Fluids, classical thermodynamics

Verlet L 1967 Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules Phys. Rev. f59 98-103... 

Verlet, L. Computer experiments on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 165 (1967) 98-103. Ryckaert, J.-P., Ciccotti,G., Berendsen, H.J.C. Numerical integration of the cartesian equations of motion of a system with constraints Molecular dynamics of n-alkanes. Comput. Phys. 23 (1977) 327-341. 

Verlet, L. Computer Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review 159 (1967) 98-103 Janezic, D., Merzel, F. Split Integration Symplectic Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 37 (1997) 1048-1054 McLachlan, R. I. On the Numerical Integration of Ordinary Differential Equations by Symplectic Composition Methods. SIAM J. Sci. Comput. 16 (1995) 151-168... 

StoKes-Einstein and Free-Volume Theories The starting point for many correlations is the Stokes-Einstein equation. This equation is derived from continuum fluid mechanics and classical thermodynamics for the motion of large spherical particles in a liqmd. 

As he gi ew older, Helmholtz became more and more interested in the mathematical side of physics and made noteworthy theoretical contributions to classical mechanics, fluid mechanics, thermodynamics and electrodynamics. He devoted the last decade of his life to an attempt to unify all of physics under one fundamental principle, the principle of least action. This attempt, while evidence of Helmholtz s philosphical bent, was no more successtul than was Albert Einstein s later quest for a unified field theory. Helmholtz died m 1894 as the result of a fall suffered on board ship while on his way back to Germany from the United States, after representing Germany at the Electrical Congress m Chicago in August, 1893. 

The conditions which lead a homogeneous fluid mixture to split into two separate fluid phases can be described by classical thermodynamic stability analysis as discussed in numerous textbooks.9 Such analysis has often been... 

The classical Kelvin equation assumes that the surface tension can be defined and that the gas phase is ideal. This is accurate for mesopores, but fails if appUed to pores of narrow width. Stronger sohd-fluid attractive forces enhance adsorption in narrow pores. Simulation studies [86] suggest that the lower limit of pore sizes determined from classical thermodynamic analysis methods hes at about 15 nm. Correction of the Kelvin equation does lower this border to about 2 run, but finally also the texture of the fluid becomes so pronounced, that the concept of a smooth hquid-vapor interface cannot accurately be applied. Therefore, analysis based on the Kelvin equation is not applicable for micropores and different theories have to be applied for the different ranges of pore sizes. 

Birkhoff et al (Ref 28) gave a fairly complete mathematical theory of cavity-effect phenomenon together with experimental data that aided the formulation and testing of the theory. They based the theory upon the classical thermodynamics of perfect fluids. It is applicable because the strength of metals used for linings can be neglected at the high pressures encountered... 

C. Classical Thermodynamic and Structural Quantities for Fluid Models... 

At this stage, undiscutable data, external of the IETs, were necessarily required to shed some light on these peculiar behaviors, which provides exact reference data for more realistic potentials. First, Nicolas et al. [33] derived an EOS for the Lennard-Jones fluid and Johnson et al. [34] provided MD results for the classical thermodynamic quantities. Notice that Heyes and Okumura [35] recently derived an EOS of the Weeks-Chandler-Andersen fluid. 

Many new technologies rely on the unusual properties of interfaces— Langmuir-Blodgett and other films, micelles, vesicles, small liquid drops, and so on. Classical thermodynamics is often inadequate as a basis for treating such systems because of their smallness, and experimental probes of the interface are limited, especially for fluid systems. Computer simulation can play an important role here, both in understanding the role of intermolecular forces in obtaining desired properties and, in combination with experiment, in designing better materials and processes [6, 28]. 

L. Verier, Phys. Rev., 159, 98 (1967). Computer Experiments on Classical Fluids. 1. Thermodynamic Properties of Lennard-Jones Molecules. 

There are two approaches in developing the conditions that govern favorable nucleation of a crystal embryo out of the liquid phase of a fluid without dissolved substances. From a structural point of view, nucleation implies that under certain favorable conditions the bond formation rendering a crystalline lattice may be competitive with the thermal motion trying to randomize and destroy bonds. A detailed molecular theory of freezing is necessarily a many-bodied problem. There exists, however, a classic thermodynamic theory of freezing that provides much insight into the process of ice nucleation (Hobbs, 1974). 

L. Verlet (1967) Computer experiments on classical fluids I. Thermodynamics properties of Lermard Jones molecules. Phys. Rev. 98, p. 159 D. Chandler (1978) Statistical mechanics of isomerization dynamics in liquids and transition-state approximation. J. Chem. Phys. 68, pp. 2959-2970... 

The classical theory of the Gibbs adsorption isotherm is based on the use of an equation of state for the adsorbed phase hence it assumes that this adsorbed phase is a mobile fluid layer covering the adsorbent surface. By contrast, in the statistical thermod)mamic theory of adsorption, developed mainly by Hill [15] and by Fowler and Guggenheim [12], the adsorbed molecules are supposed to be localized and are represented in terms of simplified physical models for which the appropriate partition function may be derived. The classical thermodynamic fimctions are then derived from these partition fimctions, using the usual relationships of statistical thermodynamics. 

Furthermore, for non-isothermal situations we need to be able to calculate the thermodynamics of fluid dynamics. However, thermodynamics deals with relatively permanent states, called equilibrium states, within uniform fields of matter [7] [145] [42] [54]. Any changes are assumed to be extremely slow. On the other hand, the fluid motions of interest in fluid mechanics are not necessary slow. Nevertheless, it has been assumed that the classical thermodynamics can be directly applied to any flow system provided that an instantaneous local thermodynamic state is considered and that the rates of change are not too large [168]. A more common statement is that the thermodynamics require that the fluids are close to local equilibrium, but may not be in global equilibrium. However, all systems are supposed to be relaxing towards a state of global thermodynamic equilibrium. 

The thermodynamics of irreversible processes should be set up from the scratch as a continuum theory, treating the state parameters of the theory as field variables [32]. This is also the way in which classical fluid mechanic theory is formulated. Therefore, in the computational fluid dynamics literature, the transport phenomena and the extensions of the classical thermodynamic relations are both interpreted as closures of the fluid dynamic theory. The validity of the thermodynamic relations for fluid dynamic systems has been approached from the viewpoint of the kinetic theory of gases [13]. However, any Arm distinction between irreversible thermodynamics and fluid mechanics... 

The discussion in this chapter has focused on the properties of liquids at interfaces. A related area of contemporary research is the study of solid gas interface. The solid surface is quite different in that atomic or molecular components of a solid are relatively motionless compared to those of liquid. For this reason it is easier to define a plane associated with a well-defined solid surface. The approach to studying adsorption on solids has been more molecular with the development of sophisticated statistical mechanical models. On the other hand, the study of liquid I gas and liquid liquid interfaces has been much more macroscopic in approach with a firm connection to classical thermodynamics. As the understanding of liquids has improved at the molecular level using contemporary statistical mechanical tools, these methods are being applied now to fluids at interfaces. 

Saul, A., and Wagner, W. (1987) International Equations for the Saturation PropertiesofOrdinary Water Substance, J. Phys. Chem. Ref. Data, 16,893 Chen, Z. Y., Albright, P. C., and Sengers, J. V. (1990) Crossover from Singular to Regular Classical Thermodynamic Behavior of Fluids, Phys. Rev. A41, 3161-3177... 

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