Relation between transport and thermodynamic properties in liquid sp-electron metals near freezing

Classical statistical mechanics based on assumed pair potentials leads, for liquid metals, to an approximate relation between shear viscosity η, surface tension σ, and thermal velocity $v_T$ defined as ${(k}_B{T/M)}^{1/2},$ with M the ionic mass. Theory predicts for the dimensionless grouping $\sigma /\eta v_T$ evaluated at the melting temperature $T_m$ a single value $\frac{15}{16};$ liquid sp-electron metals exhibit, however, a scatter from around 0.7 to 2.3. Therefore, an alternative grouping $\sigma /\eta v_s,$ with $v_s$ the velocity of sound, is considered here in detail, first using experimental data and second using both theoretical and semiempirical arguments. The scatter of $\sigma /\eta v_s$ at $T_m$ is less than for the earlier grouping, and also insight can be gained as to various physical factors determining $\sigma /\eta v_s.$ In essence, this quantity is proportional to the product of two factors, both dimensionless, namely, the surface thickness L measured in units of the mean interionic separation, and the square root of the energy ${\mathrm{Mv}}_s^2,$ measured in units of the thermal energy $k_B{T}_m.$ Theoretical estimates are made of both of these factors, in fair accord with the experimental data.