Local probe in a Rayleigh-Benard experiment in liquid helium

2014 We have measured, in a Rayleigh-Benard experiment in liquid helium, the time dependent effects occurring above the onset of convection, using a local probe. Results are very dependent on the aspect ratio 0393, ratio of the cylinder cell radius to its height. For a small aspect ratio, 0393 = 2 and 0393 = 2.5, well defined sharp oscillations are present for a large range of Rayleigh numbers. For 0393 = 6, a low frequency noise appears for R/Rc = 2, where Rc is the critical Rayleigh number for convection. No well-defined oscillations are present but the noise peaks at a dimensionless frequency around 03C9 = 14, when R/Rc > 3.5. This effect exists also for 0393 = 4 and 0393 = 12. 0393 = 3 is thus a transition point between the two regimes. LE JOURNAL DE PHYSIQUE LETTRES TOME 39, 1 er NOVEMBRE 1978, Classification Physics Abstracts 47.25Q 47.30 We report here some preliminary new results on a Rayleigh-Benard experiment in liquid helium, using for the first time a local probe. Time dependent effects above the convection threshold are the main focus of this experiment. The transitions to turbulent convection have been extensively studied recently [1, 2]. Of particular relevance to this paper is the work of G. Ahlers and R. P. Behringer [3, 4, 5] on 4He above the lambda transition. It is a detailed study, in a RayleighBenard experiment, of the various transitions occurring for the effective thermal conductivity of 4He, as one heats from below a sample of the liquid placed between two plates. The experimental advantages of low temperature techniques have been clearly demonstrated [5], i.e., thermal measurements of very high resolution and great accuracy. Up to now the two important limitations of a low temperature experiment in 4He are, first, the difficulty of direct observation (*) Laboratoire associe au Centre National de la Recherche Scientifique. of the convective roll pattern, and second the absence of local probes. We wish to report here the results obtained, using a local probe, on the time-dependent temperature fluctuations which present a completely different character, as one goes from a small aspect ratio r = 2, to a large one r = 12 (r = D/2 d, D cell diameter, d cell height). 1. Experimental situation. The experimental cell is shown on figure 1. It is a cylinder with a variable height and a diameter D = 25 mm. The top and bottom boundaries are made out of copper. The wall consists of a 0.2 mm thick stainless steel cylinder. To change the aspect ratio r, we introduce teflon gaskets which change the diameter D. The cell is surrounded by a very high vacuum, better than 10 6 torr. Thermal regulation for the top plate provides a temperature stability regulation of the order of 10-6 K. To reach such a stability, we increase the heat capacity of the temperature regulated ensemble by adding a second reservoir of helium, in series with the experimental cell and regulated by the same temperature control. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:019780039021036900 L-370 JOURNAL DE PHYSIQUE LETTRES FlG. 1. The upper part is the detail of the experimental system. The lower part is an enlarged view of the local probe seen both in a transverse cut and from the bottom. Dimensions are not conserved. This reservoir is packed with porous bronze. Another advantage of this reservoir is that it avoids the thermal problems introduced by the helium column required to fill up the experimental chamber. The fluid properties are obtained from the NBS chart [6]. The various temperatures are measured, using Allen Bradley resistors. The bolometers are thinned down to 0.3 mm and glued with a General Electric varnish to the upper and bottom plates. 2. The local probe. A local probe is placed in the upper plate, in the following manner (see the enlargement on Fig. 1). A sapphire plate of thickness 1.3 mm, glued to the top copper boundary of the cell is the support of the local probe. A small hole (diameter 0.8 mm, depth 0.4 mm) is drilled by ultrasound technique in the centre of the sapphire, being thus located on the revolution axis of the cell. A small carbon disc, taken out from an Allen Bradley resistor, fills the hole and is glued to it using stycast. The sapphire plate is then lapped with an abrasive powder for flatness, the carbon element being flush with the surface. About one micrometer of tin is then evaporated and covers the whole plate. Using a micromanipulator, an area of the carbon disc is uncovered, thus taking off the tin layer, and various cuts on the tin thin film are machined to insure the electrical connections to the bolometer. The final resistance of the bolometer at 4.02 K is about 30 000 Q. This local probe detects temperature changes on an area of about 0.2 square millimeter. A small amplitude low frequency a.c. signal is applied to the bolometer (80 Hz, 3 x 10 9 W). The measurements are performed using a lock-in detector which is placed after a balanced bridge. The bridge is at helium temperature and the local probe constitutes one arm of the bridge. The signal is then Fourier analysed using a 5420 A Hewlett Packard Digital signal analyser. Typically a spectrum is averaged a few hundred times using a sliding average program. The bolometer noise has a 1 coverall variation as shown on figure 4, in the whole frequency domain of study, which ranges from 1 mHz to 5 Hz. The fluid parameters and cell-dimensions are given in table I. 3. Experiment. In a Rayleigh-Benard experiment, the two dimensionless numbers of interest are the Rayleigh number R = grxd3 4T/Kv and the Prandtl number a = v/K where g is the acceleration of gravity, Lx the isobaric thermal expansion coefficient, positive in our case, K the thermal diffusivity and v the kinematic viscosity. The variable is the temperature difference between the two plates AT, and the onset of convection is for R = Rc where 7~ = 1 708 for large r [7]. The Prandtl number measures the relative importance of vorticity diffusion to heat conduction. In our case, where 0.6, heat diffusion and vorticity diffusion are of the same order. The convection threshold Rc is obtained from a heat conductivity measurement. In our measurement of the time-dependent fluid flow, we impose the heat current g and measure the temperature difference AT. The heat flows in parallel through the teflon boundaries and helium. Our measurements are very dependent on the aspect ratio, we will thus present them for increasing aspect ratio. .4. Small aspect ratio. 4.1 ASPECT RATIO r = 2.5. For r = 2.5, very well defined time dependent oscillations are recorded by the local