Relaxation of a supercritical fluid after a heat pulse in the absence of gravity effects: Theory and experiments Y. Garrabos Institut de Chimie de la Matie `re Condense ´e de Bordeaux, Centre National de la Recherche Scientifique, Universite ´ Bordeaux I, Avenue du Dr. Schweitzer, F-33608 Pessac Cedex, France M. Bonetti, D. Beysens,* F. Perrot, and T. Fro ¨ hlich Service de Physique de l’Etat Condense ´, Commissariat a ` l’Energie Atomique, Centre d’Etudes de Saclay, F-91191 Gif-Sur-Yvette Cedex, France P. Carle ` s Laboratoire de Mode ´lisation en Me ´canique, Centre National de la Recherche Scientifique, Universite ´ Paris VI, F-75252 Paris Cedex 05, France B. Zappoli Centre National d’Etudes Spatiales, 18 avenue Edouard Belin, F-31055 Toulouse Cedex, France Received 9 July 1996; revised manuscript received 23 December 1997 We study the response of a fluid in near-critical conditions to a heat pulse, in the absence of gravity effects. The fluid under investigation is CO 2 at critical density. It is enclosed in a thermostated sample cell. We apply a theory that accounts for hydrodynamics and a real equation of state. Comparison with experiments performed under reduced gravity on board the MIR orbital station show quantitative agreement and demonstrate that the dynamics of relaxation is ruled by two typical times, a diffusion time t D and a time t c associated to adiabatic heat transport, the so-called ‘‘Piston effect’’ PE. Three regions are observed in the fluid. First, a hot boundary layer, developing at the heat source, which shows large coupled density-temperature inhomogeneities. This part relaxes by a diffusive process, whose density and temperature relaxations are slowed down close to the critical point. Second, the bulk fluid, which remains uniform in temperature and density and whose dynamics is accelerated near the critical point and governed by the PE time. At the thermostated walls a slightly cooler boundary layer forms that cools the bulk also by a PE mechanism. The final equilibration in temperature and density of the fluid is governed by the diffusion time t D , which corresponds to the slowest mechanism. Comparison with a one-dimensional model for temperature relaxation is performed showing good agreement with experimental temperature measurements. A brief comparison is given with the situation in the presence of gravity. S1063-651X9811704-X PACS numbers: 05.70.Jk, 44.10.+i, 66.10.Cb, 64.60.Fr I. INTRODUCTION Fluids are supercritical when their temperature and pres- sure are above the critical point temperature and pressure. They exhibit a number of interesting properties large den- sity, low viscosity, large mass diffusivity, which make them intermediate between liquids and gases. In addition, their isothermal compressibility   T =(1/ )(  /  p ) T  becomes very large and their thermal diffusivity  D T = /(  Cp )  goes to zero when they approach the critical point. The use of supercritical fluids under conditions of reduced gravity, e.g., for the storage of cryogenic propellants, has raised a number of fundamental questions concerning heat and mass transport phenomena when gravity-driven convec- tions are suppressed. We address in the following the situa- tion where a source of heat is located in the fluid 1,2. This arrangement minimizes the time constant and is a current means used for pressurizing fluid reservoirs. We analyze ex- periments performed earlier under reduced gravity on board the MIR station 3,4 in the light of recent theoretical ap- proaches 5–13. A. Heat transport by the piston effect The transport of heat in dense pure fluids classically in- volves the mechanisms of convection, diffusion, and radia- tion. Recently 1,2,5–23, the understanding of thermal equilibration of a pure fluid near its gas-liquid critical point CP has evidenced a fourth mechanism, the so-called ‘‘pis- ton effect’’ PE. This effect originates from the high com- pressibility of the critical fluid. A numerical simulation of the Navier-Stokes equations for a one-dimensional 1D van der Waals gas 13 reveals the basic physical mechanisms giving rise to the PE. When homogeneous bulk fluid enclosed in a two-wall sample cell is suddenly heated from one wall, a diffusive thermal bound- ary fluid layer thickness  is formed at the wall-fluid inter- face. Here we consider a fluid sample of unit area and unit mass where L is the characteristic fluid dimension distance *Present address: De ´partement de Recherche Fondamentale sur la Matie `re Condense ´e, CEA-Grenoble, F-38054 Grenoble Cedex 09, France. PHYSICAL REVIEW E MAY 1998 VOLUME 57, NUMBER 5 57 1063-651X/98/575/566517/$15.00 5665 © 1998 The American Physical Society