To the kinetic theory of dense gases and liquids. Calculation of quasi-equilibrium particle distribution functions by the method of collective variables

Abstract

Based on a chain of BBGKI equations with a modified boundary condition that takes into account multiparticle correlations, kinetic equations in the approximate "pairs" collisions and in the polarization approximation, taking into account the interaction through the third particle, obtained. The specifics of the model representation of the pair potential of particle interaction through short-range and long-range parts were taken into account. In the case of the short-range potential in the form of the potential of solid spheres, the contribution of Enskog's revised theory to the complete integration of the collision of the kinetic equation is obtained. The collision integrals include paired quasi-equilibrium distribution functions that depend on the nonequilibrium mean values of the particle number density and the inverse temperature. The method of collective variables Yukhnovskii is applied for the calculation of pair quasi-equilibrium distribution function with an allocation of short-range and long-range parts in the potential of the interaction of particles. In this case, the system with short-range interaction is considered as a frame of reference.

Kinetic description of ion transport in the system "ionic solution -- porous environment"

“…The nonequilibrium state of the system is described using a modified one chain of equations BBGKI [37][38][39]41,42 for partial nonequilibrium distribution functions of ions and particles of the porous matrix. For this purpose, we used the approach proposed in, [37][38][39]41,42,44 where the modified chain of BBGKI equations is built taking into account the concept of the consistent description of kinetics and hydrodynamics of nonequilibrium processes of interacting particles in the Zubarev method of nonequilibrium statistical operator. A generalized kinetic equation of the revised Enskog-Vlasov-Landau theory for the nonequilibrium ion distribution function in the model of charged solid spheres is obtained, taking into account attractive short-range interactions for the ionic solution -porous medium system.…”

“…Another way is suggested in the recent work, 44 in which the paired quasi-equilibrium coordinate distribution function of a simple liquid is calculated from the statistical sum of the cor-responding quasi-equilibrium particle distribution in the method of collective variables. [48][49][50][51][52] In addition, it is important to note that the use of the Ornstein-Zernicke equation, which depends on the time, [53][54][55][56] is promising to calculate g 2 ( r 1 , r 2 |n, β; t).…”

Unification of kinetic and hydrodynamic approaches in the theory of dense gases and liquids far from equilibrium

“…From this point of view, in the general formulation of the problem of statistical description, an important issue is the calculation of the partition function Z rel (t) both for the calculation of non-equilibrium entropy and Lagrange multipliers. In work [51], one of the methods of calculating Z rel (t) using the method of collective variables [47][48][49] was proposed. At the same time, contributions from short-range and long-range interactions were separated between particles.…”

Kinetic description of ion transport in the system "ionic solution – porous environment"

“…Given the structure ρ liq rel (x Nα ; t) and the approach [37][38][39][41][42][43][44], integrating the Liouville equation with the source (1) by the corresponding coordinates and momentum of the ions of the solution and the coordinates of the particles of the porous matrix, we obtain a chain of equations BBGKI with modified boundary conditions (taking into account spatiotemporal interparticle correlations) for the system ionic solution -porous matrix:…”

“…In particular, in the case of simple fluids in the works [45][46][47], when considering the corresponding models of the collision integral for this distribution function we used the generalization of the virial decomposition by the density chosen for the time-dependent density. Another way is suggested in the recent work [44], in which the paired quasi-equilibrium coordinate distribution function of a simple liquid is calculated from the statistical sum of the corresponding quasi-equilibrium particle distribution in the method of collective variables [48][49][50][51][52]. In addition, it is important to note that the use of the Ornstein-Zernicke equation, which depends on the time [53][54][55][56], is promising to calculate g 2 (r 1 , r 2 |n, β; t).…”