Thermoacoustic boundary layers near the liquid-vapor critical point

Experimental and numerical investigations of resonant acoustic waves in near-critical carbon dioxide

Flow and transport induced by resonant acoustic waves in a near-critical fluid filled cylindrical enclosure is investigated both experimentally and numerically. Supercritical carbon dioxide (near the critical or the pseudo-critical states) in a confined resonator is subjected to acoustic field created by an electro-mechanical acoustic transducer and the induced pressure waves are measured by a fast response pressure field microphone. The frequency of the acoustic transducer is chosen such that the lowest acoustic mode propagates along the enclosure. For numerical simulations, a real-fluid computational fluid dynamics model representing the thermo-physical and transport properties of the supercritical fluid is considered. The simulated acoustic field in the resonator is compared with measurements. The formation of acoustic streaming structures in the highly compressible medium is revealed by time-averaging the numerical solutions over a given period. Due to diverging thermo-physical properties of supercritical fluid near the critical point, large scale oscillations are generated even for small sound field intensity. The strength of the acoustic wave field is found to be in direct relation with the thermodynamic state of the fluid. The effects of near-critical property variations and the operating pressure on the formation process of the streaming structures are also investigated. Irregular streaming patterns with significantly higher streaming velocities are observed for near-pseudo-critical states at operating pressures close to the critical pressure. However, these structures quickly re-orient to the typical Rayleigh streaming patterns with the increase operating pressure.

Phase diagram and thermodynamic properties of H2

A statistical mechanical-based theory is used to develop the equation of state for the molecular fluid of H(2). We incorporate in this equation the long-range correlations through the double Yukawa potential, dimerization of the H(2) molecule by treating the fluid as a hard convex body fluid, and first-order quantum correction which is important at low temperatures. We use this to calculate the liquid-vapor equilibrium of H(2), including the temperature and pressure dependence of compressibility factor, entropy, specific heat, compressibility, and sound velocity.

Predrying transition on a hydrophobic surface: statics and dynamics

For one-component fluids, we examine the predrying phase transition between a thin and thick low-density layer in liquid on a wall repelling the fluid. This is the case of a hydrophobic wall for water. A predrying line starts from the coexistence curve and ends at a surface critical point in the phase diagram. We calculate this line numerically using the van der Waals model and analytically using the free-energy expansion up to the quartic order. We also examine the predrying dynamics of a layer created on a hydrophobic spot on a heterogeneous wall. It is from a thin to thick layer during decompression and from a thick to thin layer during compression. Upon the transition, a liquid region above the film is cooled for decompression and heated for compression due to latent heat convection, and a small pressure pulse is emitted from the film into the liquid.

Thermoacoustic waves along the critical isochore

Near the liquid-gas critical point, thermal disturbances can generate sounds. We study the acoustic emission over four decades of reduced temperatures [defined as ɛ=(T-T(c))/T(c), with T(c) the critical temperature] along the critical isochore, under linear and nonlinear temperature perturbations, respectively. We identify various thermoacoustic behaviors by numerically solving the governing equations. It is shown that a homogeneous thermoacoustic-wave pattern dominates in the linear case, largely independent of ɛ; whereas under the nonlinear perturbation, variation in ɛ could lead to severe wavefront deformation. The strong nonlinear effect is found to be of a transient nature because, in due time, both cases tend to converge in terms of the energy yield of the adiabatic process.

Thermoacoustic wave propagation and reflection near the liquid-gas critical point

We study the thermoacoustic wave propagation and reflection near the liquid-gas critical point. Specifically, we perform a numerical investigation of the acoustic responses in a near-critical fluid to thermal perturbations based on the same setup of a recent ultrasensitive interferometry measurement in CO2 [Y. Miura, Phys. Rev. E 74, 010101(R) (2006)]. The numerical results agree well with the experimental data. Different features regarding the reflection pattern of thermoacoustic waves near the critical point under pulse perturbations are revealed by the proper inclusion of the critically diverging bulk viscosity.

Thermoacoustic effects in supercritical fluids near the critical point: Resonance, piston effect, and acoustic emission and reflection

We present a general theory of thermoacoustic phenomena in one phase states of one-component fluids. Singular behavior is predicted in supercritical fluids near the critical point. In a one-dimensional geometry we start with linearized hydrodynamic equations taking into account the effects of heat conduction in the boundary walls and the bulk viscosity. We introduce a coefficient Z(omega) characterizing reflection of sound with frequency omega at the boundary in a rigid cell. As applications, we examine acoustic eigenmodes, response to time-dependent perturbations, and sound emission and reflection. Resonance and rapid adiabatic changes are noteworthy. In these processes, the role of the thermal diffusion layers is enhanced near the critical point because of the strong critical divergence of the thermal expansion.

Bulk viscosity, thermoacoustic boundary layers, and adsorption near the critical point of xenon

We present an improved model for the dissipation and dispersion in an acoustic resonator filled with xenon near its critical temperature Tc. We test the model with acoustic measurements in stirred xenon that have a temperature resolution of (T - Tc)/Tc approximately 7 x 10(-6). The model includes the frequency-dependent bulk viscosity calculated numerically from renormalization-group theory and it includes critical-point adsorption. Because the density of adsorbed xenon exceeds the critical density, the bulk viscosity's effect on surface dissipation is reduced, thereby improving the agreement between theory and experiment.

High-speed observation of the piston effect near the gas-liquid critical point

We investigated adiabatic changes in a near-critical fluid on acoustic time scales using an ultrasensitive interferometer. A sound emitted by very weak continuous heating caused a stepwise adiabatic change at its front with a density change of order 10(-7) g/cm(3) and a temperature change of order 10(-5) K. Very small heat inputs at a heater produced short acoustic pulses with width of order 10 micros, which were broadened as they moved through the cell and interacted with the boundaries. The pulse broadening became enhanced near the critical point. We also examined theoretically how sounds are emitted from a heater and how applied heat is transformed into mechanical work. Our predictions agree well with our data.

Bulk viscosity of stirred xenon near the critical point

We deduce the thermophysical properties of near-critical xenon from measurements of the frequencies and half-widths of the acoustic resonances of xenon maintained at its critical density in centimeter-sized cavities. In the reduced temperature range 1 x 10-3<(T-Tc)/Tc<7 x 10 (-6), we measured the resonance frequency and quality factor (Q) for each of six modes spanning a factor of 27 in frequency. As Tc was approached, the frequencies decreased by a factor of 2.2 and the Q's decreased by as much as a factor of 140. Remarkably, these results are predicted (within +/-2% of the frequency and within a factor of 1.4 of Q) by a model for the resonator and a model for the frequency-dependent bulk viscosity zeta(omega) that uses no empirically determined parameters. The resonator model is based on a theory of acoustics in near-critical fluids developed by Gillis, Shinder, and Moldover [Phys. Rev. E 70, 021201 (2004)]. In addition to describing the present low-frequency data (from 120 Hz to 7.5 kHz), the model for zeta(omega) is consistent with ultrasonic (0.4--7 MHz) velocity and attenuation data from the literature. However, the model predicts a peak in the temperature dependence of the dissipation in the boundary layer that we did not detect. This suggests that the model overestimates the effect of the bulk viscosity on the thermal boundary layer. In this work, the acoustic cavities were heated from below to stir the xenon, thereby reducing the density stratification resulting from Earth's gravity. The stirring reduced the apparent equilibration time from several hours to a few minutes, and it reduced the effective temperature resolution from 60 mK to approximately 2 mK, which corresponds to (T-Tc)/Tc approximately =7 x 10(-6).

Two typical time scales of the piston effect

The existence of a fourth mode of heat transfer near the critical point, named the piston effect, has been known for more than a decade. The typical time scale of temperature relaxation due to this effect was first predicted by Onuki [Phys. Rev A 41, 2256 (1990)], and this author's formula has been extensively used since then to predict the thermal behavior of near-critical fluids. Recent studies, however, pointed out that the critical divergence of the bulk viscosity could have a strong influence on piston-effect-related processes. In this paper, we conduct a theoretical analysis of near-critical temperature relaxation showing that the piston effect is not governed by one (as was until now believed) but by two typical time scales. These two time scales exhibit antagonistic asymptotic behaviors as the critical point is approached: while the classical piston-effect time scale (as predicted by Onuki ) goes to zero at the critical point (critical speeding up), the second time scale (related to bulk viscosity) goes to infinity (critical slowing down). Based on this property, an alternative method for measuring near-critical bulk viscosity is proposed.