Helium II (He II), the second liquid phase of the 4He isotope described in this column in Cold Facts Spring 2010 (http://2csa.us/he2), can be modeled as consisting of two interpenetrating fluids. One, the superfluid component, has zero viscosity and entropy and the other, the normal fluid component, has nonzero viscosity and entropy. Research has shown that despite this complexity, in most engineering applications, He II obeys the classical laws of fluid dynamics. Important and useful exceptions to this rule occur in the cases of fountain pumps and phase separators.

Both of these applications take advantage of the phenomena of laminar mass flow of He II. In this situation, there is essentially no interaction between the superfluid component and the normal fluid component and a temperature gradient in the He II can be related to a pressure gradient by the equation:

∆P = ρS∆T

where S and ρ are the entropy and density of the He II. In effect, establishing a temperature gradient when in laminar mass flow conditions will create a pressure gradient and vice versa. In order to be in the laminar flow regime of He II, the superfluid component velocity must be below a critical velocity, above this critical velocity, the two components will interact with each other and the fluid enters the turbulent regime. The critical velocity goes as
1/d1/4 where D is the characteristic diameter of the flow system. As a result, for practical systems, laminar flow in He II only occurs in very small (roughly 1 micron or less) diameters. This condition is generally accomplished by the use of porous plugs or slits of the appropriate size.

A fountain pump uses this effect to pump He II without moving parts. Figure 1 is a schematic of how such a system works using a porous plug and heater. The heater establishes a temperature gradient and thus a pressure gradient across the porous plug. The resulting pressure gradient causes flow in the bulk helium. Fountain pumps have been built into practical systems. Figure 2 shows the fountain pump from the NASA Superfluid Helium On Orbit Transfer (SHOOT) experiment. Fountain pumps are also known as thermomechanical pumps. The term fountain pump comes from this technique’s earliest use in creating He II fountains to illustrate the unique properties of He II. Such helium fountains are still shown in classroom and laboratory demonstrations. A video of such a demonstration may be found at http://2csa.us/4he.

Another application of porous plugs is found in He II phase separators, also known as vapor-liquid phase separators. These devices, which separate vapor from He II, are particularly useful in space applications where the lack of gravity prevents the stratification of liquid and vapor. The problem is that any saturated bath, no matter how well insulated, will evolve vapor due to the heat leak. Without gravity driven stratification, how is the vapor removed without also removing the liquid?

In a He II phase separator, one side of the porous plug is in contact with He II with the other in contact with a venting line or space. There is a liquid-vapor interface either inside the porous plug or on the outer surface facing the vent line. Evaporation removes heat at this interface, setting up a temperature difference that causes the superfluid component to move back toward the He II reservoir. Porous plugs can be sized to keep the He II reservoir at the desired pressure and thus temperature.

The physics of vapor-liquid phase separators (VLPS) in He II are more complicated than simple fountain pumps. In order to function, the pores of the VLPS must be big enough to allow some normal fluid component in and as a result a number of flow regimes are possible; including one in which the flow is turbulent, the two components interact and the equation above doesn’t strictly apply. The importance of phase separators in space missions is such that a significant amount of research has been carried out in this area and VLPS have flown on a wide range of space missions including SHOOT and the Spitzer Space Telescope.

Detailed explanations of He II properties may be found in Helium Cryogenics by S. W. Van Sciver, Springer (2012). Examples of fountain pumps include: “Tests of a Nearly Ideal High Rate Thermal Mechanical Pump,” M. J. DiPirro et al., Proc. ICEC 12 (1988) and “Performance of a Closed Type Fountain Effect Pump,” T. Okamura et al., Cryogenics 36 (1996). A recent application of fountain pumps to sub-Kelvin cooling is given in “A sub-Kelvin Pulse Tube Refrigerator Driven by a Paramagnetic Fountain Effect Pump”, A. E. Jahromi and F. K. Miller, Cryogenics 62 (2014).

Analysis of VLPS can be found in “Vapor-Liquid Phase Separation of He II,” S. W. K. Yuan et al. Cryogenics 38 (1998), “Flow Rate of He II Liquid-Vapor Phase Separator,” X. Yu et al., J. of Thermal Science Vol. 14 No 1 (2005) and “He II Liquid/Vapour Phase Separator for Large Dynamic Range Operation,” A. Nakano et al., Cryogenics 36 (1996). Reports from space missions include: “On-Orbit Superfluid Helium Transfer: Preliminary Results from the SHOOT Flight Demonstration” M. J. DiPirro et al., Cryogenics 34 (1994) and “Mid-Mission Update of Spitzer Telescope Cryogenic Performance”, P. T. Finley et al., Adv. Cryo. Engr. Vol. 51 (2006).