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 goicox November 28, 2012 10:12

Interface mass diffusion term/flux questions

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)

where:

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

Note that , where 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 , leading to:

(2)

Or

(3)

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: and ) 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)?