Near the lambda point of ⁴He, an applied heat flux creates just such a dynamic system. In accordance with the two fluid model, the presence of a heat current induces a counterflow velocity between the superfluid and the normal fluid, giving the system an extra degree of thermodynamic freedom. It is believed that the presence of superflow depresses the superfluid density.

A number of experiments report that the transition temperature, T_c(Q), is depressed in the presence of a heat flux, confirming theoretical predictions. The heat capacity is expected to be significantly enhanced, although the magnitude and the nature of the increase should depend strongly on the experimental conditions of the measurement.  If the heat current Q is held constant during the experiment, the superfluid density will become sufficiently depressed that superflow will become unstable, and the heat capacity will diverge. This is a surprising prediction; the heat capacity not only blows up far more strongly than its near-logrithmic behavior with no heat current, but it also becomes infinite at a finite value of the superfluid density and at a temperature below that of the usual lambda transition.

Our group has taken the first experimental measurements of the specific heat of ⁴He in the presence of a constant heat flux, Q.  The excess heat capacity that we measure is enhanced as a function of Q, and follows the predicted scaling behavior. However, our ground-based measurements have yielded two important discrepancies between theory and experiment. We found that superflow is always observed to break down at a temperature, which we label T_DAS(Q), lower than the theoretically predicted value, T_c(Q). The other is that the enhancement of the specific heat is much larger than predicted by any theory.

In experiments done on Earth, gravity has a number of effects. In order to make measurements without observable dissipation in the superfluid region, the heat flux, Q, must be kept below about 4 mW/cm². At such low fluxes, the Q-dependent contribution to the heat capacity becomes detectable only within about 1 mK of the lambda transition. However, in a cell 1 cm high (roughly the height of the DYNAMX/CQ cell) on Earth, the superfluid transition temperature varies from top to bottom of the cell by more than 1 mK, because of the gravity-induced hydrostatic pressure gradient. To combat this difficulty, our own measurements of the specific heat were made in a cell 0.6 mm high. This configuration made it impossible to use sidewall thermometry, thus severely limiting both the range and the precision of the data. Our data were therefore strongly affected by gravity, and restricted to a region far from the predicted divergence.

All of these difficulties will be overcome when the CQ experiment is performed on orbit. Working in the absence of gravity, the CQ experiment should be able to examine the two discrepancies observed in our ground-based measurements, and perhaps explore the new physics of the heat capacity divergence along the instability curve in the T-Q plane.

Sample data from our ground-based measurements:

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1. Heat Capacity data : taken at various Q values 2. Heat Capacity data : taken at Q = 3.5 mW/cm2 3. Scaling data : scaled using Q0 = 6571 W/cm2 4. Scaling plot : scaled using Q0 = 3400 W/cm2