THE THERMO-ACOUSTIC NATURE OF THE CRITICAL SPEEDING-UP

A slab-like container filled with a near-critical fluid is submitted t o a given heat flux at the boundary. Matched asymptotic expansions and multiple-time-scale techniques are applied to the 1-D compressible Na vier-Stokes equations written for a Van der Waals gas, in order to des cribe the thermomechanically-driven flow appearing in the fluid and it s coupling with the acoustics. A two-time-scale analytical solution is obtained under the form of a uniformly valid approximation, which sho ws that the response of the fluid is a system of linear compression wa ves occurring on a short time-scale, driving a slower variation of the basic thermodynamic properties. This solution clearly highligthts the leading role of the acoustics in the rapid thermalisation witnessed i n near-critical fluids, and commonly called ''Critical Speeding Up''.