Kinetic Theory of Moderately Dense, Rigid‐Sphere Gases (Englisch)

Nationallizenz
in Physics of Fluids (1958-1988) ; 4 , 7 ; 816-833
Physics of Fluids (1958-1988)

By successive partial integrations of the Liouville equation, the hierarchy of BBGKY equations are obtained. The series is terminated at the second equation by the introduction of a superposition approximation. A specialization to rigid spheres is made early in the treatment. Then, after defining a nonequilibrium pair correlation function, the first BBGKY equation is identified as an Enskog equation modified by the inclusion of a momentum‐dependent correlation function in the collision integral. This equation and the second BBGKY equation completely determine the singlet distribution and pair correlation functions. An approximate solution to this pair of equations follows from the usual linearized perturbation expansion of the singlet distribution and pair correlation functions for the system near equilibrium. A set of five equations in the coefficients of the gradients are obtained, and the coupling between them is resolved by expanding these coefficients in powers of the number density. Because of the limitations imposed by the superposition approximation, only the first few terms in the density expansions are considered explicitly. The solutions to these equations and the resulting modifications of the transport coefficients are discussed.

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