Role of Hard-Core Collisions with Large Angle Deflections in the Kinetic Theory of Dense Fluids

The validity of the Fokker—Planck equation is discussed within the framework of Kirkwood's time smoothing formalism. It is shown that the equation is equivalent to the Boltzmann equation for a dilute homogeneous system in which grazing binary collisions predominate. Using this as a mathematical prescription, the Rice—Allnatt equation is modified by replacing the Boltzmann collision integral by a Fokker—Planck operator, but leaving the excluded volume term unchanged. The kinetic and collisional transport coefficients derived from the modified equation are compared with those derived from the Chapman—Enskog equation, the Rice—Allnatt equation, and the Fokker—Planck equation. It is concluded that the role of hard core collisions in the theory is to emphasize the importance of large angle deflections, which are not important in a dilute gas.