# What makes an abstract physical system describable by a "fluid" equations of motion?

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We can describe (some of) the dynamics of many systems using fluid mechanics. Of course these include classical fluids like water, more exotic fluids like photon gases and the universe as a whole and even solid(ish) things over long times, like glasses and ice. Further still we can treat general classical systems in phase space using a phase fluid, quantum systems (e.g. Madelung equations) and with a little bit of hand waving anything that happens on a symplectic manifold (which gives us a Hamiltonian and hence a flow and Louiville's theorem).

So what is it about a system that makes it obey a fluid model? Are there systems that definitely do not fit a fluid model?

(I realise that I haven't said exactly what I mean by "fluid model", this is somewhat deliberate. If you like you can take it to mean "having equations of motion which are (almost) identical in some form to the Euler equations".)

edit: Since admittedly, the original question wasn't quite clear I'll try to clarify a bit. I'm not looking for a high-school answer, or one which describes only actual literal physical fluids, e.g. "a fluid doesn't support a shear stress", "a fluid is something you can wash your hair with". I've given some examples above of situations that fit this description, and without further explanation I think it's non-obvious what a "mean free path" or similar would mean in a generalised fluid. What I'm really looking for (and there may not be any) is some overarching physical or mathematical principle, or failing that an argument as to why there isn't one. I'd even be quite happy to be directed to a book or more appropriate forum. I apologise for not being clearer before and appreciate the answers already given.

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user Sean D

asked Mar 5, 2014
retagged Mar 25, 2014
A fluid is nothing more than a material that "flows" (deforms continuously under shear stress). I think what you are really trying to ask is under what circumstances can a material be modeled as continuum. There are many systems that lend themselves to continuum approximation. Some of those systems deform continuously under shear stress and are therefore analogous to fluids. Regardless, the equations of motion remain the same, but the equation of state of a fluid will always be independent of deformation history.

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user SimpleLikeAnEgg
Comment to the question (v1): It would be good if OP (or somebody else?) would clarify/simplify/stress what is really being asked.

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user Qmechanic
@Qmechanic I've amended the question and hopefully the aim is somewhat clearer now

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user Sean D
@SeanD Your question is now even more confusing. So what is it about a system obey a fluid model? The answer is quite simple and I know you don't find it enlightening, but it really is as simple as if it "doesn't support shear stress." There is no other magical quality that makes a system a "fluid."

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user SimpleLikeAnEgg
@SimpleLikeAnEgg except that the concept of "shear stress" isn't (obviously) meaningful in many of the above-mentioned situations. Or are you saying there should be some generalised notion of this for each system?

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user Sean D
@SeanD Yes, there is a generalized notion of shear stress for each of those systems which is independent of deformation history and that is part of why you can approximate them as fluid continuum. If you want to understand shear stress on a molecular level you should look into the kinetic theory of gases. In that case shear stress is the result of momentum transport from molecular diffusion. I can imagine other sources of shear stress for other systems, but as long as it is independent of deformation history then the system is a fluid.

This post imported from StackExchange Physics at 2014-03-09 09:16 (UCT), posted by SE-user SimpleLikeAnEgg

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