Density equilibration near the liquid-vapor critical point of a pure fluid. II. Coexisting phases for T

Abstract

Measurements were carried out on the density change \ensuremath{\delta}\ensuremath{\rho}(t) in a pure fluid ${(}^{3}$He) after a small step change in the temperature of its container. The sample fluid was kept at constant average densities \ensuremath{\Delta}\ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} and in the coexisting liquid and vapor phases below the critical temperature ${\mathit{T}}_{\mathit{c}}$. The measurements were performed via two superposed capacitive sensors. At temperatures far below ${\mathit{T}}_{\mathit{c}}$, the equilibration in the liquid and vapor phases, measured, respectively, by the top and bottom sensors, are found to proceed very differently. As ${\mathit{T}}_{\mathit{c}}$ is approached, this difference diminishes; both the measured effective relaxation times level off and join smoothly the data obtained above ${\mathit{T}}_{\mathit{c}}$. This coexisting liquid-vapor system of $^{3}\mathrm{He}$ is simulated in one dimension. The results are presented for the spatial and temporal evolution of temperature and density in the fluid following a temperature step of the enclosure. The profiles \ensuremath{\delta}\ensuremath{\rho}(t) and their effective relaxation times are compared with the experimental observations in both phases. There is a qualitative agreement between the simulation and experiment for (${\mathit{T}}_{\mathit{c}}$-T)/${\mathit{T}}_{\mathit{c}}$\ensuremath{\lesssim}${10}^{\mathrm{\ensuremath{-}}3}$, and the quantitative differences further away from ${\mathit{T}}_{\mathit{c}}$ are discussed. The results of experimental measurements and of computer simulations along isotherms are discussed and lead to complementary information on the equilibration dynamics as a function of average density. The asymptotic relaxation times obtained from simulation and from a formula based on the average thermal diffusivity of the entire fluid sample are compared and discussed, both for normal gravity, and also under microgravity conditions where both diverge as ${\mathit{T}}_{\mathit{c}}$ is approached. \textcopyright{} 1996 The American Physical Society.