Abstract
We review the critical dynamics of fluids and mixtures. Special attention in the comparison with experiment is paid to nonasymptotic effects. Our theoretical results are based on the complete model H′ of Siggia, Halperin, and Hohenberg including the sound mode variables. Using the dynamic renormalization group theory, we calculate the temperature dependence of the transport coefficients as well as the frequency-dependent sound velocity and sound attenuation. In mixtures a time ratio between the Onsager coefficients related to the diffusive modes, which is directly related to the critical enhancement of the thermal conductivity near a consolute point, has to be taken into account. The sound mode contains, besides the dynamic parameters, a static coupling related to the logarithmic derivative of the weakly diverging specific heat. The deviation from the asymptotic value of this coupling at finite frequencies and temperature distance from T c leads to additional nonasymptotic effects. Our theory, which derives the phenomenological ansatz of Ferrell and Bhattacharjee for pure fluids and mixtures near a consolute point, is also applicable near a plait point.
Similar content being viewed by others
REFERENCES
V. Privman, P. C. Hohenberg, and A. Aharony, in Phase Transitions and Critical Phenomena, Vol. 14, C. Domb and J. L. Lebowitz, eds. (Academic Press, New York, 1991).
R. Folk and G. Moser, J. Low Temp. Phys. 99:11 (1995).
H. Mensah-Brown and W. A. Wakeham, Int. J. Thermophys. 16:237 (1995).
L. H. Cohen, M. Dingus, and H. Meyer, J. Low Temp. Phys. 49:545 (1982).
E. P. Sankonidou, H. R. van den Berg, C. A. ten Seldam, and J. V. Sengers, Phys. Rev. E 56:R4943 (1997); J. Chem. Phys. 109:717 (1998).
R. Folk and G. Moser, Europhys. Lett. 24:533 (1993).
K. Kawasaki, Ann. Phys. 61:1 (1970).
J. V. Sengers, in Supercritical Fluids: Fundamentals for Application, E. Kiran and J. M. H. Levelt Sengers, eds. (Kluwer, Dodrecht, 1994); J. V. Sengers, in Transport Properties of Fluids: Their Correlation, Prediction and Estimation, J. Millat, J. H. Dymond, and C. A. Nieto de Castro, eds. (Cambridge University Press, Cambridge, 1996).
E. D. Siggia, B. I. Halperin, and P. C. Hohenberg, Phys. Rev. B 13:2110 (1976); C. De Dominicis and L. Peliti, Phys. Rev. B 18:353 (1978).
R. Folk and G. Moser, Phys. Rev. Lett. 75:2706 (1995).
V. Dohm and R. Folk, Phys. Rev. Lett. 46:349 (1981); V.Dohm, J. Low. Temp. Phys. 69:51 (1987).
R. Folk and G. Moser, Phys. Rev. E 57:683, 705 (1998).
J. K. Bhattacharjee and R. A. Ferrell, Phys. Lett. A 76:290 (1980); 86:109 (1981); 88:77 (1982).
R. A. Ferrell and J. K. Bhattacharjee, Phys. Rev. A 31:1788 (1985).
R. Dengler and F. Schwabl, Europhys. Lett. 4:1233 (1987).
R. Folk and G. Moser, Proceedings of the RG96-conference, Dubna, Aug. 1996.
A. Onuki, Phys. Rev. E 55:403 (1997).
T. Doiron, D. Gestrich, and H. Meyer, Phys. Rev. B 22:3202 (1980).
L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed. (Pergamon, New York, 1987).
M. Giglio and A. Vendramini, Phys. Rev. Lett. 35:561 (1975.
A. Zielensny, J. Schmitz, S. Limberg, A. G. Aizpiri, S. Fusenig, and D. Woerman, Int. J. Thermophys. 15:67 (1994).
R. Folk and G. Moser, Condensed Matter Phys. (Ukraine) 7:27 (1996); R. Folk and G. Moser, in Lectures on Cooperative Phenomena in Condensed Matter, D. I. Uzunov, ed. (Heron Press, Sofia, 1996).
J. Pankert and V. Dohm, Phys. Rev. B 40:10842, 10856 (1989).
G. Moser, J. Pankert, and V. Dohm, unpublished manuscript.
R. Dengler and F. Schwabl, Z. Phys. B 69:327 (1987).
R. A. Ferrell, Int. J. Thermophys. 10:369 (1989).
D. B. Roe, B. A. Wallace, and H. Meyer, J. Low Temp. Phys. 16:51 (1974).
D. B. Roe and H. Meyer, J. Low Temp. Phys. 30:91 (1978).
D. Sarid and D. S. Cannell, Phys. Rev. A 15:735 (1977).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Folk, R., Moser, G. Nonasymptotic Transport Properties in Fluids and Mixtures Near a Critical Point. International Journal of Thermophysics 19, 1003–1017 (1998). https://doi.org/10.1023/A:1022669121290
Issue Date:
DOI: https://doi.org/10.1023/A:1022669121290