Andrei B. Kogan

Onset of convection in a very compressible fluid: the transient toward steady state.

We analyze the time profile deltaT(t) of the temperature difference, measured across a very compressible supercritical 3He fluid layer in its convective state. The experiments were done along the critical isochore in a Rayleigh-Bénard cell after starting the vertical constant heat flow q. For q sufficiently well above that needed for the convection onset, the transient deltaT(t) for a given epsilon identical with (T-T(c))/T(c), with T(c)=3.318 K, shows a damped oscillatory profile with period t(osc) modulating a smooth base profile. The smooth profile forms the exponential tail of the transient which tends to the steady-state deltaT( infinity ) with a time constant tau(tail). The scaled times t(osc)/t(D) and tau(tail)/t(D) from all the data could be collapsed onto two curves as a function of the Rayleigh number over approximately 3.5 decades. Here t(D) is the characteristic thermal diffusion time. Furthermore, comparisons are made between measurements of a third characteristic time t(m) between the first peak and the first minimum in the deltaT(t) profile and its estimation by Onuki et al. Also, comparisons are made between the observed oscillations and the two-dimensional simulations by Onuki et al. and by Amiroudine and Zappoli. For epsilon<9 x 10(-3), the experiments show a crossover to a different transient regime. This regime, which we briefly describe, is not understood at present.

Sound Propagation in 3He and 4He Above the Liquid-Vapor Critical Point

A scaled plot is presented of published sound attenuation and dispersion data of3He and4He along the critical isochore above Tcas a function of the reduced frequency ω*. Here ω*≡ω/Γ with ω the frequency and Γ the order parameter relaxation rate, where the latter is determined from experimental transport and thermodynamic data. For a given isotope, the scaled data obtained at different frequencies lie on a single curve. These curves are different, however, for3He and4He. The resulting scaled plot is compared with recent predictions by Onuki, and by Folk and Moser. The crossover-term contribution in Γ from the background thermal conductivity data is compared with the form derived by Bhattacharjee and Ferrell. In the Appendix, the calculation of Γ for both3He and4He from experiments is described and discussed.

Density Response and Equilibration in a Pure Fluid Near the Liquid-Vapor Critical Point: 3He

AbstractWe report measurements of the local density response inside a quasi 1-D horizontal3He fluid layer to a step-like change ΔT of the boundary temperature, where |ΔT| ≍ 80 μK and much smaller than |T − Tc| where Tcis the critical temperature. These experiments used a new cell design, described in the text, and were carried out along the critical isochoren

Heat transfer in a pure near-critical fluid: diffusive and convective regimes in 3He

bar rho = rho _c

Dynamics of density equilibration near the liquid-vapor critical point of3He

n both above and below Tc. The observed temporal and spatial density response δρ(t, z) and its equilibration time are described adequately by the relations developed from the thermodynamic theory of Onuki and Ferrell. We verify that over the temperature range of low stratification, where computer simulations and closed-form calculations can be compared, they are in exact agreement. The systematic differences of experimental results from predictions can be accounted for by the departure of the cell from the ideal 1-D geometry. The much larger disagreement between the experimental and predicted equilibration time scale in earlier experiments is also explained. Finally, deviations from linearity observed in the density response for steps |ΔT| larger than ≍ 90 μK are reported and the implications of such nonlinearity for the δρ(t, z) profile and especially the effective relaxation time τeffare analyzed. We also discuss the predicted onset of convection near Tcfor the conditions in our experiment. In the Appendix, the likely sources for systematic deviations in the density response function for the experimental cell from calculations in the ideal 1-D geometry are presented and their effects calculated. The so-obtained response function ZF(ω, z) is compared with previously published data.

Heat transfer and convection onset in a compressible fluid: 3He near the critical point.

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 functionZF(ω, ε,z) is calculated for3He in the absence of stratification, where ω is the angular frequency, ε=(T−Tc)/Tc the reduced temperature,Tc=3.316 K the critical temperature, andz 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 frequencyf=ω/2π is varied between 10−4 and 2 Hz. Over the experimental range 5×10−4<ε<5×10−2 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 inZF 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 toZF for the effects of the cell sidewalls are calculated.

RAYLEIGH-BENARD CONVECTION ONSET IN A COMPRESSIBLE FLUID : 3HE NEAR TC

Abstract Results are presented on the heat transport in 3 He below and above the onset of convection in a Rayleigh–Benard cell with aspect ratio of 57. The experiments were conducted along the critical isochore, where the temperature difference Δ T across the fluid layer was measured as a function of time t for various values of heat current q . The transients Δ T ( t ) upon turning the heat flow on and off are described. As q is increased, unusual damped oscillatory patterns in Δ T ( t ) are observed until a steady state is reached. These patterns evolve as the Rayleigh number increases.

Convection in a very compressible fluid: comparison of simulations with experiments.

Abstract We analyze the observed temporal profile ΔT(t) of the temperature difference, measured across a very compressible supercritical 3 He fluid layer in the convective state. The experiments were done along the critical isochore in a Rayleigh–Benard cell after starting the vertical heat flow q. For q>qons (“convection onset”), the transient ΔT(t) under given conditions of q and e≡(T−T c )/T c (T c =3.318 K ) shows a damped oscillatory profile with period tosc modulating a smooth base profile. The latter forms the tail of the transient which relaxes exponentially to the steady-state ΔT(∞) with a time constant τtail. The scaled times tosc/tD and τtail/tD from all the data could be collapsed onto two curves as a function of the Rayleigh number over ∼3.5 decades. Here tD is the diffusion time.