Local equations of state in nonequilibrium heterogeneous physicochemical systems

Abstract

Equations describing local thermal and caloric equations of state in heterogeneous systems at any degree of their states’ deviation from equilibrium are derived. The state of a system is described by equations of the transfer of mixture components; these generalize the equations of classical non-equilibrium thermodynamics for strongly nonequilibrium processes. The contributions from reactions and external fields are taken into account. The equations are derived using the lattice gas model with discrete molecular distributions in space (on a scale comparable to molecular dimensions) and continuous molecular distributions (at short distances inside cells) during their translational and vibrational motions. For simplicity, it is assumed that distinctions between the sizes of mixture components are small. Contributions from potential functions of intermolecular interaction (of the Lennard-Jones type) to some coordination spheres are considered. The theory provides a unified description of the dynamics of distributions of concentrations and pair functions of mixture components in three aggregate states, and at their interfaces. Universal expressions for the local components of the pressure tensor and internal energy inside multicomponent bulk phases and at their interfaces are obtained. Local components of the pressure tensor and the internal energy are universally expressed through local unary and pair distribution functions (DFs) in any nonequilibrium state. The time evolution of the unary and pair DFs themselves is determined from the derived system of equations of mass, momentum, and energy transfer that ensure the transition of the system from a strongly nonequilibrium state to both the local equilibrium state described within traditional nonequilibrium thermodynamics and the complete thermodynamic equilibrium state postulated by classical thermodynamics.