# The role of capillaries in a dilution refrigerator

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• Foreverlearning
The pressure in each tube would be different, and it would be impossible for the helium to flow from one side of the tube to the other without passing through the capillary.I believe that the Bernoulli equation is the primary tool for understanding fluid mechanics. Other mechanisms come into play in flow through porous media and capillaries, but the pressure variations are primarily due to the flow restriction caused by the capillary.f

#### Foreverlearning

I've been trying to understand how dilution refrigerators work and inbetween intermediate steps, between different temperature points, I see capillaries here and there under the name of impedances.

After some googling, I somewhat convinced myself that it's to build up pressure before and after the capillary to prevent liquid He from reevaporation. But it still isn't crystal clear to me what the capillaries are exactly doing.

Considering the Bernoulli's equation, the pressure inside the capillary is less than the pressure before and after, I believe. Are the pressure values exactly the same before and after the capillary (impedance)?

Are capillaries just there in various phases of the cooling process just to keep the pressure high to prevent He from evaporating?

The links below are some of the references I read before posting the question.

http://www.roma1.infn.it/exp/cuore/pdfnew/Fridge.pdf

Are capillaries just there in various phases of the cooling process just to keep the pressure high to prevent He from evaporating?
According to my reading of your second reference (pgs 2,3) the answer is "Yes". I agree that the explanation of Dilute Phase and Concentrated Phase are about as clear as mud. They seem to contradict each other to some extent, probably just my poor understanding of the jargon used in that field though. I printed Fig. 9 (on pg. 19) for reference as I was reading the HISTORY AND PRINCIPLE OF OPERATION section. Having that reference made it possible to mostly follow what was being said.
But it still isn't crystal clear to me what the capillaries are exactly doing.
The Primary Impedance and Capillaries act as flow restrictors on the high pressure side of the pumps and, as you said, keep the back-pressure up in the Condensor and capillaries to avoid re-evaporation. Additionally, the Heat Exchangers, between the Dilute Phase plumbing and the Capillaries, cool the Capillaries to help avoid re-evaporation. And the Capillaries, being small, supply much surface area for thermal transfer from the 3He.

The main evaporation and cooling is done in the Mixing chamber, which is on the low pressure or suction side of the pumps. The evaporating 3He mixes with the 4He to create the Dilute Phase.

The Still, being on the low pressure side of the pumps, is where the 3He is boiled out of the Dilute Phase (3He/4He) mixture and starts the cycle over again.

The rest of it is housekeeping.

A rather clever design, me thinks!

Hope this helps.

Cheers,
Tom

According to my reading of your second reference (pgs 2,3) the answer is "Yes". I agree that the explanation of Dilute Phase and Concentrated Phase are about as clear as mud. They seem to contradict each other to some extent, probably just my poor understanding of the jargon used in that field though. I printed Fig. 9 (on pg. 19) for reference as I was reading the HISTORY AND PRINCIPLE OF OPERATION section. Having that reference made it possible to mostly follow what was being said.

The Primary Impedance and Capillaries act as flow restrictors on the high pressure side of the pumps and, as you said, keep the back-pressure up in the Condensor and capillaries to avoid re-evaporation. Additionally, the Heat Exchangers, between the Dilute Phase plumbing and the Capillaries, cool the Capillaries to help avoid re-evaporation. And the Capillaries, being small, supply much surface area for thermal transfer from the 3He.

The main evaporation and cooling is done in the Mixing chamber, which is on the low pressure or suction side of the pumps. The evaporating 3He mixes with the 4He to create the Dilute Phase.

The Still, being on the low pressure side of the pumps, is where the 3He is boiled out of the Dilute Phase (3He/4He) mixture and starts the cycle over again.

The rest of it is housekeeping.

A rather clever design, me thinks!

Hope this helps.

Cheers,
Tom
For some reason, I had trouble logging into my old account so I created a new one. Sorry for my late response.

Your response helped me understand the role of capillaries better but I'm still confused about one aspect.

Doesn't the Bernoulli's equation tell you if you have a capillary connecting two champers, it's inside the capillary where the pressure is the lowest?

Wouldn't helium just remain stuck there and refuse to flow to the next stage?

Do you think that the Bernoulli equation is all that there is to know about fluid mechanics, or do you think that other fluid mechanical mechanisms come into play in flow through porous media and capillaries? What do you think is the primary cause of pressure variations in flow through capillaries?

Do you think that the Bernoulli equation is all that there is to know about fluid mechanics, or do you think that other fluid mechanical mechanisms come into play in flow through porous media and capillaries? What do you think is the primary cause of pressure variations in flow through capillaries?
I pictured the capillaries in helium fridges as just thin medal pipes with kinks (sharp bending), which is why I thought Bernoulli's equation is what i needed to focus on. I will have to think more..

I pictured the capillaries in helium fridges as just thin medal pipes with kinks (sharp bending), which is why I thought Bernoulli's equation is what i needed to focus on. I will have to think more..
Think viscous flow, and Darcy's law of flow through porous media.