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Exact nonlocal hydrodynamics predict rarefaction effects.

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This summary is machine-generated.

We developed optimal hydrodynamics using linearized Boltzmann equations and Maxwell

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Area of Science:

  • Kinetic theory
  • Fluid dynamics
  • Statistical mechanics

Background:

  • Linearized Boltzmann equations describe rarefied gas dynamics.
  • Maxwell's boundary conditions model particle-surface interactions.
  • Spectral closure theory provides a framework for solving kinetic equations.

Purpose of the Study:

  • To derive optimal hydrodynamic equations from kinetic theory.
  • To incorporate arbitrary accommodation coefficients into the hydrodynamic model.
  • To analyze shear-mode dynamics in rarefied gases.

Main Methods:

  • Combining slow spectral closure theory with Maxwell's kinetic boundary conditions.
  • Deriving explicit steady-state solutions for shear-mode dynamics.
  • Analyzing Fourier integrals and closed-form expressions for flow and stress.

Main Results:

  • Obtained optimal hydrodynamic equations valid for arbitrary accommodation.
  • Derived explicit solutions for mean flow and stress in shear-mode dynamics.
  • Demonstrated accurate prediction of rarefaction effects like Couette flow and thermal creep.

Conclusions:

  • The derived nonlocal fluid model accurately captures rarefaction phenomena.
  • The approach provides a robust framework for kinetic-fluid coupling.
  • This work advances the understanding of rarefied gas dynamics with realistic boundary interactions.