CFD Online Logo CFD Online URL
Home > Forums > Main CFD Forum

Information on 'second viscosity'

Register Blogs Members List Search Today's Posts Mark Forums Read

LinkBack Thread Tools Display Modes
Old   September 23, 2005, 15:07
Default Information on 'second viscosity'
Posts: n/a
Can anyone provide references to information on 'the second viscosity'?

Obvious Stokes (gas) & incompressible deletion are understood.

Thanks, diaw...
  Reply With Quote

Old   September 26, 2005, 12:04
Default Re: Information on 'second viscosity'
Posts: n/a

Here are a few thoughts. The Chapman-Enskog procedure for obtaining approximate solutions to the Boltzmann Eqn. is usually truncated at the first term. This is generally referred to as the Navier-Stokes approximation. If you keep the second term, you get the Burnett equations. The stress tensor is the sum of the Euler, Navier-Stokes, Burnett, super-Burnett , etc. We truncate at the NS level. The Euler term is the regular pressure. The NS contribution includes a relaxation pressure and terms proportional to the divergence and deformation of the velocity. The relaxation pressure occurs when there are two distinct relaxation time scales, say rotational and chemical. As to the terms related to velocity:

lambda*Dilatation*IdentityTensor + 2*mu*RateOfDeformation

where lambda is the second viscosity but

RateOfDeformation = RateOfDeformationDeviator - (1/3)*Dilatation*IdentityTensor

Hence, the portion of the viscous stress tensor we care about is

(lambda - 2/3mu)*Dilatation*IdentityTensor + 2*mu*RateOfDeformationDeviator.

In kinetic theory, one usually calls the term

(lambda - 2/3mu) = kappa

We have now separated the material stretching into a constant volume component and what remains. If you want kinetic theory estimates for kappa, look for some papers by Geoffrey Maitland around 1982. He is also the lead author of a book entitled "Intermolecular Forces." If you want to learn about the relaxation pressure, look into the work of Ekaterina Nagnibeda.

Keep in mind that the Chapman-Enskog procedure demands that the stress tensor be composed of gradients of the hydrodynamic variables only. It is not assured that this particular construct is fully capable of representing complicated relaxation phenomena. There's another good book out there by Vladimir Zhdanov entitled "transport processes ..."

Good luck.

  Reply With Quote

Old   September 26, 2005, 14:22
Default Re: Information on 'second viscosity'
Posts: n/a
Wow, thank you so much for answering in so much detail - it is very much appreciated... Some additional areas to work through.

My reason for asking about 'Second Viscosity', is that when a compressible development of the momentum equation is performed, we may not just 'lose' lambda (as for incompressible assumption) & it appears in the final equations. At that point, some level of calculation has to be made regarding its value.


  Reply With Quote


Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Power - Law Viscosity Model for Polymers NickolasPl OpenFOAM 2 August 12, 2011 08:26
Eulerian Modeling: Frictional Viscosity Help meangreen FLUENT 0 July 8, 2009 14:46
kinematic viscosity at diff temperatures,pressures Mecobio Main CFD Forum 0 November 7, 2005 13:55
Terrible Mistake In Fluid Dynamics History Abhi Main CFD Forum 12 July 8, 2002 09:11
Problem of Turbulent Viscosity Ratio Limited David Yang FLUENT 3 June 3, 2002 06:13

All times are GMT -4. The time now is 07:12.