On the Principle of Corresponding States for Transport Properties of Simple Dense Fluids

Abstract

It was observed from experiments that the excess thermal conductivity:

$$\widetilde\lambda = \lambda \left({\rho ,T}\right)\,\,-\lambda\left({{\rm O},T}\right) = \lambda - {\lambda_o}$$

((1))

and the excess viscosity:

$$\widetilde\mu = \mu \left({\rho ,T}\right) - \mu\left({{\rm O},{\rm T}}\right) = \mu - {\mu_o}$$

((2))

of noble gases were temperature independent in a restricted temperature range. By application of the principle of corresponding states to noble gases according to the relation:

$${\widetilde\lambda ^ \star } = \frac{{{\sigma ^2}\,{m^{1/2}}}}{{{\varepsilon ^{1/2}}\,k}}\,\widetilde\lambda $$

((3))

$${\widetilde\mu^\star} =\frac{{{\sigma^2}\,}}{{{{\left({m\varepsilon}\right)}^{1/2}}}}\,\widetilde\mu$$

((4))

$${T^\star} = \frac{{k\,}}{\varepsilon }\,\,T$$

((5))

$${\rho^ \star } = \frac{{{\sigma^3}\,}}{m}\,\,\rho$$

((6))

where σ and ε are the parameters of the Lennard-Jones potential, T the absolute temperature and ρ the density, we consider to what extend μ̃* and λ̃* can be considered as temperature independent. As we will show we get one curve in reduced coordinates for each transport preperty which can be compared to the Enskog theory. The excess viscosity is found to be temperature independent. The excess thermal conductivity is slightly temperature dependent in T*^1/6.