Derivation of Hydrodynamic Equations from Interacting Particles

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The discussion centers on finding a detailed derivation of hydrodynamic equations, specifically the Navier-Stokes equations, from the perspective of interacting particles. The original poster, Dario, seeks a comprehensive explanation that accounts for scenarios where the free streaming length is comparable to the averaging box size, which is not typically covered in standard textbooks. A participant suggests several resources, including "Principles of Condensed Matter Physics" by Chaikin and Lubensky, "Molecular Hydrodynamics" by Boon and Yip, and "Macrotransport Processes" by Brenner and Edwards, although they express uncertainty about fully grasping the material. The conversation highlights the need for more specialized literature to address this complex topic. Understanding these derivations is essential for advanced studies in fluid dynamics.
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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
 
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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.
 
dario.bettoni said:
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.
 

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