Thermodynamic Behaviour of Fluids near Critical Points

Thermodynamic Behaviour of Fluids near Critical Points 

Institute for Physical Science and Technology and Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, MD 20742, U.S.A. 

The nonanalytic critical behaviour of fluids and fluid mixtures is universal in terms of so-called scaling fields that are analytic functions of the physical fields. The variety of critical phenomena that are actually observed in fluids and fluid 

Edited by A. R. H. Goodwin, J. V. Sengers and C. J. Peters International Union of Pure and Applied Chemistry 2010 Published by the Royal Society of Chemistry, www.rsc.org 

We shall proceed as follows. In Section 10.2 we provide the general theoretical frame work for the asymptotic thermodynamic critical behaviour of Ising-like systems. In Section 10.3 we consider the application of the theory to one-component fluids near the vapour-liquid critical point. In Section 10.4 we discuss the extension of the theory to binary fluid mixtures. In Section 10.5 we address the problem of nonasymptotic crossover behaviour of fluids. Concluding remarks are presented in Section 10.6. 

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Thermodynamic Behaviour of Fluids near Critical Points 331... 

Sengers, J. V. Levelt Sengers, J. M. H. (1986). Thermodynamic behaviour of fluids near the critical point. Ann. Rev. Phys. Chem., 37, 189-222. 

It is now established both theoretically and experimentally that many thermodynamic variables assume a simple power-law behaviour at or near critical points in both pure and mixed fluids. The actual functional dependence of one variable on another can be characterized by the so-called critical indices a, 5, etc. The critical index j8, for example, defines both the shape of the gas-liquid coexistence curve for a pure fluid and the liquid-liquid coexistence curve of a binary mixture in the vicinity of either an upper or a lower critical solution temperature. The correspondence between critical phenomena in one-, two-,... 

The van der Waals one-fluid theory for mixtures assumes the properties of a mixture can be represented by a hypothetical pure fluid. Thus the thermodynamic behaviour of a mixture of constant composition is assumed to be isomorphic to that of a one-component fluid this assumption is not true near the critical point where the thermodynamic behaviour of a mixture at constant thermodynamic potential is isomorphic with that of a one-component fluid and this is discussed further in Chapter 10. 

In this section, we consider vapour-liquid equilibrium in binary fluid mixtures. A locus of vapour-liquid critical points may emanate from the critical point of either component. In the simplest case a single continuous locus of vapour-liquid critical points may connect the critical points of the two components. It is important to consider the thermodynamic behaviour of the mixture at constant chemical potential p.2. On comparing eq 10.57 with eq 10.35, we see that, at constant /I21, the scaling fields become identical to those of a one-component fluid. Hence, the thermodynamic behaviour of mixtures at constant fiji can be described by exactly the same equations as for one-component fluids near the vapour-liquid critical point, except that the critical parameters and the system-dependent coefficients will depend parametrically on the hidden field B2 - Use of p,2 as the hidden field is not convenient, since it diverges in the two one-component limits. This problem is avoided by adopting an alternative hidden field proposed by Leung and Griffiths ... 

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