Theory of dynamic shear viscosity and normal stress coefficients of dense fluids

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Abstract
On the basis of the nonlinear evolution equation for the stress tensor derived from the kinetic equation for dense simple fluids, we examine the shear rate and frequency dependence of the shear viscosity and normal stress coefficients. An analytic expression for nonlinear shear viscosity has been obtained, which is in agreement with nonequilibrium molecular dynamic simulation results. Based on the material functions obtained in the analysis, a theory of rheological corresponding states is developed by showing that there exists a set of reduced material functions which depend on the reduced shear rate, reduced frequency, reduced static normal coefficients and limiting values of the reduced imaginary parts of dynamic normal stress coefficients. It is also shown that the dynamic normal stress coefficients can change its sign as the critical value of the frequency is crossed.

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