Beyond NavierStokes equations: capillarity of ideal gas
Abstract
The system of NavierStokesFourier equations is one of the most celebrated systems of equations in modern science. It describes dynamics of fluids in the limit when gradients of density, velocity and temperature are sufficiently small, and loses its applicability when the flux becomes so nonequilibrium that the changes of velocity, density or temperature on the length compatible with the mean free path are nonnegligible. The question is: how to model such fluxes? This problem is still open. (Despite the fact that the first 'final equations of motion' modified for analysis of thermal creep in rarefied gas were proposed by Maxwell in 1879.) There are, at least, three possible answers: (i) use molecular dynamics with individual particles, (ii) use kinetic equations, like Boltzmann's equation or (iii) find a new system of equations for description of fluid dynamics with better accounting of nonequilibrium effects. These three approaches work at different scales. We explore the third possibility using the recent findings of capillarity of internal layers in ideal gases and of saturation effect in dissipation (there is a limiting attenuation rate for very short waves in ideal gas and it cannot increase infinitely). One candidate equation is discussed in more detail, the Korteweg system proposed in 1901. The main ideas and approaches are illustrated by a kinetic system for which the problem of reduction of kinetics to fluid dynamics is analytically solvable.
 Publication:

Contemporary Physics
 Pub Date:
 January 2017
 DOI:
 10.1080/00107514.2016.1256123
 arXiv:
 arXiv:1702.00831
 Bibcode:
 2017ConPh..58...70G
 Keywords:

 Kinetics;
 fluid dynamics;
 Boltzmann;
 capillarity;
 invariant manifold;
 thermal creep;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Corrected misprints in Eqs (7) and (22), thanks to E. Azadi