Dynamics of Nonequilibrium Processes in Fluids

Gonzalez, and J. A. Pople, Gaussian 95, Development Version , Gaussian, PitLsburgh, PA, 1995. 

University of Tennessee, Knoxville, TN and Oak Ridge National Laboratory, Oak Ridge, TN, USA 

GK = Green-Kubo LIT = linear irreversible thermodynamics LRT = linear response theory NEMD = nonequilibrium molecular dynamics NESS = nonequilibrium steady state TTC = thermal transport coefficient TTCF = transient time correlation function. 

If a fluid system is in thermodynamic equilibrium, all of its intensive state variables (i.e., the temperature, the pressure and the chemical potential for each chemical component) are uniform in space. In the absence of this uniformity, energy, momentum, and matter flow in order to restore the equilibrium state of the system. Most of the calculations termed 

The primary targets of these calculations are the thermal (or Navier-Stokes) transport coefficients (TTCs) which are characteristic properties of the fluid at a given thermodynamic state and inhomogeneity. The latter is quantified by the gradient of an intensive variable and, formally, can be described as an external field acting on the system. It is an essential simplification both in theoretical and in numerical studies to fix these external fields in time and consider only time-independent (i.e., steady) states. 

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Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Classical Trajectory Simulations Final Conditions Mixed... 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

The simulation of condensed phase systems by statistical mechanical methods has become a major research area in recent years. Of course, much of this work has been directed toward biologically relevant systems. The contributions in this section of ECC tend toward theory as much as computation and include the articles by Rob Coal son Poisson-Boltzmann Type Equations Numerical Methods), Peter Cummings Classical Dynamics of Nonequilibrium Processes in Fluids), a second article by Cummings Supercritical Water and Aqueous Solutions Molecular Simulation), Brian Laird Interfaces Liquid-Solid), Chi Mak Condensed-... 

Kinetic Theory. In the kinetic theory and nonequilibrium statistical mechanics, fluid properties are associated with averages of pruperlies of microscopic entities. Density, for example, is the average number of molecules per unit volume, times the mass per molecule. While much of the molecular theory in fluid dynamics aims to interpret processes already adequately described by the continuum approach, additional properties and processes are presented. The distribution of molecular velocities (i.e., how many molecules have each particular velocity), time-dependent adjustments of internal molecular motions, and momentum and energy transfer processes at boundaries are examples. 

William Russel May I follow up on that and sharpen the issue a bit In the complex fluids that we have talked about, three types of nonequilibrium phenomena are important. First, phase transitions may have dynamics on the time scale of the process, as mentioned by Matt Tirrell. Second, a fluid may be at equilibrium at rest but is displaced from equilibrium by flow, which is the origin of non-Newtonian behavior in polymeric and colloidal fluids. And third, the resting state itself may be far from equilibrium, as for a glass or a gel. At present, computer simulations can address all three, but only partially. Statistical mechanical or kinetic theories have something to say about the first two, but the dynamics and the structure and transport properties of the nonequilibrium states remain poorly understood, except for the polymeric fluids. 

The kinetic equations serve as a bridge between the microscopic domain and the behavior of macroscopic irreversible processes through the description of hydrodynamics in terms of intermolecular collisions. Hydrodynamics can specify a large number of nonequilibrium states by a small number of reproducible properties such as the mass, density, velocity, and energy density of a fluid conserved during the collision of molecules. Therefore, the hydrodynamic equations can describe a wide range of relaxation processes of nonequilibrium states to equilibrium state. We call such processes decay processes represented by phenomenological equations, such as Fourier s law of heat conduction. The decay rates are determined by the transport coefficients. Reliable transport coefficients provide microscopic and macroscopic information, and validate the results of molecular dynamics. 

Phase-separation phenomena are commonly observed in various kinds of condensed matter, including metals, semiconductors, simple liquids, and complex fluids such as polymers, surfactants, colloids, and biological materials. The study of these processes of pattern evolution is very important for both engineering applications and basic understanding of nonequilibrium dynamics of pattern formation [1]. Phase separation in each material group of... 

As one would expect, developments in the theory of such phenomena have employed chemical models chosen more for analytical simplicity than for any connection to actual chemical reactions. Due to the mechanistic complexity of even the simplest laboratory systems of interest in this study, moreover, application of even approximate methods to more realistic situations is a formidable task. At the same time a detailed microscopic approach to any of the simple chemical models, in terms of nonequilibrium statistical mechanics, for example, is also not feasible. As is well known, the method of molecular dynamics discussed in detail already had its origin in a similar situation in the study of classical fluids. Quite recently, the basic MD computer model has been modified to include inelastic or reactive scattering as well as the elastic processes of interest at equilibrium phase transitions (18), and several applications of this "reactive" molecular dynamicriRMD) method to simple chemical models involving chemical instabilities have been reported (L8j , 22J. A variation of the RMD method will be discussed here in an application to a first-order chemical phase transition with many features analogous to those of the vapor-liquid transition treated earlier. 

Various flow problems involving evaporation and condensation phenomena are quite common in ordinary circumstances and have aroused an interest of scientists not only in the field of fluid dynamics but also of kinetic theory. The reason for this is that the ordinary continuum-based fluid dynamics cannot describe qualitatively correctly the process of evaporation and condensation occurring at the interface even in ihe continuum limit because of the existence of a nonequilibrium region, the thickness of which is of the order of the molecular mean free path, in the close vicinity of the interface between the condensed phase and the gas phase. Such a nonequilibrium region is called the Knudsen layer, in which collisions between molecules are not so frequent that the momentum and energy exchanges between the molecules leaving the interface... 

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