Vertex corrections to the shear viscosity critical exponent

Garisto, Frank; Kapral, Raymond

doi:10.1103/physreva.14.884

Cited by 31 publications

(9 citation statements)

References 6 publications

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“…[7][8][9][10] One of the important notions in the studies of the static and dynamic critical phenomena is the universality. This insists that phenomena with the same set of critical exponents form a universality class.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Critical Phenomena of Polymer Solutions

Furukawa

2003

J. Phys. Soc. Jpn.

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Recently, a systematic experiment measuring critical anomaly of viscosity of polymer solutions has been reported by H. Tanaka and his co-workers (Phys.Rev.E, 65, 021802, (2002)). According to their experiments, the dynamic critical exponent of viscosity y_c drastically decreases with increasing the molecular weight. In this article the kinetic coefficients renormalized by the non-linear hydrodynamic interaction are calculated by the mode coupling theory. We predict that the critical divergence of viscosity should be suppressed with increasing the molecular weight. The diffusion constant and the dynamic structure factor are also calculated. The present results explicitly show that the critical dynamics of polymer solutions should be affected by an extra spatio-temporal scale intrinsic to polymer solutions, and are consistent with the experiment of Tanaka, et al.Comment: 17 pages, 2 figures, to be published in J.Phys.Soc.Jp

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Section: Introductionmentioning

confidence: 99%

Dynamic Critical Phenomena of Polymer Solutions

Furukawa

2003

J. Phys. Soc. Jpn.

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“…-The very complicated problem of the critical behaviour of transport coefficients has been widely studied. The recent refmement of mode-mode coupling theory [13][14][15] and the success of renormalization group theory [16,17] have enabled the critical exponent z for the shear viscosity to be examined more rigorously. The theories predict that the shear viscosity along with the critical isochore may be written as with pn =z" v, where A is a microscopic cut-off wave number, , = '0 e-v is the correlation length, and e is given by (T /Tc -1).…”

Section: Classificationmentioning

confidence: 99%

Shear viscosity measurements in the binary mixture butyl cellosolve-water near its upper and lower critical consolute points

et al. 1981

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2014 Afin de tester l'universalité des concepts régissant les phénomènes critiques, la viscosité de cisaillement de mélanges binaires n-butylglycol (1)-eau a été étudiée au voisinage des deux températures critiques LCST et UCST respectivement d'origine entropique et enthalpique. Les valeurs des exposants critiques ~n de la viscosité de cisaillement sont obtenues par une analyse des résultats utilisant une renormalisation des coefficients de transport. Soient, pour le mélange UCST, ~ = 0,039 ± 0,001 (30,14 % en poids de n-butylglycol) et 0,036 ± 0,007 (24,78 %) tandis que pour le mélange LCST, ~ = 0,038 ± 0,001 (30,14 %) et 0,037 ± 0,003 (24,78 %). Ces exposants sont en bon accord avec le concept de couplage mode-mode et les prévisions du groupe de renormalisation. Abstract. 2014 To further probe the hypothesis of universality of critical phenomena, the shear viscosity has been measured for a two-component critical liquid system, butyl cellosolve-water, in the region of both the entropydriven lower (LCST) and the enthalpy-driven upper (UCST) critical solution temperature. The values of the critical exponents ~n for the shear viscosity were obtained by analysing the results from the viewpoint of multiplicative renormalization of transport coefficients. We have obtained ~n = 0.038 ± 0.001 (30.14 wt. %) and 0.036 ± 0.007 (24.78 wt. %) for the UCST mixture, and ~n, = 0.038 ± 0.001 (30.14 wt. %) and 0.037 ± 0.003 (24.78 wt. %) for the LCST mixture. These exponent values agree well with mode-mode coupling and renormalization-group predictions and satisfy the universality hypothesis.

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“…From mode-mode coupling theory the critical exponent q5,, is found to be 0.033 (Kawasaki and Gunton, 1978) using the self-consistent approximation and 0.043 with vertex correction (Garisto and Kapral, 1976), while renormalization group theory predicts $,, to be 0.033 in the E expansion to first order (Halperin, Hohenberg and Siggia, 1974) and 0.040 in the E expansion to second order for the dimensionality d = 3 (Siggia, Halperin and Hohenberg, 1976).…”

Section: Introductionmentioning

confidence: 97%