On *04/17/2008* composite agency posts:
Hi Rohan,

The diffusion coefficient of - or friction coefficient - of species A is always dependent on other species - like A, but also B or C - in the mixture.

In a binary liquid mixture of similar components, of similar size - being A, but also B or C - diffusivities are a linear function of mole fraction of either component. Let's a assume the previous mixture, with A and B. The mutual diffusion coefficient of A in B is given by the Darken formula:

Dab = (xa * Da) + (xb * Db)

with Da:

Da= (k*T) / (3 * pi * viscosity of a * diameter of b)

and Db:

Db= (k*T) / (3 * pi * viscosity of b * diameter of a)

Special cases:

xa = 1,

Then Dab =Da =(k*T) / (3 * pi * viscosity of a * diameter of a)

Dab is then the so called self diffusion coefficient of a

xa -> 0 [a is very diluted]

Dab = Db = (k*T) / (3 * pi * viscosity of b * diameter of a)

For a binary gas mixture and a binary viscous liquid, similar equations apply. Unfortunately, for multicomponent mixtures, more complex formulae have to be used, of which we recommend the "Free Volume Theory of Diffusion", developed by Cohen, Turnbull, Vrentas, Duda, Wesselingh, Hirschfelder, Cullinan and others.

Going back to your question: it is a pity but the diffusivity of for example component A is not only a function of temperature and pressure, but also on the mole fraction and size of the other components. Especially when more than two species involved, this function of mole fraction is - unfortunately - also not linear (our free volume based chemical-physical simulations can deal with many components).

Regards,

Composite Agency

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