On the Singularity of the Liquid-Gas Coexistence Curve Diameter
DOI:
https://doi.org/10.15407/ujpe65.9.802Keywords:
gas-liquid coexistence curve, diameter singularity, heterophase fluctuations, mesoscopic model, heterophase fluid, mesoscopic asymmetry parametersAbstract
A simplified Anisimov–Wang variant of the complete scaling approach makes it possible to determine the amplitudes of singularities for the diameter of the phase coexistence curve (CXC) on the basis of the coefficients in the power series expansion of the mean-field free energy in the reduced temperature and pressure near the critical point. This method is applied to obtain the amplitudes for the leading critical singularities of the CXC diameter in the case of a fluid described in the framework of the mesoscopic mean-field model. The results obtained demonstrate that the amplitudes of leading singularities of the CXC diameter are determined by the mesoscopic asymmetry parameters of the heterophase fluid.
References
J. Weiner, K.H. Langley, N.C. Ford, Jr. Experimental evidence for a departure from the law of the rectilinear diameter. Phys. Rev. Lett. 32, 879 (1974). https://doi.org/10.1103/PhysRevLett.32.879
M. Ley-Koo, M. S. Green. Revised and extended scaling for coexisting densities of SF6. Phys. Rev. A 16, 2483 (1977). https://doi.org/10.1103/PhysRevA.16.2483
L. Bulavin, Yu. Shimanskii, Singularity of the diameter of the coexistence curve of ethane. JETP Lett. 29, 438 (1979).
E.T. Shimanskaya, I.V. Bezruchko, V.I. Basok, Yu.I. Shimanskii. Experimental determination of the critical exponent and of the asymmetric and nonasymptotic corrections to the equation of the coexistence curve of Freon-113. Sov. Phys. JETP 53, 139 (1981).
S. J¨ungst, B. Knuth, F. Hensel. Observation of singular diameters in the coexistence curves of metals. Phys. Rev. Lett. 55, 2160 (1985). https://doi.org/10.1103/PhysRevLett.55.2160
L.P. Kadanoff. Scaling laws for Ising models near Tc. Physics 2, 263 (1966). https://doi.org/10.1103/PhysicsPhysiqueFizika.2.263
K.G. Wilson, J. Kogut. The renormalization group and the
K.G. Wilson. The renormalization group: Critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773 (1975). https://doi.org/10.1103/RevModPhys.47.773
I.R. Yukhnovskii, M.F. Golovko. Statistical Theory of Classical Equilibrium Systems (Naukova Dumka, 1987) (in Russian).
T.D. Lee, C.N. Yang. Statistical theory of equations of state and phase transitions. II. Lattice gas and Ising model. Phys. Rev. 87, 410 (1952). https://doi.org/10.1103/PhysRev.87.410
M.E. Fisher, G. Orkoulas. The Yang-Yang anomaly in fluid criticality: experiment and scaling theory. Phys. Rev. Lett. 85, 696 (2000). https://doi.org/10.1103/PhysRevLett.85.696
Y.C. Kim, M.E. Fisher, G. Orkoulas. Asymmetric fluid criticality. I. Scaling with pressure mixing. Phys. Rev. E 67, 061506 (2003). https://doi.org/10.1103/PhysRevE.67.061506
M.A. Anisimov, J. Wang. Nature of asymmetry in fluid criticality. Phys. Rev. Lett. 97, 025703 (2006). https://doi.org/10.1103/PhysRevLett.97.025703
J. Wang, M.A. Anisimov. Nature of vapor-liquid asymmetry in fluid criticality. Phys. Rev. E 75, 051107 (2007). https://doi.org/10.1103/PhysRevE.75.051107
O. Bakai. Mesoscopic equation of state of the heterophase fluid and its application to description of the liquid-gas asymmetry. J. Mol. Liq. 235, 135 (2017). https://doi.org/10.1016/j.molliq.2016.12.002
R.A. Perkins, J.V. Sengers, I.M. Abdulagatov, M.L. Huber. Simplified model for the critical thermal-conductivity enhancement in molecular fluids. Int. J. Thermophys. 34, 191 (2013). https://doi.org/10.1007/s10765-013-1409-z
J. Frenkel. A general theory of heterophase fluctuations and pretransition phenomena. J. Chem. Phys. 7, 538 (1939). https://doi.org/10.1063/1.1750484
J.I. Frenkel. Kinetic Theory of Liquids (Oxford Univ. Press, 1946).
V.I. Yukalov. Phase transitions and heterophase fluctuations. Phys. Rep. 208, 395 (1991). https://doi.org/10.1016/0370-1573(91)90074-V
L.P. Kadanoff. Relating theories via renormalization. Stud. Hist. Philos. Sci. B 44, 22 (2013). https://doi.org/10.1016/j.shpsb.2012.05.002
L.S. Ornstein, F. Zernike. Accidental deviations of density and opalescence at the critical point of a single substance. Proc. Sect. Sci. K. Ned. Akad. Wet. 17, 793 (1914).
O. Bakai. The van der Waals idea of pseudo associations and the critical compressibility factor. Cond. Mat. Phys. 23, 13603 (2020). https://doi.org/10.5488/CMP.23.13603
M.E. Fisher. The theory of condensation and the critical point. Physics 3, 255 (1967). https://doi.org/10.1103/PhysicsPhysiqueFizika.3.255
K.S. Kiang, D. Stauffer. Application of Fisher's droplet model for liquid-gas transition near Tc. Z. Phys. A 235, 130 (1970). https://doi.org/10.1007/BF01395163
I.R. Yukhnovskyi. Phase transitions near the gas-liquid critical point. Ukr. Fiz. Zh. Oglyady 10, 33 (2015) (in Ukrainian).
J.D. van der Waals. The equation of state for gases and liquids. In: Nobel Lectures, Physics 1901-1921 (Elsevier, 1967), p. 254.
O. Bakai, M. Bratchenko, S. Dyuldya. Three-state mesoscopic model of a heterophase fluid in application to the gas-liquid and dielectric-semiconductor-metal transformations in expanded mercury. J. Mol. Liq. 260, 245 (2018). https://doi.org/10.1016/j.molliq.2018.03.068
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