Nonlinear Effects in the Shear Viscosity of Critical Mixtures

概要

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Unless the velocity gradient is small, the shear viscosity of fluids generally depends on the velocity gradient d, hence extra nonlinear terms in d appear in the hydrodynamic equations. We extend the method developed by Kawasaki and by Deutch and Zwanzig for studying the usual linear shear viscosity of critical mixtures to the investigation of the nonlinear terms which appear in the power series expansion of this effective shear viscosity η(d). By the symmetry consideration we obtain η(d)=η^<(0)>+ η^<(1)>d^2+η^<(2)>d^4+・・・・・・. η^<(1)> is found to increase as k^<-9> near the critical point, where k^<-1> is a parameter which measures the correlation range of concentration fluctuations assuming the Ornstein-Zernike type for the correlation, indicating the importance of the nonlinear effects near the critical point since η^<(0)> increases only as k^<-1>. This η^<(1)> agrees with Botch and Fixman's except for a small correction to the numerical coefficient. On the other hand the k-integral contained in η^<(2)> has been found to diverge as k^<-3> at small k even when k≠0, where k is a wave vector characterizing the local concentration fluctuation. Similar divergences appear in the two dimensional mixture already in η^<(1)> which diverges as lnk, and in the linear bulk viscosity which again diverges as ln k. The nature and possible consequences of these divergences are discussed.
理論物理学刊行会の論文
1967-11-25