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Gas-Liquid Film Mass Transfer Expression For Instantaneous Rxn

rate expression for gasliquid gas absorption in liquid film

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#1 meer

meer

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Posted 02 October 2016 - 08:31 AM

Pl. see the attached file.....

 

For a case of Instantaneous Reaction (Fluid-Fluid Reaction Kinetics by Octave Levenspill Chapter 23)

 

the expression for gas film mass transfer has no film thickness involved in terms of x but the expressions for liquid film include the film thickness in terms of xand x , why ? 

 

The reason is given there in the attached file picture but still doesn't make clear sense to me...pl. help.

Attached Files



#2 Francisco Angel

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Posted 02 October 2016 - 03:24 PM

Hi Meer:
I think the key is this, the text says: "the coefficients corresponds to those without reaction, only mass transfer with reference to the whole distance x0".

 

First lets review some fundamentals. Lets think in a simplified case, in which diffusion described by Fick law will be applicable, you would obtain for the flux (N):

 

N = D*CAi/x0

 

with D: diffusivity, CAi: Concentration at interphase, x0: width of the liquid film, we are assuming here that the bulk concentration is zero for simplicity. Now, the text would introduce a mass transfer coefficient, k, and say:
 

N = k*CAi

 

and obviously k=D/x0, the last expression valid for the most simple case. Next the text will explain that in other circumstances k is not simply D/x0, so you could measure k, say experimentally, make correlations, etc.

 

Now for the case in the picture you provided, you will have (Nreacc: flux when a reaction is ocurring):

 

Nreacc=D*CA_i/x

 

Please note that I used x, the effective distance A component is travelling, now remember what the text says: "the coefficients corresponds to those without reaction, only mass transfer with reference to the whole distance x0", I want to express the flux in terms of k without reaction, I don't want this:
 

k_reacc = D/x (Note the "divided by x")

 

I want this:

 

k_NOreacc= D /x0 (Note the "divided by x0")

 

I achieve that by rearranging the terms:

 

Nreacc=D*CAi/x

              =D*CAi*x0/(x*x0)

              =(D/x0)*CAi*x0/x

              =k_NOreacc*CAi*x0/x

 

So, long story short, the text is trying to express the flux when a reaction is happening, in terms of the mass transfer coefficient measured when NO reaction is happening, x0/x turns out to be a scale factor, same goes for the factor:
x0/(x0-x)

 

in the expression for the flux of B.

 

Best regards.



#3 meer

meer

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Posted 03 October 2016 - 10:32 PM

Thank you very much for such an elaboration :)






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