Hydrodynamic theory of density relaxation in near-critical fluids

This paper gives a complete hydrodynamic theory of density relaxation after a temperature step at the boundary of a cell filled with a nearly supercritical pure fluid in microgravity conditions. It uses the matched asymptotic expansion technique to solve the one-dimensional Navier-Stokes equations written for a viscous, low-heat-diffusing, near-critical van der Waals gas. The continuous description obtained for density relaxation in space and time confirms that it is governed by two fundamental mechanisms, the piston effect and heat diffusion. It gives a space-resolved description of density inside the cell during the divergently long heat diffusion time, which is shown to be the ultimate one to achieve complete thermodynamic equilibrium. On that very long time scale, the still measurable density inhomogeneities are shown to follow the diffusion of the vanishingly small temperature perturbations left by the piston effect. Temperature, which relaxes first to nonmeasurable values, and density, which relaxes on a much longer time scale, may thus appear to be uncoupled. The relaxation of density on the diffusion time scale is shown to be driven by a bulk expansion-compression process slowly moving at the heat diffusion speed, which is generated by heat diffusion coupled with the large compressibility of the near-critical fluid. The process is shown to be the signature of the thermoacoustic events that occur during the very short piston effect time period. The generalization of the theory to real critical behavior opens the present results to future experimental investigation.