0

RD1.11 or 11.1 per cent increase

PROBLEM 10.40

According to the penetration theory for mass transfer across an interface, the ratio of the
concentrationCAat a depthyand timetto the surface concentrationCAsat the liquid is
initially free of solute, is given by

CA

CAs

Derfc

y

2

p

Dt

whereDis the diffusivity. Obtain a relation for the instantaneous rate of mass transfer at
timetboth at the surfaceyD 0
and at a depthy.
What proportion of the total solute transferred into the liquid in the first 90 s of exposure
will be retained in a 1 mm layer of liquid at the surface, and what proportion will be
retained in the next 0.5 mm? The diffusivity is 2ð 10 ^9 m^2 /s.

Solution

For a rectangular particle:

Thiele ModulusDD9L

Thus: 9 D

√

k

D

D

√

5 ð 10 ^4

2 ð 10 ^9

D500 m^1