Kinetic Theory and Fluid Dynamics: Study & ...

Kinetic Theory and Fluid Dynamics: Study & the Role of the Boltzmann Equation

Author Name : Mariam M. O. Alsoufi, Aljawhari MA. M. Direedar

ABSTRACT The kinetic theory of gases provides a fundamental framework for understanding the microscopic behavior of particles in a fluid, linking molecular motion to macroscopic physical quantities such as pressure, temperature, and viscosity. Central to this theory is the Boltzmann equation, a statistical equation that describes the evolution of the distribution function of particle velocities in a gas. This equation serves as a critical bridge between microscopic dynamics and macroscopic fluid behavior, playing a foundational role in the field of fluid dynamics. Through appropriate approximations and scaling limits—such as the Chapman-Enskog expansion, the Boltzmann equation leads to the derivation of classical fluid equations, including the Euler and Navier-Stokes equations. Moreover, the Boltzmann equation captures non-equilibrium phenomena, rarefied gas dynamics, and transport processes that cannot be fully described by continuum fluid models. This abstract reviews the central role of the Boltzmann equation in connecting kinetic theory with fluid dynamics, highlighting its mathematical structure, physical significance, and applications in both theoretical and applied contexts.