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.
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.
- Calculate Diffusion Coefficient in Gases
- Calculate Diffusion Coefficient in Liquids
- Heat Capacities of dissolved solids & organic solutions - Quickest methods
- Heat capacities with dissolved solids
- Kinematic viscosity of air Vs Temperature
- Thermal Conductivity of air Vs Temperature
- How to calculate viscosity of liquid mixtures
- Surface Tension
- Viscosities of Pure Gases at Low Pressure - 1
- Viscosities of Pure Gases at Low Pressure - 2
- Viscosities of Pure Gases at High Pressure
1 comments:
you may write a blog on www.processglobe.com . this will help process engineers.
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