Osmotic Pressure in Helium Mixtures
The osmotic pressure of helium-3 dissolved in superfluid helium-4 drives the circulation of a dilution refrigerator and sets its internal flows.
An osmotic engine
A dilution refrigerator circulates helium-3 not by a pump inside the cold region but by an osmotic-pressure gradient in the dilute phase. Because superfluid helium-4 flows freely and carries no entropy, it acts like a passive solvent, while dissolved helium-3 behaves as a solute whose concentration and temperature set an osmotic pressure. Differences in this osmotic pressure between the mixing chamber and the still drive helium-3 to flow.
How the gradient forms
At the still, helium-3 is removed by evaporation, lowering its concentration there. At the mixing chamber, helium-3 enters the dilute phase from the concentrated phase, keeping its concentration higher. The dilute helium-3 flows from high osmotic pressure at the mixing chamber toward low osmotic pressure at the still, carrying enthalpy and completing the internal circuit. The superfluid helium-4 background provides an essentially frictionless medium for this flow.
Temperature and concentration
Osmotic pressure in these mixtures depends on both helium-3 concentration and temperature, reflecting the Fermi-liquid nature of the dilute helium-3. Analyzing the balance of osmotic pressures, together with the enthalpy the helium-3 carries, is how designers predict internal flow rates and the temperature profile along the dilute channel from mixing chamber to still.
Why frictionless flow matters
If the dilute helium-3 had to flow through a viscous ordinary liquid, the pressure drops would throttle circulation and cripple cooling. The superfluidity of helium-4 removes viscous resistance for the background, so only the helium-3 quasiparticles carry momentum. This is another way the peculiar physics of the helium isotopes conspires to make continuous millikelvin cooling practical.
- Osmotic-pressure gradient drives internal helium-3 flow
- Still lowers concentration; mixing chamber keeps it higher
- Osmotic pressure depends on concentration and temperature
- Superfluid helium-4 provides frictionless background flow