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 eta, surface tension sigma, and thermal velocity vT defined as (kBT/M)(1/2), with M the ionic mass. Theory predicts for the dimensionless grouping sigma/etav(T) evaluated at the melting temperature Tm a single value 15 / 16; liquid sp-electron metals exhibit, however, a scatter from around 0.7 to 2.3. Therefore, an alternative grouping sigma/etav(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/etav(s) at Tm is less than for the earlier grouping, and also insight can be gained as to various physical factors determining sigma/etav(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 Mv(2)s, measured in units of the thermal energy kBTm. Theoretical estimates are made of both of these factors, in fair accord with the experimental data.