Phenomenological viscous factor in the nonequilibrium distribution function for liquids.
An improved formula of shear viscosity for liquids is presented by introducing a phenomenological viscous factor in the nonequilibrium term in the doublet distribution function, which improves an incomplete formula of shear viscosity presented in an early work of Born and Green. The phenomenological viscous factor effectively counts some higher-order interactions, and is constrained so that, in the limit of hard-sphere liquids, the magnitude of the improved formula of shear viscosity reduces to that of Enskog for dense fluids. The improved formula does not require any adjustable parameters except for the pair potential to describe liquids. In order to verify the improved formula, a liquid of Ar near the triple point is studied in detail. In addition, liquids of Pb in wide ranges of temperature are examined to test the temperature dependence of the phenomenological viscous factor. Here an available integral equation is employed to calculate the radial distribution function by prescribed pair potentials. One finds that the present formula is capable to describe the shear viscosity in accord with those of experimental data for both cases of Ar and Pb. The phenomenological viscous factor plays a crucial role in the evaluation of shear viscosity for liquids.
Morioka
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Key Laboratory of Liquid Structure and Heredity of Materials, College of Materials Science and Engineering, Shandong University, Jinan, Shandong 250061, China.