Transport Properties of a Dense Fluid of Hard Spheres

From the two assumptions, that the pair distribution function of relative position is independent of the rate of strain or the temperature gradient and that the velocity distribution is locally Maxwellian, expressions are derived for the shear viscosity η, the bulk viscosity κ and the thermal conductivity λ of a hard‐sphere fluid at high densities. An expression is also derived for the coefficient of self‐diffusion D at any density by assuming that the autocorrelation function for the velocity of a given particle decays exponentially. The results are $$\begin{array}{cc}\mathrm{\eta =}\frac{\text{4a}}{5}{\left(\frac{\mathrm{mkT}}{\pi }\right)}^{\frac{1}{2}}\left(\frac{P}{\mathrm{kT}}-\frac{N}{V}\right),& \text{λ=2ak}{\left(\frac{\mathrm{kT}}{\mathrm{\pi m}}\right)}^{\frac{1}{2}}\left(\frac{P}{\mathrm{kT}}-\frac{N}{V}\right),\\ \mathrm{\kappa =}\frac{\text{4a}}{3}{\left(\frac{\mathrm{mkT}}{\pi }\right)}^{\frac{1}{2}}\left(\frac{P}{\mathrm{kT}}-\frac{N}{V}\right),& \mathrm{D=}\frac{a}{2}{\left(\frac{\mathrm{\pi kT}}{m}\right)}^{\frac{1}{2}}{\left(\frac{\mathrm{PV}}{\mathrm{RT}}\text{−1}\right)}^{\text{−1}},\end{array}$$ where m and a are the mass and radius of the spheres.