Hydrodynamic theory of density relaxation in near-critical fluids

Thermal relaxation and critical instability of near-critical fluid microchannel flow

We present two-dimensional numerical investigations of the temperature and velocity evolution of a pure near-critical fluid confined in microchannels. The fluid is subjected to two sides heating after it reached isothermal steady state. We focus on the abnormal behaviors of the near-critical fluid in response to the sudden imposed heat flux. New thermal-mechanical effects dominated by fluid instability originating from the boundary and local equilibrium process are reported. Near the microchannel boundaries, the instability grows very quickly and an unexpected vortex formation mode is identified when near-critical thermal-mechanical effect is interacting with the microchannel shear flow. The mechanism of the new kind of Kelvin-Helmholtz instability induced by boundary expansion and density stratification processes is also discussed in detail. This mechanism may bring about innovations in the field of microengineering.

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.

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.

Critical temperature shift in pure fluid SF6 caused by an electric field

A systematic study of the effect of an electric field on the critical temperature of a pure fluid is made for the first time to our knowledge. An ac electric field is applied to a spherical capacitor filled with SF6 at its critical density, while the temperature is slowly ramped down through its critical temperature T(c). By continuously observing the light transmission through the fluid during the temperature ramp, a shift in T(c), DeltaT(c), is found at various electric fields. By shining the light vertically through the fluid, we utilize the density gradient induced by the fluid's weight to compensate for the effects of density changes from electrostriction. This technique effectively keeps the system at constant critical density with respect to the observation of T(c). We observe an increase in T(c) as expected from thermodynamic stability and renormalization group theory, but quantitatively larger by an order of magnitude.

Fast heat transfer calculations in supercritical fluids versus hydrodynamic approach

This study investigates the heat transfer in a simple pure fluid whose temperature is slightly above its critical temperature. We propose an efficient numerical method to predict the heat transfer in such fluids when the gravity can be neglected. The method, based on a simplified thermodynamic approach, is compared with direct numerical simulations of the Navier-Stokes and energy equations performed for CO2 and SF6. A realistic equation of state is used to describe both fluids. The proposed method agrees with the full hydrodynamic solution and provides a huge gain in computation time. The connection between the purely thermodynamic and hydrodynamic descriptions is also discussed.

Piston-effect-induced thermal oscillations at the Rayleigh-Bénard threshold in supercritical 3He

We perform a Navier-Stokes numerical simulation of the transient Rayleigh-Bénard convection onset in nearly supercritical 3He in the exact conditions in experiments performed by Kogan, Murphy, and Meyer [Phys. Rev. Lett. 82, 4635 (1999)]Phys. Rev. E 63, 056310 (2001)]]. We find an interpretation of the observed unexpected temperature oscillations at the convection onset in terms of the piston effect. This is our first result towards the exploration of the whole instability diagram as recently mapped in those experiments.

Density relaxation of a near-critical fluid in response to local heating and low frequency vibration in microgravity

The response of a confined near-critical fluid to local heating in the presence of vibration is studied by means of two-dimensional numerical simulations of the compressible and unsteady Navier-Stokes equations written for a van der Waals fluid. As in the experiments performed two years ago onboard the Mir orbital station, two different regimes of density distribution are observed. For sufficiently low frequency and high amplitude vibration, two thermal plumes develop from the heat source along the vibration axis. Otherwise (higher frequency and/or lower amplitude), density inhomogeneities caused by heating stay around the heat source. For this regime, the pair of vortices created in each half period absorbs the preceding one, while it is convected away for the double-plume regime. As time goes on, this process repeats, with a lateral extension of the low density region. At lower frequencies, instabilities appear in the flow, thus corroborating again microgravity experiments.