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

Hydrodynamic equations for dense fluid mixtures with multistep interaction between particles

“…As it is known, when the dense system approaches equilibrium, the fast kinetic processes are superimposed with slower hydrodynamic processes related to the local conservation laws -one says that kinetics and hydrodynamics are closely connected with each other [28,29]. In our case this connection is realized by means of the potential energy density which appears as a contribution to the slow variable, the total energy density, and simultaneously it manifests the non-hydrodynamic (kinetic) behavior due to the presence of the source in its transport equation caused by some subset of the microscopic pair processes, namely, the exchange processes.…”

A Consistent Description of Kinetics and Hydrodynamics of Systems of Interacting Particles by Means of the Nonequilibrium Statistical Operator Method

“…Therefore, in dense gases and liquids, the kinetics and hydrodynamics are closely connected and should be considered simultaneously. That is why many-particle correlations, related to the local conservation laws of mass, momentum and total energy, cannot be neglected [1,5,9,10]. The local conservation laws affect the kinetic processes due to an interaction of the selected particles group with other particles of the system.…”

“…The modification of weakening correlation conditions to a chain of equations by Bogolubov was developed in papers [2][3][4][5][6][7][8][9][10][11][12]. An important achievement of the given approach is the fact that the modified boundary condition gives the possibility [4,7,14] to derive consequently the kinetic equation of the RET theory [34] for the first time.…”

“…Then, at the construction of kinetic equations for high densities, it is necessary to choose the abbreviated description of a nonequilibrium system in the form to satisfy the true dynamics of conserved quantities automatically. To this end, the densities of hydrodynamic variables should be included together with the one-particle distribution function f 1 (x; t) into the initial set of parameters of the abbreviated description [1,5,9,10]. The next phase functions correspond to the densities of the hydrodynamic variables ρ(r; t), j(r; t) and E(r; t):…”

“…One of the approaches to the unification of kinetics and hydrodynamics in the theory of transport phenomena for systems of interacting particles was proposed by Zubarev and Morozov in [1] and developed in further papers [2][3][4][5][6][7][8][9][10][11][12]. This statistical approach is based on a modification of the boundary conditions for the weakening of correlations to the BBGKY hierarchy for many-particle distribution functions and to the Liouville equation for a full nonequilibrium distribution function (nonequilibrium statistical operator -NSO).…”