This chapter provides a foundational review of the kinetic theory of gases, highlighting its importance in modeling non-continuum and rarefied gas flows. It begins by contrasting classical fluid mechanics with molecular approaches and outlines the limitations of continuum assumptions in applications such as microscale devices and high-altitude aerospace flows. The historical evolution of matter theory, from ancient philosophy to atomic theory, sets the stage for exploring kinetic and statistical mechanics. The chapter introduces flow regimes based on the Knudsen number and explains the transition from continuum to free molecular flow. Key components, including molecular spacing, binary collisions, intermolecular forces, and potentials, are discussed in detail using models such as the Lennard–Jones, Hard-Sphere, and Variable Hard-Sphere models. The derivation of pressure and viscosity from molecular principles is demonstrated, and statistical distributions such as the Poisson and Gaussian are used to describe molecular number fluctuations. This comprehensive overview prepares readers for advanced topics in non-equilibrium gas dynamics and methods such as the Direct Simulation Monte Carlo (DSMC) technique.

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A Brief Review of Kinetic Theory

  • Ehsan Roohi,
  • Hassan Akhlaghi,
  • Stefan Stefanov

摘要

This chapter provides a foundational review of the kinetic theory of gases, highlighting its importance in modeling non-continuum and rarefied gas flows. It begins by contrasting classical fluid mechanics with molecular approaches and outlines the limitations of continuum assumptions in applications such as microscale devices and high-altitude aerospace flows. The historical evolution of matter theory, from ancient philosophy to atomic theory, sets the stage for exploring kinetic and statistical mechanics. The chapter introduces flow regimes based on the Knudsen number and explains the transition from continuum to free molecular flow. Key components, including molecular spacing, binary collisions, intermolecular forces, and potentials, are discussed in detail using models such as the Lennard–Jones, Hard-Sphere, and Variable Hard-Sphere models. The derivation of pressure and viscosity from molecular principles is demonstrated, and statistical distributions such as the Poisson and Gaussian are used to describe molecular number fluctuations. This comprehensive overview prepares readers for advanced topics in non-equilibrium gas dynamics and methods such as the Direct Simulation Monte Carlo (DSMC) technique.