Bruce Scott TOK ] wrote in
:

John Schutkeker wrote:

Has the theory of viscous heating of an ordinary fluid been developed?

Are you interested in Navier Stokes fluids (i.e., gasdynamics) or
actual liquids where the quantum physics determines the
microproperties?

AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making me
ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you mentioned?
There should be only one equation, and it's NS, although the viscosity
may be a complicted function, rather than a constant. But it should
still be NS, shouldn't it?

I'm interested in a fluid whose properties are hardly even known:
planetary mantles and cores, like Earth and Enceladus. Nobody
knows exactly what are those fluid properties, raising a whole 'nother
theory question that I plan to gloss over.

I'm thinking that under such high pressures, Enceladus' "mantle" may be
a highly viscous liquid, which might be something like a solution of
liquids like N2, NH3, and CH4, etc. Unfortunately, it may also be the
mixture of solid/liquid phases that we colloquially know as "slush."

Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.

Yes in both cases though I'm only familiar with the details of the
first. Have a look at _Physical Kinetics_ in the Landau/Lif****z
series.

I'm planning to get stared by taking the momentum equation and
applying P = F dot v. A viscous force of F = mu Del^2 v, gives P = v mu
del^2 v, and (ha ha) all that's needed is the velocity profile. Again,
I'm sure I can make some primitive assumptions from known tidal
geometries, to get started, but the next correction would involve
self-consistent flows, which is a whole 'nother physics problem to
solve.

I might try my hand at that one, once I've got the zero order model down
on paper. For that, I'll need the tidal force field of a body under
tidal distortion. Where would you look for that, if you had to?

If you're interested in non-equilibrium thermodynamics then there are
several texts on that as well. Look up a book called _Process
Thermodynamics_ for a decent example. I've got it loaned out long
enough to have forgotten the author's name.

Thanks, that sounds very useful.