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Interface mass diffusion term/flux questions

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Old   November 28, 2012, 10:12
Default Interface mass diffusion term/flux questions
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Javier Goicochea
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Dear Colleagues,

I am trying to model mass transfer among components of two phases. At the moment I am facing problems implementing the mass transfer at the interface.

Specifically, I have two phases having two components flowing co- or counter-current to each other, one phase is vapour and the other is liquid. Such as in the case of a liquid falling film in a tube, with vapour flowing in the center of the tube.

So if we ignore the convective mass transferred between phases, the diffusive flux between them can be written as:

(1) \frac{(x^{L}-x^{I})}{(R^L)}=\frac{(y^{I}-y^{V})}{(R^V)} = \dot{{N}''}

where:

L = Liquid
V = Vapour
I = Interface
x = mass / molar fraction of phase A (liquid)
y = mass / molar fraction of phase B (vapour)
\dot{{N}''} = mass / molar flux per unit of interfacial area

Note that y^{I} = K * x^{I}, where K is the K-factor that relates the mass / molar fractions at the interface.

After some manipulation, one could cast Eq. 1 to be a function of the (x^{L}-y^{V}), leading to:

(2) \frac{(x^{L}-y^{V})}{R_{eq}}+\Omega*x^{L}= \dot{{N}"}

Or

(3) \frac{(x^{L}-y^{V})}{R_{eq}}+\Theta *(y^{I}-x^{I})*(\dot{{N}"*R^{L}}+1)= \dot{{N}"}

This last representation is convenient since one could treat the first term of the equation as a standard heat transfer problem that keeps the mass / molar fractions (unknowns: x^{L} and y^{V}) between 0 and 1. It also allows to treat the second term explicitly (using values from the previous iteration).

Now the questions:

How would you include the second term in the system of equations? In Patankar's finite volume method the diffusion term resembles that of the first term of Eqs. 2 or 3.

Should I include the second term explicitly in the source term of both phases (using Eq. 3) or in one phase only (using Eq. 2)?

Thank you in advance for your advice, Javier
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