Continuous Heat Exchangers
Counterflow heat exchangers precool the incoming helium-3 against the outgoing dilute stream, and their design sets the base temperature of a dilution refrigerator.
Why they matter
Between the still and the mixing chamber, the concentrated helium-3 stream returning toward the cold end must be cooled from still temperature down toward mixing-chamber temperature. It does this in counterflow heat exchangers against the cold, outgoing dilute stream. The quality of these exchangers is the single largest factor in how low a base temperature the fridge reaches.
The Kapitza wall
At these temperatures the dominant obstacle is Kapitza boundary resistance, the thermal resistance at the interface between liquid helium and a solid surface. Kapitza resistance scales roughly as one over T cubed, so as the exchanger gets colder it becomes dramatically harder to move heat across the wall. Overcoming this requires enormous surface area.
Two exchanger regimes
Refrigerators typically use two kinds. Continuous tubular exchangers, effective at the warmer end near the still, use concentric or coaxial tubes. Below roughly 30 to 50 millikelvin these are inadequate, so step exchangers packed with sintered silver powder are used. The sinter presents surface areas of many square meters per gram of metal, defeating Kapitza resistance by brute force of area.
Design tradeoffs
More sinter lowers base temperature but adds heat capacity, slowing cooldown, and adds viscous flow impedance that can limit circulation rate. Designers balance surface area, flow resistance, and the parasitic heat leak from higher stages. A well-built exchanger set is what separates a 10-millikelvin machine from one stuck near 20 or 30 millikelvin.
- Counterflow: warm incoming stream against cold outgoing stream
- Tubular exchangers at the warm end, sintered step exchangers at the cold end
- Kapitza resistance rises as one over T cubed
- Base temperature is largely set here