Breakdown of Superfluidity for Cylinders in Saturated Liquid Helium II

In the past few years. studies of boiling and vaporization have been extended to liquid helium temperatures above the λ point (T λ = 2.172°K) in liquid He I and below the λ point in liquid He II. The phase change in ordinary liquid He I is consistent, in essential details, with the boiling conditions of other classical liquids. Liquid He II. however, is a superfluid, whose thermohydrodynamic behavior [1,2] is radically different from classical liquids. For instance, nucleate boiling is suppressed because of the excellent heat transport capability of He II. Without boiling, heat from an immersed dissipative solid (e.g., a horizontal cylinder as shown in the insert of Fig. 1) is transported through the liquid He II bath to the upper liquid—vapor interface where vapor is pumped off to maintain the bath temperature below T λ . After a certain limiting peak heat flux has been exceeded, however, boiling similar to classical film boiling initiates, i.e., an insulating vapor film forms adjacent to the heater surface, which lowers the heat transfer rate substantially. This type of boiling sets in, after breakdown of superfluidity, when the local thermodynamic state has reached saturation conditions of vapor liquid equilibrium (temperature T* and pressure P* as noted in Fig. 1). This transport limit of liquid He II near a heated single solid appears, for the present, to be predictable only for a few ideal situations (upper bound). Therefore, a number of experiments have been carried out in recent years to determine the superfluidity breakdown at the peak flux for several configurations. In particular, studies with horizontal cylinders (Table I) showed that the peak heat flux depends on the cylinder diameter D, the bath temperature T, and the submersion depth H (Fig. 1). No detailed consistent account of these effects has been given so far. Very recent work [3–5], however, suggests that a large variety of He II transport phenomena may be accounted for within a common thermohydrodynamic frame of reference for He II. Along this line of approach the present study was conducted to eliminate the lack of a theoretical account for the liquid impedance which opposes entropy transport near a single dissipative horizontal cylinder in a large pool of He II. The next section of the paper considers the pertinent thermohydrodynamic conditions and similarity rules. This theory includes special power law approximations. Subsequently, the experimental data (Table I) are compared with the power laws. The data agree satisfactorily with the theory within the data scatter encountered during the experiments.