MadSci Network: Physics
Query:

Re: How to find viscosity of a mix of fluids, given the individual viscosities?

Date: Tue Jan 2 11:37:01 2001
Posted By: Allan Harvey, Staff,National Institute of Standards and Technology
Area of science: Physics
ID: 976133008.Ph
Message:

No, in general you can't know the viscosity of a mixture from just knowing 
the pure components.  This is actually the case for any mixture property 
(density, vapor pressure, refractive index, etc.), but for many properties 
you can make a good estimate based on pure-component numbers, especially 
for systems where the components are chemically similar.  The situation 
for viscosity is worse than for most properties in that there is not even 
a theoretical "ideal" mixture behavior to use as an approximation.

There have been various procedures developed to estimate mixture 
viscosities.  The most common is the Grunberg equation, which is:

ln(VS) = sum(Xi*ln(VSi)) + sum(sum(Xi*Xj*Gij))
which for a binary mixture reduces to:
ln(VS) = X1*ln(VS1) + X2*ln(VS2) + X1*X2*G12

where VS is the viscosity, VSi is the viscosity of pure component i, Xi is 
the mole fraction of component i, and Gij is a parameter that has to be 
fitted to binary viscosity data between components i and j.  For mixtures 
of similar nonpolar components (like simple hydrocarbons of similar 
molecular weight), it is often not a bad approximation to set the Gij to 
zero.  Another common approximation, again mainly good for similar 
nonpolar components, is to use a mole-fraction average of the cube roots 
of the viscosities.  I should mention that the large difference in 
viscosity between your two components probably means that the simple 
methods for "similar" fluids would be less likely to apply.  So if you 
really need a good value you might have to find some binary data for your 
mixture (the place to look would be the book by D.S. Viswanath, "Data Book 
on the Viscosity of Liquids," Hemisphere Publishing, New York, 1989) or 
else take some yourself.

If you have access to a good library, you can find more about estimating 
viscosities for mixtures in the book by Reid et al. "The Properties of 
Gases and Liquids", and in a journal review by W.D. Monnery et al., 
Canadian Journal of Chemical Engineering, vol. 73, pp. 3-40 (1995).

Allan Harvey, Physical & Chemical Properties Division, NIST
"Don't blame the government for what I say, or vice-versa."


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