Thermal response of a fluid near its critical point: He-3 at T>T-c

The local density response is studied in a simple fluid near the liquid-vapor critical point, subjected to temperature oscillations of its container. This investigation provides a new approach in the study of the adiabatic energy transfer (''piston effect'') in the fluid. The density response function Z(F)(omega, epsilon, z) is calculated for He-3 in the absence of stratification, where omega is the angular frequency, epsilon = (T - T-c)/T-c the reduced temperature, T-c = 3.316 K the critical temperature, and z the vertical position in the container. Experiments are described where the density is measured by two superposed capacitive sensors in a cell of 3.5 mm height, and where the temperature oscillation frequency f = 2 omega/2 pi is varied between 10(-4) and 2 Hz. Over the experimental range 5 x 10(-4) < 5 x 10(-2) there is in general reasonable agreement between predictions and experiments. The systematic departures might be accounted for by deviations from 1D geometry, which were not included in the calculations. Over the frequency and reduced temperature ranges, the damping effect from the critical bulk viscosity is predicted to be too small to be detectable. The observed effect of the stratification and its frequency dependence in Z(F) are briefly discussed. In the appendix, the predicted critical acoustic attenuation from the bulk viscosity is compared with published data, the effect from finite thermal conductivity of the fluid container plates and also the corrections to Z(F) for the effects of the cell sidewalls are calculated.