Limit of Continuum approximations

[FredTheTed]

Hi all!

I'm after some advice on the limits of continuum based simulations of fluids.
More specifically, the point at which the fluid can no longer be considered a continuous media, and the effect of discrete atoms/molecules starts to dominate the dynamics.

Can anyone offer some suggestions as to where i should start looking?

many thanks

Pete

 

[RungeKuttaMethods]

Pete,

Here are some quick, unresearched thoughts. Let me stick to gases.
The kinetic theory derivation of the Navier-Stokes eqns makes the
assumption that the mean time between molecular collisions is much
faster than any other time scale present. Switching from time to
length scales, the Knudsen number must be small. You can leave the
continuum regime in gases by increasing the Knudsen number beyond
zero.

I'm going to change the question a bit. When do the Navier-Stokes
equation become invalid? Besides when the Knudsen number grows, it
may also occur across shock waves and inside chemical reaction zones.
The reason for the 2 latter issues is that the molecular velocity
distribution can become excessively perturbed over its equilibrium
shape. With reactions, there can be a small segment of molecules
that have extremely high velocities and cause a bump at the high
end of the velocity distribution that was otherwise nearly gaussian.

Sometimes people use the (David) Burnett equations to refine
a Navier-Stokes calculation but I believe the concensus is that the
Burnett equations do not extend the validity of the NSE but rather
refine it when it is valid. As this get more rarefied or the velocity
distribution gets more perturbed, you can also move to (Harold) Grad's
moment method.

On a side note:

http://www.eng-tips.com/viewthread.cfm?qid=113733&page=1

 

[FredTheTed]

Hi there,

Thanks for the reply! my work so far has been on the molecular simulation side, so any info on the NS side of things helps me a lot.
I've noticed that there seems to be loads of information available about the continuum limit of gasses, but not for liquids. Is there an equivalent to the kn for liquids, or is there another method for gauging the continuum-isation of a fluid?

Sorry, but I dont know of any positions for fluid/dynamicists around here at the moment (unless your after an academic career )

Many thanks for the info

Pete

 

[RungeKuttaMethods]

Pete,

The kinetic theory of liquids makes the kinetic theory of gases
look simple. You could try looking at this:

Dynamics of Polymeric Liquids, Vol. 2, Kinetic Theory
RB Bird, CF Curtiss, RC Armstrong, O Hassager
New York: Wiley Intersci, 1987

Another thing that is intermediate between the usual gas treatment
and liquids is dense gases. How serious do you want to get?
Look at the book by Ferziger and Kaper (1972). Maybe these will
tell you something about the underlying assumptions??

http://scitation.aip.org/getabs/ser...00008000004000667000001&idtype=cvips&gifs=yes

http://content.aip.org/JCPSA6/v86/i2/963_1.html

http://content.aip.org/JCPSA6/v80/i1/408_1.html

http://content.aip.org/JCPSA6/v79/i9/4509_1.html

http://content.aip.org/JCPSA6/v78/i5/2746_1.html