CHEMICAL ENGINEERING

266 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

xT/xBm,LandCAare as in case 1.

∴ N^0 AD

D^0

L

CA

xT

xBm

D

1

L

CA

xT

xBm

Ð 41. 5

N^0 A (^2)
N^0 A (^1)

D

41. 5

31. 9

D 1. 30 or 1.3 times greater in the second case.

The observed ratio of two rates is only 1.25. This may be explained by:

1. Steady-state film conditions do not exist and there is some periodic partial disruption
   of the film.
   Penetration model!N^0 A/D^0.^5 c/f./Dfor film model.
   In this problem observed result would be accounted for by:
   N^0 A/D^0 m.
   where 1. 3
   mD 1 .25 ormD 0. 85.


2. The assumption of a gas-film controlled process may not be valid. If there is a
   liquid-film resistance, the effect of increasing the gas-film diffusivity will be less
   than predicted for a gas-film controlled process.


3. The value of the film thicknessLis not the same because of different hydrodynamic
   conditions (second mixture having a lower viscosity).
   In this case, the film thickness would be expected to be reduced giving rise to the
   reverse effect so this is not a plausible explanation.


4. Experimental inaccuracies!

PROBLEM 10.37

Using a steady-state film model, obtain an expression for the mass transfer rate across
a laminar film of thicknessLin the vapour phase for the more volatile component in a
binary distillation process:

(a) where the molar latent heats of two components are equal.

(b) where the molar latent heat of the less volatile component (LVC) isftimes that

of the more volatile component (MVC).

For the case where the ratio of the molar latent heatsfis 1.5. what is the ratio of the
mass transfer rate in case (b) to that in case (a) when the mole fraction of the MVC falls
from 0.75 to 0.65 across the laminar film?

Solution

Case (a):With equal molar latent heats, equimolecular counter diffusion takes place and
there is no bulk flow.
Writing Fick’s Law for the MVC gives:

NADD

dCA

dy

(equation 10.4)