 Mutual diffusion coefficient in binary mixtures

Posting by rohan wanchoo on April 17, 2008 at 15:55:52.

Hi,

Is diffusion coefficient or diffusivity a constant for a particular substance at a fixed temperature and pressure? Or does it depend on the other substances in the mixture too?

For example, I have three substances A, B and C. A&B together form one mixture and A&C form another mixture. Will the diffusion coefficient of substance A in both the mixtures be a constant or variable? If not, how do we calculate the diffusion coefficient of A in the mixtures separately.

Thanks,

Rohan

On 04/17/2008 Composite Analytica 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 Analytica
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On 04/17/2008 rohan wanchoo posts: Thank you so much for the information. Your explanation made my concepts about diffusion coefficients much clearer. My problem concerns Styrene vapor and I need to simulate evaporation of styrene in the atmosphere. Could you suggest me a reference where I can look up for all the properties of Styrene vapor at 25 degrees C. I tried looking at it on the web and some references but was not able to obtain all the properties and wasn't sure of the values I did obtain. The properties I needed specifically were density, viscosity, thermal conductivity, specific heat and mass diffusivity. I was able to find all of this for liquid styrene, but not for vapor styrene at 25 degrees C.