Two calculations are presented that clarify how the density profile equilibrates near the liquid-vapor critical point. Both use the equation of heat transfer recently improved to account for the large compressibility 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 modes 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 calculation indicates that gravity-induced stratification plays an insignificant role in determining the final relaxation rate. This is done by estimating the size of the vdelP term in the improved heat-transfer equation.
Citation: Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
Pub Type: Journals