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Chapman–Enskog theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation. The technique justifies the otherwise phenomenological constitutive relations appearing in hydrodynamical descriptions such as the Navier–Stokes equations .
The fusion of Chapman's and Enskog's theories later became known as the Chapman–Enskog method for solving the Boltzmann equation. In a 1939 book called The Mathematical Theory of Non-Uniform Gases, written by Chapman and Thomas Cowling and dedicated to David Enskog, the authors expanded this theory under the Chapman-Enskog designation.
One of the key predictions of the theory is the following relationship between viscosity , thermal conductivity, and specific heat : k = f μ c v {\displaystyle k=f\mu c_{v}} where f {\displaystyle f} is a constant which in general depends on the details of intermolecular interactions, but for spherically symmetric molecules is very close to 2. ...
The kinetic theory of gases allows accurate calculation of the temperature-variation of gaseous viscosity. The theoretical basis of the kinetic theory is given by the Boltzmann equation and Chapman–Enskog theory, which allow accurate statistical modeling of molecular trajectories.
The gas viscosity model of Chung et alios (1988) [5] is combination of the Chapman–Enskog(1964) kinetic theory of viscosity for dilute gases and the empirical expression of Neufeld et alios (1972) [6] for the reduced collision integral, but expanded empirical to handle polyatomic, polar and hydrogen bonding fluids over a wide temperature ...
At moderate densities (i.e. densities at which the gas has a non-negligible co-volume, but is still sufficiently dilute to be considered as gas-like rather than liquid-like) this simple relation no longer holds, and one must resort to Revised Enskog Theory. [9] Revised Enskog Theory predicts a diffusion coefficient that decreases somewhat more ...
An example of such a procedure is the Sutherland approach for the single-component gas, discussed above. For gas mixtures consisting of simple molecules, Revised Enskog Theory has been shown to accurately represent both the density- and temperature dependence of the viscosity over a wide range of conditions. [55] [53]
The kinetic theory of gases entails that due to the microscopic reversibility of the gas particles' detailed dynamics, the system must obey the principle of detailed balance. Specifically, the fluctuation-dissipation theorem applies to the Brownian motion (or diffusion ) and the drag force , which leads to the Einstein–Smoluchowski equation ...