Film Theory: Understanding Gas-Liquid Mass Transfer with Nernst and Lewis-Whitman Models, Thesis of Chemical Processes

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TWO FILM THEORY

Ref: ceeserver.cee.cornell.edu

Gas transfer rates If either phase concentration can not be predicted by Henry's law then there will be a transfer of mass across the interface until equilibrium is reached. The mechanisms and rate expressions for this transfer process have been conceptualized in a variety of ways so that quantitative descriptions are possible. One common conceptualization method is the film theory.

In this film transport is governed essentially by molecular diffusion. Therefore, Fick's law describes flux through the film.

C mg J D (typical units ) X (^) cm^2 sec

    (^) 

If the thickness of the stagnant film is given by dn then the gradient can be approximated by:

C C b Ci

X n

 d

Cb and Ci are concentrations in the bulk and at the interface, respectively.

Mass transfer coefficients

To simplify calculations we usually define a mass transfer coefficient for either the liquid or gas phase as kl or kg (dimensions = L/t).

n

kl,g

D

d

Calculation of Ci is done by assuming that equilibrium (Henry's Law) is attained instantly at the interface. (i.e., use Henry's law based on the bulk concentration of the other bulk phase.) Of course this assumes that the other phase doesn't have a "film". This problem will be addressed later. So for the moment:

Cg Ci Hc

^ (if the film side is liquid and the opposite side is the gas phase).

The same assumptions apply to the two films as apply in the single Nernst film model. The problem, of course, is that we will now have difficulty in finding interface concentrations, Cgi or Cli. We can assume that equilibrium will be attained at the interface (gas solubilization reactions occur rather fast), however, so that:

C li c

C

gi H



Unfortunately, concentrations at the interface cannot be measured so overall mass transfer coefficients are defined. These coefficients are based on the difference between the bulk concentration in one phase and the concentration that would be in equilibrium with the bulk concentration in the other phase.

Define:

J

J

K C C*

l l^ l

K C* C

g g g

Kl = overall mass transfer coefficient based on liquid-phase concentration.

Kg = overall mass transfer coefficient based on gas- phase concentration.

Expand the liquid-phase overall flux equation to include the interface liquid concentration.

J K C C C C*

l l li li l

  ^ ^   ^  

Then substitute Cgi Cli Hc

 and

* Cg

Cl

Hc

to get:

J  K (^) l  Cl C (^) li (^)   C (^) gi Cg / H c

Since all J’s are equal:

J J J Kl k (^) l H (^) c kg

   ^    (^)    

This can be arranged to give:

1 1 l k^ l kg

1 K Hc

 



A similar manipulation starting with the overall flux equation based on gas phase concentration will give:

H (^) c 1 k k

1 K (^) g l g

 