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 supercri tical pure fluid in microgravity conditions. It uses the matched asymptotic expansion technique to solve the one-dimensional Navier-Stokes equations w ritten for a viscous, low-heat-diffusing, near-critical van der Waals gas. The continuous description obtained for density relaxation in space and tim e confirms that it is governed by two fundamental mechanisms, the piston ef fect-and heat diffusion. It gives a space-resolved description of density i nside the cell during the divergently long heat diffusion time, which is sh own to be the ultimate one to achieve complete thermodynamic equilibrium. O n that very long time scale, the still measurable density inhomogeneities a re shown to follow the diffusion of the vanishingly small temperature pertu rbations left by the piston effect. Temperature, which relaxes first to non measurable 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 s lowly moving at the heat diffusion speed, which is generated by heat diffus ion coupled with the large compressibility of the near-critical fluid. The process is shown to be the signature of the thermoacoustic events that occu r during the very short piston effect time period. The generalization of th e theory to real critical behavior opens the present results to future expe rimental investigation.