The results presented earlier are valid only for the liquid phase and under condition that thermody­namic coefficients do not depend on pressure. In order to take into account the pressure dependence of the LM thermodynamic parameters, different thermal EOS were developed and applied to LM. Two main directions were followed with more suc­cess: the generalization of the well-known EOS of Van der Waals (VdW) and the use of statistical mechanics and intermolecular potentials for EOS development.

The generalized three-parameter VdW EOS was used by Martynyuk73 to find the critical parameters

of many pure metals (including Na and Pb). Morita and Fischer74 proposed a modification for the EOS of Redlich and Kwong75 to describe a metal vapor with dimer and monomer molecules and applied it for Na coolant. Later, this approach was extended by Morita et al. to Pb-Bi(e)52 and to Pb.56 A simple EOS for liquid phase was developed by Srinivasan and Ganesan76 based on the concept of the internal pres­sure of liquids and applied to sodium. Later, it was used by Azad58 for the calculation of the critical tem­peratures of Pb and Pb-Bi(e).

Eslami77 applied a perturbed hard-sphere-chain EOS developed by Song et a/.78 to calculate the den­sity of liquid Na and Pb on the saturation line up to very high pressures.

Comparison of different approaches shows that better results in large temperature and pressure ranges can be obtained with the modified Redlich and Kwong EOS74 and with the perturbed hard — sphere-chain EOS.78

2.14.5 Transport Properties

The most important transport properties of liquid metal coolants are viscosity, thermal conductivity, and electric resistance.

2.14.5.1 Viscosity

Accurate and reliable data on the viscosity of LM are not abundant. Some discrepancies between experi­mental data can be attributed to the high reactivity of metallic liquids, to the difficulty of taking
precise measurements at elevated temperatures. All three LM: Na, Pb, and Pb-Bi(e), are believed to be Newtonian liquids and the temperature depen­dence of their dynamic viscosity (q) is usually described by an Arrhenius-type equation:

V(T, p) = Viip) exp(Ev{p)/RT) [17]

where En is the activation energy of motion for nor­mal viscous flow and — the asymptotic value of q at T! 1 In a large temperature range, a more complicated formula is often used for more precise fitting of the experimental results on LM dynamic

viscosity: a

V(T; p)=TL exp(E, (p)/RT) [18]

where An and n are constants.

The viscosity of liquid Na at normal atmospheric pressure was well measured in the liquid range from normal melting point to normal boiling point at nor­mal atmospheric pressure3,6-8,11,22,26,79; the variation in the most reliable recommendations does not exceed ±5%.34

Data on the viscosity of Pb and Pb-Bi(e) were reviewed in Sobolev and Benamati24 and Imbeni et a/.48; it was measured up to about 1270 K for

lead79 and up to 1180 K for Pb-Bi(e).80 A good agree­ment exists among the different sets of experimental data and the values calculated by means of the empirical equations reported in different publica­tions. In the temperature range from TM,0 to 1270 K, the viscosity of liquid Pb can be described with the Arrhenius-type eqn [17] with uncertainty of ±5%. A higher variation (7-10%) exists between the values and recommendations given by different sources for Pb-Bi(e).

The recommended coefficients of correlation [17] are given in Table 11, and the calculated tempera­ture behavior of the dynamic viscosity of liquid Na, Pb, and Pb-Bi(e) is presented in Figure 11.

In engineering hydrodynamics, the kinematic vis­cosity (n) is also often used, which is a ratio of the liquid dynamic viscosity to the density:

The kinematic viscosities of liquid Na, Pb, and Bi versus temperature at normal atmospheric pressure, calculated with formula [19], and the recommended correlation for their dynamic viscosities and densities presented earlier, are presented in Figure 12.