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Journal ArticleDOI

A kinetic theory of liquids

22 Feb 1947-Nature (Nature)-Vol. 159, Iss: 4034, pp 251-254
TL;DR: The solution of the general equations should be established as rigorously as the present knowledge of the fundamental law permits ; the solution of these equations may, however, be obtained by approximations suited to the case.
Abstract: THE problem of formulating a rigorous mathematical description of the molecular motion in .liquids has always been regarded as much more difficult than that of the kinetic theory of gases or of solids, because one has the simplifying features of low density in the case of gases, and of a regular lattice structure in the case of solids, while the molecules of a liquid are in a dense and disordered state. It is clear that only approximate solutions may be expected ; but, in introducing the approximations, we think that the following principle should be accepted. The general equations should be established as rigorously as the present knowledge of the fundamental law permits ; the solution of these equations may, however, be obtained by approximations suited to the case.
Citations
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Book
01 Jan 1981
TL;DR: In this article, the authors discuss the properties of phase diagrams for single-component systems, including the influence of interfaces on the equilibrium of binary solutions in Heterogeneous Systems (Heterogeneous Binary Phase Diagrams).
Abstract: Thermodynamics and Phase Diagrams Equilibrium Single-Component Systems Binary Solutions Equilibrium in Heterogeneous Systems Binary Phase Diagrams Influence of Interfaces on Equilibrium Ternary Equilibrium Additional Thermodynamic Relationships for Binary Solutions Computation of Phase Diagrams Kinetics of Phase Transformations Exercises References Further Readings Diffusion Atomic Mechanisms of Diffusion Interstitial Diffusion Substitutional Diffusion Atomic Mobility Tracer Diffusion in Binary Alloys Diffusion in Ternary Alloys High-Diffusivity Paths Diffusion in Multiphase Binary Systems Exercises References Further Readings Crystal Interfaces and Microstructure Interfacial Free Energy Solid=Vapor Interfaces Boundaries in Single-Phase Solids Interphase Interfaces in Solids Interface Migration Exercises References Further Readings Solidification Nucleation in Pure Metals Growth of a Pure Solid Alloy Solidification Solidification of Ingots and Castings Solidification of Fusion Welds Solidification during Quenching from the Melt Metallic Glasses Case Studies of Some Practical Castings and Welds Exercises References Further Readings Diffusional Transformations in Solids Homogeneous Nucleation in Solids Heterogeneous Nucleation Precipitate Growth5 Overall Transformation Kinetics-TTT Diagrams Precipitation in Age-Hardening Alloys Precipitation of Ferrite from Austenite Cellular Precipitation Eutectoid Transformations Massive Transformations Ordering Transformations Case Studies Exercises References Further Readings Diffusionless Transformations Characteristics of Diffusionless Transformations Martensite Crystallography Theories of Martensite Nucleation Martensite Growth1 Premartensite Phenomena Tempering of Ferrous Martensites Case Studies Exercises References Further Readings Solutions to Exercises Compiled by John C. Ion

4,104 citations

Journal ArticleDOI
TL;DR: In this paper, the authors developed analytical relationships and computations of power dissipation in magnetic fluid (ferrofluid) subjected to alternating magnetic field and showed that the dissipation results from the orientational relaxation of particles having thermal fluctuations in a viscous medium.

2,111 citations

Journal ArticleDOI
TL;DR: In this article, a comprehensive review of the current state of the art of the study of elastic properties, the establishments of correlations between elastic moduli and properties/features, and the elastic models and elastic perspectives of metallic glasses is presented.

1,070 citations


Cites background from "A kinetic theory of liquids"

  • ...Frenkel [40] is the first to point out the analogies to solids of a liquid in elastic properties, that is, a nonvanishing shear modulus at comparable atomic packing densities....

    [...]

  • ...When the probe frequency is larger than the relaxation frequency, the measured elastic longitudinal and shear moduli become so-called clamped properties [40]....

    [...]

Journal ArticleDOI
TL;DR: In this review, classical nucleation theory, as well as established concepts of spinodal decomposition and liquid-liquid demixing, is introduced together with a description of the recently proposed pre-nucleation cluster pathway.
Abstract: Crystallisation is at the heart of various scientific disciplines, but still the understanding of the molecular mechanisms underlying phase separation and the formation of the first solid particles in aqueous solution is rather limited. In this review, classical nucleation theory, as well as established concepts of spinodal decomposition and liquid–liquid demixing, is introduced together with a description of the recently proposed pre-nucleation cluster pathway. The features of pre-nucleation clusters are presented and discussed in relation to recent modifications of the classical and established models for phase separation, together with a review of experimental work and computer simulations on the characteristics of pre-nucleation clusters of calcium phosphate, calcium carbonate, iron(oxy)(hydr)oxide, silica, and also amino acids as an example of small organic molecules. The role of pre-nucleation clusters as solute precursors in the emergence of a new phase is summarized, and the link between the chemical speciation of homogeneous solutions and the process of phase separation via pre-nucleation clusters is highlighted.

704 citations

Book ChapterDOI
TL;DR: A review of recent experimental, numerical and theoretical investigations on the subject can be found in this article, where the authors present a complex behavior at a liquid/solid interface involving an interplay of many physico-chemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.
Abstract: The no-slip boundary condition at a solid-liquid interface is at the center of our understanding of fluid mechanics. However, this condition is an assumption that cannot be derived from first principles and could, in theory, be violated. In this chapter, we present a review of recent experimental, numerical and theoretical investigations on the subject. The physical picture that emerges is that of a complex behavior at a liquid/solid interface, involving an interplay of many physico-chemical parameters, including wetting, shear rate, pressure, surface charge, surface roughness, impurities and dissolved gas.

607 citations


Cites background from "A kinetic theory of liquids"

  • ...It appears that Tolstoi was the first to try to quantify the importance of surface energies on slip at the molecular level [12, 53, 159]....

    [...]

References
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Journal ArticleDOI
Lars Onsager1
TL;DR: In this article, the eigenwert problem involved in the corresponding computation for a long strip crystal of finite width, joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum.
Abstract: The partition function of a two-dimensional "ferromagnetic" with scalar "spins" (Ising model) is computed rigorously for the case of vanishing field. The eigenwert problem involved in the corresponding computation for a long strip crystal of finite width ($n$ atoms), joined straight to itself around a cylinder, is solved by direct product decomposition; in the special case $n=\ensuremath{\infty}$ an integral replaces a sum. The choice of different interaction energies ($\ifmmode\pm\else\textpm\fi{}J,\ifmmode\pm\else\textpm\fi{}{J}^{\ensuremath{'}}$) in the (0 1) and (1 0) directions does not complicate the problem. The two-way infinite crystal has an order-disorder transition at a temperature $T={T}_{c}$ given by the condition $sinh(\frac{2J}{k{T}_{c}}) sinh(\frac{2{J}^{\ensuremath{'}}}{k{T}_{c}})=1.$ The energy is a continuous function of $T$; but the specific heat becomes infinite as $\ensuremath{-}log |T\ensuremath{-}{T}_{c}|$. For strips of finite width, the maximum of the specific heat increases linearly with $log n$. The order-converting dual transformation invented by Kramers and Wannier effects a simple automorphism of the basis of the quaternion algebra which is natural to the problem in hand. In addition to the thermodynamic properties of the massive crystal, the free energy of a (0 1) boundary between areas of opposite order is computed; on this basis the mean ordered length of a strip crystal is ${(\mathrm{exp} (\frac{2J}{\mathrm{kT}}) tanh(\frac{2{J}^{\ensuremath{'}}}{\mathrm{kT}}))}^{n}.$

5,081 citations

Book
01 Jan 1946

3,198 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field.
Abstract: The investigation of a preceding paper has shown that the temperature variation of viscosity, as determined experimentally, can be satisfactorily explained in many gases on the assumption that the repulsive and attractive parts of the molecular field are each according to an inverse power of the distance. In some cases, in argon, for example, it was further shown that the experimental facts can be explained by more than one molecular model, from which we inferred that viscosity results alone are insufficient to determine precisely the nature of molecular fields. The object of the present paper is to ascertain whether a molecular model of the same type will also explain available experimental data concerning the equation of state of a gas, and if so, whether the results so obtained, when taken in conjunction with those obtained from viscosity, will definitely fix the molecular field. Such an investigation is made possible by the elaborate analysis by Kamerlingh Onnes of the observational material. He has expressed the results in the form of an empirical equation of state of the type pv = A + B/ v + C/ v 2 + D/ v 4 + E/ v 6 + F/ v 8, where the coefficients A ... F, called by him virial coefficients , are determined as functions of the temperature to fit the observations. Now it is possible by various methods to obtain a theoretical expression for B as a function of the temperature and a strict comparison can then be made between theory and experiment. Unfortunately the solution for B, although applicable to any molecular model of spherical symmetry, is purely formal and contains an integral which can be evaluated only in special cases. This has been done up to now for only two simple models, viz., a van der Waals molecule, and a molecule repelling according to an inverse power law (without attraction), but it is shown in this paper that it can also be evaluated in the case of the model, which was successful in explaining viscosity results. As the two other models just mentioned are particular cases of this, the appropriate formulae for B are easily deduced from the general one given here.

2,046 citations