Density equilibration near the liquid-vapor critical point of a pure fluid: Single phaseT>Tc

Abstract

A systematic study is reported, both experimental and theoretical, on the density equilibration in a pure fluid, $^{3}\mathrm{He}$, near the liquid-vapor critical point. Measurements of the density \ensuremath{\rho} were carried out with capacitive sensors located in the upper and the lower half of a flat horizontal cell. The density change \ensuremath{\delta}\ensuremath{\rho}(t) after a step change in temperature of the cell walls was recorded along the critical isochore and along several isotherms above the critical temperature ${\mathit{T}}_{\mathit{c}}$. Direct observation of the sharp response from adiabatic energy transfer into the bulk fluid (``piston effect'') is reported. The \ensuremath{\delta}\ensuremath{\rho}(t) transients also show the effect from the stratification change, and the relaxation time of the equilibration process is found to diverge and then tend to a constant value as ${\mathit{T}}_{\mathit{c}}$ is approached. The entropy transport equation is solved numerically in one dimension for $^{3}\mathrm{He}$ in the critical region above ${\mathit{T}}_{\mathit{c}}$ and in the approximation of negligible mass flow velocity and instantaneous local hydrostatic equilibrium. The predictions for the temporal and spatial evolution of temperature, pressure, and density of the fluid layer following a temperature step of the enclosure are presented. The predictions for the profile \ensuremath{\delta}\ensuremath{\rho}(t) are compared with the experimental results and show good agreement in shape and amplitude, but a difference in time scale. The approximations in the theory and the geometry of the cell are discussed. Predictions are also made for the equilibration under reduced gravity along the critical isochore, and the fluid steady-state rms density deviation 〈\ensuremath{\delta}${\mathrm{\ensuremath{\rho}}}^{2}$${\mathrm{〉}}^{1/2}$ is computed for two temperature ramping rates at zero gravity. In Appendix A, expressions for critical properties of $^{3}\mathrm{He}$ used in the computation are listed. Also, the convection onset near the $^{3}\mathrm{He}$ in the critical region is discussed.