276 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS
Case2: diameterD 0. 9 dDd 2 , Q 2 D 1. 25 Q 1
The number of drops per unit time is:6 Q 2
d^32D
7. 5 Q 1
0. 9 d 1
3D
10. 29 Q 1
d^31Rising velocityDKd^21 DK 0. 9 d 1
2 D 0. 81 Kd^21
Downward liquid velocityD^54 ð^12 Kd^21 D 0. 625 Kd^21 relative to continuous phase
Rising velocity relative to containerD 0. 81 Kd^21 0. 625 Kd^21 D 0. 185 Kd^21Contact time,te 2 DH
0. 185 Kd^21Mass transfer in timete 2 per unit area/kte^1 / 22 /√
H
0. 185 K
1
d 1/ 2. 325
√
H
K
d 11Mass transfer per drop / 2. 325√
H
K
d 11 ð 0. 9 d 1
2 / 1. 883√
H
K
d 1Mass transfer per unit time / 1. 883√
H
K
d 1 ð10. 29 Q 1
d^31/ 19. 37
√
H
K
Q 1
d^21Thus, the factor by which mass transfer rate is increased is: 19. 37 / 8. 48
D 2. 28
PROBLEM 10.44
According to Maxwell’s law, the partial pressure gradient in a gas which is diffusing
in a two-component mixture is proportional to the product of the molar concentrations
of the two components multiplied by its mass transfer velocity relative to that of the
second component. Show how this relationship can be adapted to apply to the absorption
of a soluble gas from a multicomponent mixture in which the other gases are insoluble,
and obtain an effective diffusivity for the multicomponent system in terms of the binary
diffusion coefficients.
Carbon dioxide is absorbed in alkaline water from a mixture consisting of 30% CO 2
and 70% N 2 , and the mass transfer rate is 0.1 kmol/s. The concentration of CO 2 in the
gas in contact with the water is effectively zero. The gas is then mixed with an equal
molar quantity of a second gas stream of molar composition 20% CO 2 , 50%, N 2 and 30%
H 2. What will be the new mass transfer rate, if the surface area, temperature and pressure
remain unchanged? It may be assumed that a steady-state film model is applicable and
that the film thickness is unchanged.
Diffusivity of CO 2 in N 2 D 16 ð 10 ^6 m^2 /s.
Diffusivity of CO 2 in H 2 D 35 ð 10 ^6 m^2 /s.