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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.

### #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