## June 05, 2009

### Viscosity of Gaseous Mixtures

In the previous few posts, I discussed about methods for calculating viscosities of pure gases using different methods at low & high pressures. What about mixtures?

Calculating property of any mixture is more tedious than pure components. They vary significantly if components widely vary. Also its very difficult to search for applicable & trusted correlations to calculate the mixture properties.

So in this part we will discuss the method which are applicable for gaseous mixtures at low & high pressures.

The method used in this case is called Wilke correlation which is very easy for binary mixtures and can be used for multi components mixtures also.

The equation is

vism = Sum (i = 1 to n) [ yi visi / Sum (j = 1 to n) yi phi(i,j) ]

Where
vism = viscosity of mixture
Sum (i = 1 to n) = Sigma sign for i = 1 to n which is represented here in language term due to non availability of symbols in blogger.
yi = mole graction of component i in the mixture
visi = viscosity of pure gas for i compnents
phi(i,j) = double parametric symbol given as below

phi(i,j) = 1 if i = j

phi (1,2) = [ 1 + (vis1/vis2)^0.5 * (M2/M1)^0.25 ]^2 / [8 ( 1 + M1/M2 )]^0.5

Where M1, M2 are molecular weights
Vis1, Vis2 are pure component viscosity

Therefore,

phi(2,1) = vis2/vis1 * M1/M2 * phi (1,2)

So for Binary mixture it reduces to

vism = [ y1 vis1 / (y1 + y2 phi(1,2))] + [y2 vis2 / (y2 + y1 phi(2,1))]

Viscosity of Gas Mixture at High Pressure
The correlation used is of Dean & Stiel for non polar gases mixture.

(vism - vism0) * zetam = 1.08 [ exp(1.439 Drm) - exp(-1.111 Drm ^ 1.858)]

Where
vism = viscosity of mix at high pressure
vis0 = viscosity of mix at atm pressure
zetam = for mixture as defined in the article of Viscosity at High Pressure.
Drm = Reduced density for mixture

To calculate the reduced density of mixture you need to know the critical properties of the mixture for which following general equations are used.

Tcm = Sum (i = 1 to n ) yi x Tci
Zcm = Sum (i = 1 to n ) yi x Zci
Vcm = Sum (i = 1 to n ) yi x Vci
Pcm = Zcm R Tcm / Vcm

So Drm = 1/ Vrm
& Vrm = Vm/Vcm

Yes dear you are right again the unit of viscosity here is micropoise.

List of other property estimation methods on this Blog.

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