Critical Frequency Dependence of the Shear Viscosity

Recent low-gravity measurements of the shear viscosity in xenon near its critical point are compared with theoretical results obtained within the field theoretical renormalization group (RG) theory. Nonasymptotic effects and gravity effects are included in our theoretical description, which allows a comparison outside the asymptotic region as well as with earthbound experiments affected by gravity. Comparisons are also made with the theoretical result of the mode coupling theory. In both theories no agreement with the frequency dependence of the real part of the shear viscosity within one-loop theory can be reached. The experimental value of the ratio of the imaginary part to the real part of the shear viscosity at Tc is found to be in agreement with the value calculated within the decoupled mode theory using the two-loop value for the critical exponent of the temperature dependence of the shear viscosity, but not with the one-loop value obtained in RG theory. Thus a complete two-loop calculation of the vertex function for the shear viscosity is required.