Acoustic saturation of the critical speeding up

Abstract

It has recently been found that the heat transfer in the vicinity of the liquid-vapor critical point is governed by a fourth heat transfer process called Piston Effect. This effect has been described as the strong expansion of a thin initial thermal boundary layer (due to the diverging compressibility of near-critical fluids), driving in the rest of the fluid a set of compression waves which adiabatically increase the temperature, on a shorter and shorter time-scale as the critical point is approached (Critical Speeding Up). In the present work, matched asymptotic descriptions techniques applied to the Navier-Stokes equations show that very near the critical point, a new regime of heat transfer appears where thermal equilibration is governed only by acoustic phenomena. In this new regime, temperature relaxation takes place within a few acoustic typical times only, showing that the Piston-Effect mechanism can be as fast as the acoustic propagation, but no faster. This phenomenon is called the Acoustic Saturation of the Piston Effect.