The role of capillaries in a dilution refrigerator

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Discussion Overview

The discussion revolves around the role of capillaries in dilution refrigerators, focusing on their function in maintaining pressure and preventing the re-evaporation of liquid helium during the cooling process. Participants explore the implications of fluid mechanics, particularly in relation to Bernoulli's equation and other mechanisms affecting flow through capillaries.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that capillaries act as flow restrictors on the high-pressure side of pumps, helping to maintain back-pressure to avoid helium re-evaporation.
  • Others argue that the capillaries provide significant surface area for thermal transfer from the 3He, which is crucial for the cooling process.
  • A participant questions whether the pressure inside the capillary is indeed lower than the pressure before and after it, suggesting that this might impede helium flow to the next stage.
  • Another participant raises the question of whether Bernoulli's equation is sufficient to explain fluid mechanics in this context, suggesting that other mechanisms may also be relevant.
  • Some participants mention the importance of considering viscous flow and Darcy's law when discussing flow through porous media and capillaries.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the role of capillaries and the application of Bernoulli's equation. There is no consensus on whether Bernoulli's equation alone can adequately describe the fluid dynamics involved, indicating ongoing debate and exploration of the topic.

Contextual Notes

Participants acknowledge the complexity of the terminology and concepts involved, with some expressing confusion over the explanations of the Dilute Phase and Concentrated Phase. There are indications of unresolved assumptions regarding the behavior of helium in capillaries and the interplay of different fluid mechanical principles.

Foreverlearning
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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://dicarlolab.tudelft.nl/wp-content/uploads/2012/10/Pobell_3rdEd_Ch7_The3He%E2%80%934He-DilutionRefrigerator.pdf

http://www.roma1.infn.it/exp/cuore/pdfnew/Fridge.pdf
 
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Foreverlearning said:
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.
Foreverlearning 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
 
Tom.G said:
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?
 
Chestermiller said:
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..
 
blackwidow123 said:
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.