Rf. Berg, THERMAL EQUILIBRATION NEAR THE CRITICAL-POINT - EFFECTS DUE TO 3 DIMENSIONS AND GRAVITY, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(3), 1993, pp. 1799-1805
Two calculations are presented that clarify how the density profile eq
uilibrates near the liquid-vapor critical point. Both use the equation
of heat transfer recently improved to account for the large compressi
bility near the critical point. Previous work by others indicated that
in one dimension the slowest mode of this equation relaxes at a rate
four times faster than that predicted by the older, usual equation of
heat transfer. However, this is not always true in higher dimensions.
The first calculation demonstrates this for the cases of isobaric mode
s excited by temperature gradients in a rectangle and in a thin disk.
For thin experimental cells with isothermal walls the slowest mode is
accurately estimated by the usual heat-transfer equation. The second c
alculation indicates that gravity-induced stratification plays an insi
gnificant role in determining the final relaxation rate. This is done
by estimating the size of the v.delP term in the improved heat-transfe
r equation.