Thermodynamic properties of sulfurhexafluoride in the critical region

Supercritical Fluid Gaseous and Liquid States: A Review of Experimental Results

We review the experimental evidence, from both historic and modern literature of thermodynamic properties, for the non-existence of a critical-point singularity on Gibbs density surface, for the existence of a critical density hiatus line between 2-phase coexistence, for a supercritical mesophase with the colloidal characteristics of a one-component 2-state phase, and for the percolation loci that bound the existence of gaseous and liquid states. An absence of any critical-point singularity is supported by an overwhelming body of experimental evidence dating back to the original pressure-volume-temperature (p-V-T) equation-of-state measurements of CO₂ by Andrews in 1863, and extending to the present NIST-2019 Thermo-physical Properties data bank of more than 200 fluids. Historic heat capacity measurements in the 1960s that gave rise to the concept of "universality" are revisited. The only experimental evidence cited by the original protagonists of the van der Waals hypothesis, and universality theorists, is a misinterpretation of the isochoric heat capacity C_v. We conclude that the body of extensive scientific experimental evidence has never supported the Andrews-van der Waals theory of continuity of liquid and gas, or the existence of a singular critical point with universal scaling properties. All available thermodynamic experimental data, including modern computer experiments, are compatible with a critical divide at T_c, defined by the intersection of two percolation loci at gaseous and liquid phase bounds, and the existence of a colloid-like supercritical mesophase comprising both gaseous and liquid states.

Thermodynamic Fluid Equations-of-State

As experimental measurements of thermodynamic properties have improved in accuracy, to five or six figures, over the decades, cubic equations that are widely used for modern thermodynamic fluid property data banks require ever-increasing numbers of terms with more fitted parameters. Functional forms with continuity for Gibbs density surface ρ(p,T) which accommodate a critical-point singularity are fundamentally inappropriate in the vicinity of the critical temperature (T_c) and pressure (p_c) and in the supercritical density mid-range between gas- and liquid-like states. A mesophase, confined within percolation transition loci that bound the gas- and liquid-state by third-order discontinuities in derivatives of the Gibbs energy, has been identified. There is no critical-point singularity at T_c on Gibbs density surface and no continuity of gas and liquid. When appropriate functional forms are used for each state separately, we find that the mesophase pressure functions are linear. The negative and positive deviations, for both gas and liquid states, on either side of the mesophase, are accurately represented by three or four-term virial expansions. All gaseous states require only known virial coefficients, and physical constants belonging to the fluid, i.e., Boyle temperature (T_B), critical temperature (T_c), critical pressure (p_c) and coexisting densities of gas (ρ_cG) and liquid (ρ_cL) along the critical isotherm. A notable finding for simple fluids is that for all gaseous states below T_B, the contribution of the fourth virial term is negligible within experimental uncertainty. Use may be made of a symmetry between gas and liquid states in the state function rigidity (dp/dρ)_T to specify lower-order liquid-state coefficients. Preliminary results for selected isotherms and isochores are presented for the exemplary fluids, CO₂, argon, water and SF₆, with focus on the supercritical mesophase and critical region.

Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-Bénard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.

Thermal-noise effect on the transition to Rayleigh-Bénard convection

We report measurements of fluctuation and roll patterns near the transition to Rayleigh-Bénard convection which are consistent with a fluctuation-induced first-order transition, as predicted by Swift and Hohenberg. Above onset, we find convection rolls with noise-induced fluctuations, time-dependent amplitude modulation and roll undulation, and homogeneous dislocation nucleation.

Reentrant hexagons in non-Boussinesq Rayleigh-Bénard convection: effect of compressibility

We present experimental studies of a new pattern sequence observed in non-Boussinesq convection in a compressible fluid near its gas-liquid critical point (CP). Besides the known hysteretic transitions among conduction state, hexagons, and rolls, another hysteretic transition from rolls to hexagons at higher values of the control parameter is found. This reentrance phenomenon is observed in a rather narrow range of about 60- to 100-microm cell heights and is attributed to large compressibility of a fluid near the CP.

Thermalization of a two-phase fluid in low gravity: heat transferred from cold to Hot

We present an experimental study of the thermal response to a positive temperature quench in two-phase fluid SF6 in low gravity for temperature ranging from 10.1 to 0.1 K from the critical temperature. The temperature was measured simultaneously in the gas, the liquid, and the cell wall by thermistors and the density distribution was observed by interferometry. During the quench the gas temperature considerably exceeded the temperature of the heating walls (overheating up to 23%). This striking observation is discussed in the light of the adiabatic heat transfer in this highly compressible fluid while the key role of the localization in low gravity of the gas and liquid phases is revealed.