Derivation of Hydrodynamic Equations from Interacting Particles

[dario.bettoni]

Hi there, does any of you know a place where I can find the derivation of the hydrodynamic equations (navier stokes, etc) starting from interacting particles? I need this done in a pedantic way as I have to deal with the case in which the free streaming length is of the same order of the averaging box, which is not the case in standard textbooks.

Thanks,

Dario

 

[boneh3ad]

I'm not familiar with the terminology "free streaming length" but the Navier-Stokes equations assume a continuous medium, so they aren't derived from individual particle collisions.

 

[Andy Resnick]

Hi there, does any of you know a place where I can find the derivation of the hydrodynamic equations (navier stokes, etc) starting from interacting particles? I need this done in a pedantic way as I have to deal with the case in which the free streaming length is of the same order of the averaging box, which is not the case in standard textbooks.

Thanks,

Dario

Chaikin and Lubensky's book "Principles of Condensed Matter Physics" has a derivation, as does Boon and Yip, "Molecular Hydrodynamics" and to some degree Brenner and Edwards "Macrotransport Processes". I wouldn't claim to fully understand the material, tho.