What Tube Length Is Needed for Helium-4 Flow at 4.2K?

[coolnessitself]

I've got a very small tube (about .01" outer diameter, I can't recall the inner diameter $D$ at the moment) of length $L$. It's going to run from a helium bath to a near vacuum ($\Delta P$ ). I'm trying to calculate the length of this tube required to get a flow of $\dot{N}$ (in mols or liters for example) of Helium-4 (viscosity $\eta$) through the tube at temp $T=4.2K$. Several equations I've looked at have given drastically different results, and I'm guessing they just fail in this regime of something very small. Anyone know a good model or approx for this type of thing?

 

[cliff]

I can't offer much help on a correct formula. But I'll throw this in as a general comment. When the diameter of a tube becomes less than a millimeter, the laws of nano physics start coming into play with the ever decreasing diameter of the tube. And then there is the flow characteristics of Helium 4. That in itself goes against the norm in flow characteristics in the normal world. Still... there is quite a bit on the web on nano flows.

 

[sir-pinski]

There are a few factors to consider when calculating the length of the tube required for a specific flow rate of helium-4 at a low temperature of 4.2K. The first factor is the viscosity of the helium-4, which is significantly lower at low temperatures compared to room temperature. This means that the flow rate will be higher for a given pressure and tube diameter.

The second factor is the pressure difference ($\Delta P$) between the helium bath and the vacuum. This pressure difference will determine the driving force for the flow and will directly affect the flow rate.

The third factor is the tube diameter ($D$), which will also have a significant impact on the flow rate. As the tube diameter decreases, the flow rate will decrease due to increased resistance to flow.

To accurately calculate the required length of the tube, you will need to use the Hagen-Poiseuille equation, which takes into account the viscosity, pressure difference, and tube diameter. However, as you mentioned, this equation may not be accurate for such small tube diameters and low temperatures.

In this case, it may be more appropriate to use a computational fluid dynamics (CFD) model to simulate the flow and determine the required tube length. CFD models take into account more complex factors such as fluid compressibility and non-Newtonian behavior, which may be relevant in this scenario. Additionally, CFD models can accurately capture the behavior of fluids at very small scales.

Overall, it is important to consider all the relevant factors and use appropriate models or simulations to accurately determine the required tube length for your specific scenario.