chapter  19
3 Pages

Fundamentals of the calculation of non-equilibrium functions of molecular distributions

Continuous distribution. In a macroscopic volume of a gas or liquid, the Liouville equations serve as the starting position for constructing transport equations, which operate with the total distribution function of the molecules of the system. Six variables describing its spatial coordinates and velocities are used to describe the state of each molecule [6,15,21,22,84-86]. In describing the dynamics of the system, we must pass to the generalized chain of coupled Bogolyubov equations [6] for time (non-equilibrium) distribution functions. They are written as follows: the expression for the function θ(s) can be written as

L B n B dxθ θ θ+ + + ≤ ≤ ≤ ≤

− =∑ ∑ ∫ (19.1)

where: t is the time 1

1 ( )

L F t r p≤ ≤

∂ ∂ ∂ = + +

∂ ∂ ∂∑ v , F4 = −∂u(ri) / ∂ri is the external force, u(ri) is the potential energy of the molecule i in the external field (Section 13), xi = (ri, vi), vi is the velocity of


r p r p ∂ ∂∂ ∂

= + ∂ ∂ ∂ ∂

, Eij is the

intermolecular interaction potential between molecules i and j (13.1). Because of the extreme complexity of the chain of equations for

the sequence of distribution functions θ(1), θ(2), … it is natural to seek approximate closed equations for the simplest distribution functions, which is achieved by a more crude description of processes in the system under consideration.