Effect of Isotopic Mass on Viscosity of Molten Lithium

Abstract

The viscosity of the separated isotopes of molten lithium was measured by observing the damped oscillations of a torsion pendulum whose bob contained a spherical cavity filled with the material under test. For both ${\mathrm{Li}}^6$ and ${\mathrm{Li}}^7$, the viscosity varies approximately as $\exp \left(\frac{B}{T}\right)$ over the temperature range 180 to 300°C; $B$ has the value 458°K for ${\mathrm{Li}}^6$ and 631°K for ${\mathrm{Li}}^7$. The viscosity of ${\mathrm{Li}}^6$ is 4.18±0.05 mP (millipoise) at 180.4°C, its melting point; of ${\mathrm{Li}}^7$, 6.00±0.05 mP at 180.7°C, its melting point. A linear interpolation for ${\mathrm{Li}}^{\mathrm{nat}}$ (7.4% ${\mathrm{Li}}^6$, 92.6% ${\mathrm{Li}}^7$) gives 5.86 mP at 180.5°C, only slightly lower than the value of 6.02 mP reported earlier by Andrade and Dobbs. The ratio of the viscosity of ${\mathrm{Li}}^7$ to that of ${\mathrm{Li}}^6$ is 1.44 at the melting point, in contrast with the value of 1.08, the square root of the mass ratio, as predicted on simple theoretical arguments. Actually, a thorough dimensional analysis shows that the viscosity varies as ${\mathrm{}\left(\mathrm{mkT}\right)\mathrm{}}^{\frac{1}{2}}$ times a complementary dimensionless function containing—among other arguments— the mass as a consequence of quantum effects. The function evidently depends strongly on these effects, as indicated not only by the present results on molten ${\mathrm{Li}}^6$ and ${\mathrm{Li}}^7$, but also by the results of others on other isotopically-substituted liquids.