Cargas aplicadas sobre el voladizo del puente Centenario

The experience of the low temperature group at Northwestern University has shown that the very fine structure of aerogel can crush under the sur- face tension of3He during cell filling procedure. Their suggested approach is to fill the cell supercritically, i. e. with3He safely above the critical point (Tc =3.32 K and pc =1.146 bar [90]). Once the temperature is lower thanTc,

the pressure can be lowered and liquid3He fills the cell without the creation of a vapour-liquid interface. To ensure that the cell does not explode during the procedure, pressurizing above about 5 bar should be avoided. Unfortu- nately, estimating the exact cell pressure is difficult. There is a gauge that monitors the cell pressure at the mixing chamber level, but the pressure drop on the thin capillary that connects it with the cell is very hard to pre- dict, especially during cooldown. To roughly estimate the cell pressure, the dependence of resonant frequency and width on pressure was calibrated for both tuning forks inside the cell (TFtop and TFbot respectively).

6.6.1

Tuning fork pressure calibration

Using the two-fluid model of superfluid and neglecting the acoustic damp- ing, Blaauwgeers et. al. [59] suggest the frequency dependence on density as follows f0vac f0 2 =1+ ρ ρq β+BS V r η πρf0 , (6.4)

while the dependence of the width∆f2 is described by

∆f2 = 1 2 r ρηf0 π CS (f0/f0vac)2 mvac , (6.5)

where V = TW L and S = 2(T+W)L. T,W and L are fork dimensions shown in Figure4.2. There are three more dimensionless constants β, Band

C that depend on the geometry of the fork. f0vac is the intrinsic frequency

- the frequency of the resonator in vacuum without fluid damping. After measuring f0vac, f0 and ∆f2 for several different densities or temperatures,

we can minimize both equations for the parameters β, B and C. Once the

parameters are estimated, equations (6.4) and (6.5) can be solved for f0 and

∆f2 for any pressure and temperature as long as the parameters of the gas

are known.

At room temperature, density as a function of pressure and temperature can be conveniently approximated with very good precision by the ideal gas equation

ρ = pM

TRspec , (6.6)

where Rspec is the ideal gas constant and M is the molar mass. However,

for the measurements at temperatures around Tc, fitting the data based on

literature values is necessary ([91] for 4He and [92, 93] for 3He). The tem- perature dependence of viscosity can be found in [94, 95].

To find the parameters β, Band C for the tuning forks inside the exper-

imental cell, the cell was cooled down to 4 K and pressurized with 3He to various pressures between 0 and 1.5 bar. The pressure was measured using a capacitance gauge mounted on the mixing chamber plate. To minimise

of pressures in the critical temperature range are shown in Figure6.9. These plots can then be used a rough guide when estimating the cell pressure during cooldown.

Figure6.9: Calculated f₀and∆f₂ dependence on temperature for various

pressures. f0 and ∆f2 along the saturated vapour pressure and at fixed density passing the critical point are also shown.

6.6.2

Practical realisation

Standard procedure involves pressurising the cell to around 1.8 bar and keeping the pressure constant as the3He-4He mixture condenses. The crit- ical point is just above 3 K, so it’s important to have the cell pressurized prior to the start-up of the dilution refrigerator. Unfortunately, it turned out that the pressure as measured by the pressure gauge at the mixing chamber

became highly unstable. During multiple cooldowns we encountered nu- merous situations when the seemingly stable pressure suddenly dropped at astonishing speed, see Figure 6.10. We suspect that the 3He condenses somewhere in the vicinity of the pressure gauge volume which is one of the coldest parts of the refrigerator at the time. The cell with the aerogel sample is indeed warmer than the mixing chamber at this time, but since the exact pressure in the cell is unknown, sudden pressure changes should be avoided nevertheless.

It was thus very important to stay alert during the condensation of the mixture and take immediate action when the cell pressure starts dropping. During condensing one should always keep the high pressure volume full of3He and immersed in liquid4He - ready to increase the cell inlet pressure when needed. Often a simple increase in inlet pressure was not sufficient and one had to heat the mixing chamber with the built-in resistor. Using the mixing chamber heater has proven to be the most efficient and sensitive method of raising the3He pressure, but it slows down the mixture conden- sation process.

We tried other more desperate ways to increase the3He pressure as well. For instance one can stop the condensation and fill the 1 K pot with warm

4_{He gas. Even this quite violent action was sometimes not enough and one}

had to introduce warm mixture into the still of the dilution fridge. It proved useful to keep the still pressure below about 15 mbar during the condensing process and raise it up to 100 mbar or more only when really needed. The introduction of warm mixture into the still results in immediate warm up and increase in cell pressure, but it slows down the condensation process. It can take more than an hour to pump the still back to 15 mbar in order to start condensing again.

The volume of the cell requires about 50 l of 1 bar room temperature

3_{He to be condensed. Once the cell was full, no sudden pressure drops}

would occur and the refrigerator was safe to leave without supervision - condensing the remains of the3He-4He mixture overnight.

Since cooldowns and warmups must be performed with overpressure, it proved to be particularly useful to flush the cell multiple times before every run, decreasing the risk of blocking the filling lines. Partially closed filled lines significantly prolong the warmup procedure which once started must be finished in one session.

10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 P re ss ur e (m ba r) Time Critical pressure

Figure 6.10: Cell pressure during the start of the dilution refrigerator as

measured by the pressure gauge thermalised at the mixing chamber plate. Sudden drops in the pressure are probably caused by condensation of3He

in the vicinity of the pressure gauge.