Superfluid flow

This problem was studied earlier in the context of the vortex core for the Gross-Pitaevskii equation which describes a superfluid flow. It is known that the solution of this problem exists and is unique. The solution can be found only numerically. For large p, the asymptotics of the solution is i o 1 1 +—... 

W. Ketterle, J.-i. Shin, Fermi gases go with the superfluid flow. Phys. World June, 38 (2007)... 

When the superfluid component flows through a capillary connecting two reservoirs, the concentration of the superfluid component in the source reservoir decreases, and that in the receiving reservoir increases. When both reservoirs are thermally isolated, the temperature of the source reservoir increases and that of the receiving reservoir decreases. This behavior is consistent with the postulated relationship between superfluid component concentration and temperature. The converse effect, which maybe thought of as the osmotic pressure of the superfluid component, also exists. If a reservoir of helium II held at constant temperature is coimected by a fine capillary to another reservoir held at a higher temperature, the helium II flows from the cooler reservoir to the warmer one. A popular demonstration of this effect is the fountain experiment (55). 

The 1996 Nobel Prize in physics went to three researchers who studied liquid helium at a temperature of 0.002 K, discovering superfluid helium. A superfluid behaves completely unlike conventional liquids. Liquids normally are viscous because their molecules interact with one another to reduce fluid motion. Superfluid helium has zero viscosity, because all of its atoms move together like a single superatom. This collective behavior also causes superfluid liquid helium to conduct heat perfectly, so heating a sample at one particular spot results in an immediate and equal increase in temperature throughout the entire volume. A superfluid also flows extremely easily, so it can form a fountain, shown in the photo, in apparent defiance of gravity. 

Figure 7.4 illustrates the phase diagram of the 4He isotope in the low-temperature condensation region. The thermodynamic properties of 4He are fundamentally distinct from those of the trace isotope 3He, and the two isotopes spontaneously phase-separate near IK. Both isotopes exhibit the spectacular phenomenon of superfluidity, the near-vanishing of viscosity and frictional resistance to flow. The strong dependence on fermionic (3He) or bosonic (4He) character and bizarre hydrodynamic properties are manifestations of the quantum fluid nature of both species. 3He is not discussed further here. 

SUPERFLUIDITY. The term used to describe a property of condensed matter in which a resistance-less flow of current occurs. The mass-four isotope of helium in the liquid state, plus over 20 metallic elements, are known to exhibit this phenomenon. In the case of liquid helium, these currents are hydrodynamic. For the metallic elements, they consist of electron streams. The effect occurs only at very low temperatures in the vicinity of the absolute zero (-273.16°C or 0 K). In die case of helium, the maximum temperature at which the effect occurs is about 2.2 K. For metals, the highest temperature is in die vicinity of 20 K. 

A superfluid is a liquid that will flow endlessly when placed in a closed loop. Some elements, most notably helium (He), become superfluids at temperatures near absolute zero. This phase is considered a second liquid phase and has been known since the late 1930s, but relatively little is understood about it. 

A supersolid is actually a superfluid with the crystal-like structure of a traditional solid. Inside a supersolid, the atoms are moving and flowing as superfluids, but outside, the substance maintains its shape. Supersolids had been predicted to exist in theory, but were only created in a laboratory in 2004. 

Superfluid A liquid that will flow endlessly when placed in a closed loop. 

As helium gas is cooled below -268.95°C, it forms a liquid. At -270.97°C, helium still looks like a liquid, but a liquid with unusual properties. Suddenly, liquid density drops and this "liquid" gains the ability to move through very small holes that helium gas cannot pass through. It flows up the walls of its container defying gravity, and has zero viscosity. Below -270.97°C, helium becomes a superfluid, the only one discovered so far. Helium never changes to a solid. —... 

Furthermore, the complex relaxation requirements of a double resonance technique mean that low temperatures are required in all cases. In general, temperatures below that of liquid nitrogen are needed. These are obtained either with a variable temperature flow cryostat using liquid helium ( 4-40 K) or with a liquid helium immersion dewar ( 4 K, or 2 K for pumped (superfluid) helium). 

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