Exponents for Binary Fluid Mixtures

If modern phenomenological theories are valid, the exponents associated with different properties are interrelated by a %ries of equations (the scaling laws ) which will be detailed in Section 4. 

France 1907,6,667 see also C. Kittel, Introduction to Solid State Physics , 3rd edn., Wiley, New York, 1966, ch. 15. 

Fowler and E. A. Guggenheim, Statistical Thermodynamics , Cambridge University Pf, London, 1939, pp. 314-318. 

Less widely appreciated is the fact that substantially the same departures from the behaviour predicted by mean-field theories occur in fluid mixtures in the region of the critical solution point. The same failures of analytic theories are found and similar critical exponents are deduced from experiment. It is the purpose of this chapter to review the thermodynamic principles underlying critical phenomena, to emphasize the analogies with pure-fluid gas-liquid equilibrium, to outline some of the difficulties encountered when one tries to determine critical exponents precisely, and to summarize the presently available experimental results from binary fluid mixtures. (For a review of the related situation in magnetism and in pure fluids, see Stanley and Levelt Sengers. ) 

What are the exact values of the critical exponents for binary mixtures  

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Scott R L 1978 Critical exponents for binary fluid mixtures Specialist Periodical Reports, Chem. Thermodynam. 2 238-74... 

Scott, R. L. Critical Exponents for Binary Fluid Mixtures, Special Report... 

Exponent values derived from experiments on fluids, binary alloys, and certain magnets differ substantially from all those derived from analytic (mean-field) theories. Flowever it is surprising that the experimental values appear to be the same from all these experiments, not only for different fluids and fluid mixtures, but indeed the same for the magnets and alloys as well (see section A2.5.5). 

Table 9 summarizes the results of some recent light-scattering measurements on binary mixtures. We see a gratifying uniformity about the values of y and v. Indeed Chu has concluded that if the exponents y and v are the same for all fluid systems (one-, two-, and three-components), y — 1.23 0.02 and V = 0.63 0.02. Assuming scaling (equation (45)), this yields rj = 0.05 0.06, hardly a useful result in itself. 

Within experimental error the critical exponents j3, y, and v appear to be the same for all binary mixtures. The same statement (within wider limits) can be made about the exponents 8, a, and t), but the evidence is more fragmentary. When allowance is made for the analogies between one, two, and three components, the exponents appear to be the same for all fluids.f... 

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