Derivation of Hydrodynamic Equations from Interacting Particles

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The discussion centers on the derivation of hydrodynamic equations, specifically the Navier-Stokes equations, from the perspective of interacting particles. Dario seeks a detailed, pedantic derivation that addresses scenarios where the free streaming length is comparable to the averaging box size. Key references provided include "Principles of Condensed Matter Physics" by Chaikin and Lubensky, "Molecular Hydrodynamics" by Boon and Yip, and "Macrotransport Processes" by Brenner and Edwards, which contain relevant derivations.

PREREQUISITES
  • Understanding of Navier-Stokes equations
  • Familiarity with particle interaction models
  • Knowledge of free streaming length concepts
  • Basic principles of condensed matter physics
NEXT STEPS
  • Study the derivation of Navier-Stokes equations from particle interactions in "Principles of Condensed Matter Physics"
  • Explore "Molecular Hydrodynamics" by Boon and Yip for insights on molecular interactions
  • Review "Macrotransport Processes" by Brenner and Edwards for applications in transport phenomena
  • Research advanced topics in statistical mechanics related to hydrodynamic modeling
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Researchers, physicists, and graduate students in fluid dynamics and condensed matter physics seeking a deeper understanding of hydrodynamic equations derived from particle interactions.

dario.bettoni
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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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