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Volumn 55, Issue 1, 1997, Pages 403-420

Dynamic equations and bulk viscosity near the gas-liquid critical point

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EID: 0001494561     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.403     Document Type: Article
Times cited : (137)

References (78)
  • 1
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    • Phase Transition and Critical Phenomena, edited by C. Domb and M.S. Green (Academic, New York, 1976), Vol. 5A
    • K. Kawasaki, Phys. Rev. 150, 291 (1966); in Phase Transition and Critical Phenomena, edited by C. Domb and M.S. Green (Academic, New York, 1976), Vol. 5A;
    • (1966) Phys. Rev. , vol.150 , pp. 291
    • Kawasaki, K.1
  • 15
    • 0023546069 scopus 로고    scopus 로고
    • K. Nitsche and J. Straub, Proceedings of the Sixth European Symposium on Material S9ciences under Microgravity Conditions, Bordeaux, France, 1986 (European Space Agency, Paris, 1987), Vol. SP-256, p. 109
    • K. Nitsche and J. Straub, Proceedings of the Sixth European Symposium on Material S9ciences under Microgravity Conditions, Bordeaux, France, 1986 (European Space Agency, Paris, 1987), Vol. SP-256, p. 109.
  • 17
  • 44
    • 85037198676 scopus 로고    scopus 로고
    • To be precise, it is not appropriate to adopt the entropy in the renormalization group theory as the order parameter, because all the coefficients in the model should be regular functions of h and τ at the starting point of the renormalization
    • To be precise, it is not appropriate to adopt the entropy in the renormalization group theory as the order parameter, because all the coefficients in the model should be regular functions of h and τ at the starting point of the renormalization.
  • 47
    • 0000954471 scopus 로고
    • A. Onuki, Phys. Rev. A 43, 6740 (1991). In this reference (Formula presented) was incorrectly identified with (Formula presented) and was estimated as (Formula presented)≅0.485. See also Ref. 39 in this previous reference for discussions of ((Formula presented)(Formula presented).
    • (1991) Phys. Rev. A , vol.43 , pp. 6740
    • Onuki, A.1
  • 49
    • 0004894852 scopus 로고
    • G.R. Brown and H. Meyer, Tabulation of Specific Heat Data near the Gas-Liquid Critical Point of (Formula presented) and 80% (Formula presented)- 20% (Formula presented)t, 1972, (unpublished)
    • G.R. Brown and H. Meyer, Phys. Rev. Aibid. 6, 364 (1972); G.R. Brown and H. Meyer, Tabulation of Specific Heat Data near the Gas-Liquid Critical Point of (Formula presented) and 80% (Formula presented)- 20% (Formula presented)t, 1972, (unpublished);
    • (1972) , vol.6 , pp. 364
    • Brown, G.R.1    Meyer, H.2
  • 50
    • 0001975869 scopus 로고
    • R. Behringer, A. Onuki and H. Meyer, J. Low Temp. Phys. 81, 71 (1990). These papers treat abnormally long thermal relaxations in the presence of an interface separating gas and liquid regions. In particular, the last paper showed a schematic temperature profile of the calorimetric cell used in the first two papers. However, the effect is not yet explained quantitatively. On this aspect see Appendix B also.
    • (1990) J. Low Temp. Phys. , vol.81 , pp. 71
    • Behringer, R.1    Onuki, A.2    Meyer, H.3
  • 51
    • 5544309450 scopus 로고
    • Yu. R. Chashkin, A.V. Voronel, V.A. Smirnov and V.G. Gobunova, Zh. Éksp. Teor. Fiz. 52, 112 (1966) [Sov. Phys. JETP 25, 72 (1967)]. They stirred a near-critical fluid to successfully avoid the gravity effect. Below (Formula presented) they should have realized a two phase state mixed by stirring.
    • (1966) Zh. Éksp. Teor. Fiz. , vol.52 , pp. 112
    • Voronel, A.V.1    Smirnov, V.A.2    Gobunova, V.G.3
  • 52
    • 33646656242 scopus 로고
    • M.E. Fisher, J. Math. Phys. 5, 944 (1964). This paper first discussed the critical behavior of ((Formula presented)(Formula presented).
    • (1964) J. Math. Phys. , vol.5 , pp. 944
    • Fisher, M.E.1
  • 55
    • 0010690953 scopus 로고
    • P.C. Hohenberg and M. Barmartz, Phys. Rev. A 6, 289 (1972). In the former paper (Formula presented) in Ising spin systems was calculated in a simple form. In the latter paper (Formula presented) in fluids was calculated, which is nothing but (Formula presented). It has an amplitude independent of a parameter θ if another parameter b is chosen to satisfy a minimization condition. Then the parametric model yields (Formula presented)/A=((Formula presented)-1(Formula presented)≅1 in good agreement with the estimate in Sec. II of this paper. This ratio is smaller than the ratio (Formula presented)/(Formula presented) for (Formula presented) at h=0 in Ising spin systems by 1+(Formula presented), where (Formula presented)=α(γ-2Β)/(γ-1(Formula presented)≅1 from the parametric model.
    • (1972) Phys. Rev. A , vol.6 , pp. 289
    • Hohenberg, P.C.1    Barmartz, M.2
  • 59
    • 0042958201 scopus 로고
    • D.E. Siggia and D.R. Nelson, Phys. Rev. Bibid. 15, 1427 (1977).
    • (1977) , vol.15 , pp. 1427
    • Siggia, D.E.1    Nelson, D.R.2
  • 73
    • 0002866498 scopus 로고
    • D. Roe and H. Meyer, J. Low Temp. Phys.ibid. 30, 91 (1978).
    • (1978) , vol.30 , pp. 91
    • Roe, D.1    Meyer, H.2


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