Designing Experiments Near Absolute Zero
As a mechanical engineer specializing in fluid dynamics, I am interested in studying the behavior of liquid drops and jets and their interactions with solid and liquid surfaces. The properties of the liquid and the surrounding gas can have significant effects on the dynamics. I conduct experiments systematically varying these properties to improve our understanding of the underlying physics of these interactions. Liquid helium is interesting to study because over a small temperature range it exhibits large variations in important thermodynamic and transport properties such as density, viscosity, surface tension, and thermal conductivity. One of the main challenges in working with liquid helium is that it does not become a liquid until near absolute zero.
Absolute zero is the coldest temperature possible (-273.15 °C, -459.67 °F) and is the start of absolute temperature scales, such as the Kelvin scale (K), where 1 K has the same magnitude as 1 °C. Most matter becomes solid as this temperature is approached, except helium. Helium does not become a liquid at atmospheric pressure until 4.2 K (-268.95 °C). If the temperature is further reduced below 2.17 K, the liquid becomes a superfluid, which among other things means that the liquid no longer has viscosity, or in other words, it has no resistance to flow. The lowest energy state for helium is actually as a liquid, and to solidify helium the pressure has to be increased to above 20 atmospheres.
How to Liquefy Helium
We perform experiments within a custom-built cryostat with optical access to the experimental cell. The cell is suspended beneath 3 sequential stages of cooling plates and is protected by 2 gold-plated, copper radiation shields all of which are contained within a cylindrical stainless-steel vacuum chamber. Figure 1 shows a photograph of the cryostat along with a simplified drawing of the interior.
Figure 1: Cryostat for studying the dynamics of liquid helium at KAUST with a line drawing schematic of the interior of the cryostat.
The first step in the cooling process is to isolate the cooling stages and cell by evacuating the stainless-steel vacuum chamber using a turbomolecular pump. This reduces the pressure within the chamber to one ten-millionth of an atmosphere (0.0000001 atm) at room temperature. We then turn on a commercial cryo-refrigerator, which cools the first stage to 40 K and the second stage to roughly 4 K. At this point, we can introduce helium gas to the cell and it will condense into a liquid.
To reach the lowest temperatures, we thermally isolate the 1 K plate from the 4 K plate. Then a custom evaporative helium refrigerator cools the 1 K plate and the experimental cell to our bottom temperature of 1.2 K. The entire cool down process takes about 24 hours to go from room temperature to the bottom temperature, and as it cools the pressure in the stainless-steel chamber reduces an additional 2 orders of magnitude to one-billionth of an atmosphere. The warm-up process also takes about a day.
A Liquid Helium Experiment
The following example presents an experiment from a recent study on the breakup of liquid helium jets. Liquid jets will break up into droplets in various ways depending on the flow velocity of the jet and the properties of the gas and jet. Understanding the breakup behavior is important for many applications such as in fuel injection in internal combustion engines or inkjet printing. Figure 2 shows examples of these breakup regimes. One of the challenges with this experiment was designing a method to generate a jet of liquid helium in both its normal fluid and superfluid states because there is not a large reservoir of liquid helium to draw from nor is there a pump that can fit within our experimental cell and operate at these extremely low temperatures. The solution that we developed uses a nozzle with a pressure impedance connected to a cylinder of gaseous helium that is at room temperature. The helium gas enters the cryostat through a small pipe and passes through several heat exchangers to cool down and liquefy. The pressure impedance ensures that the flow rate is sufficiently small to allow the helium to liquefy before coming out of the nozzle. We then control the velocity of the jet by adjusting the pressure of the gas. This process increases the heat load on the cooling stages and can significantly raise the temperature of the cell if not monitored carefully.
Figure 2: Various modes of jet breakup for a 50 micrometer jet of liquid helium at a temperature of 1.5 K.
By designing experiments for this environment, I have learned 3 lessons that can be applied to a broader variety of design situations.
Lesson #1: Sometimes you only have to innovate the last 1% of the solution.
In order to cool the helium from room temperature to the superfluid regime, there is a commercially available product that can achieve 99% of the goal. However, it is unable to reach the target, and the last 1% is vitally important. Instead of trying to develop a new product and process that could cool from 295 K to 1 K on its own, we only needed to design a solution to cool the final 3 K. The custom evaporative refrigerator that we use, in fact, only works to cool the last 1% and is ineffective outside of that range.
In other design problems, there may already exist a product or process that achieves the majority of the goal. You can leverage the already existing technology allowing you to focus your efforts on creating innovative solutions to meet the last 1% of the target. Many times this 1% is what makes the difference between ordinary and extraordinary.
Lesson #2: There’s no substitute for testing the design in the intended environment.
Once the cryostat is closed and cold, there is no way to alter the experimental setup within the cell. This means that each experiment has to be carefully planned and constructed in order to run while only being able to control the temperature and pressure within the cell. Each time we alter the experiment we do the necessary modeling and calculations to predict what we think will happen and do mockup tests at room temperature. However, there is no way to simulate the extreme cold and the odd behaviors of superfluid helium. A design that works in theory and would work with normal liquids may not ultimately be feasible because superfluid helium can escape through the tiniest of imperfections. All of the planning and theoretical design won’t predict exactly how the apparatus works in reality. Even though there are time and money costs with testing a new design, there’s no substitute for testing in the intended environment. The feedback gained will inform the next iteration of the design or the need for an altogether new design.
By testing your design in its intended environment, you can learn many things that are difficult if not sometimes impossible to learn otherwise. Perhaps a target user will interact with or use your product in a different way than you had imagined or maybe there are part clearance or interference issues that you had not yet considered. Building and testing mock-ups and prototypes throughout the design process can help you to develop a good design faster than designing on paper alone.
Lesson #3: Know when to iterate a design and when to let it be.
I am a perfectionist at heart, and usually, I will have ideas on how to tweak a design even if it is working well enough. When I am doing experiments in normal laboratory settings with a normal liquid like water, the cost of tweaking the experimental design is relatively low. Sometimes the tweaks are worth it and other times not. In the cryostat, there are times that our design is deficient in some regard. Before we make the decision to warm up and alter the design, we carefully consider if we can collect the data we are seeking with the current design, or in other words, if the current design is good enough even though it is not perfect. If we decide to warm up and alter the design, there is the possibility that the alterations do not solve the underlying problem and we could introduce unforeseen issues with the system that could delay progress by weeks or months. When the experiment has a fatal flaw, the decision to warm up is easy, but if the target data can be collected from an imperfect system, we have to weigh the value added by altering the system. In my experience, it has often been better to collect the data while everything is working rather than tinker to make the system perfect.
In your designs, if you are able to meet your target, how much value is added by “perfecting” the design versus letting it be? If there is only a little added value, it may not be worth altering because you can easily introduce unforeseen interactions that could worsen the overall product.
Summary
As you embark on your design adventures, remember that you do not always have to create a completely brand new solution, sometimes you only need to innovate the last 1% of a pre-existing solution to reach your design targets. Although you will spend much time designing your solution on paper, there is no substitute for testing your design in your intended environment. Lastly, seemingly small changes to your design can have unforeseen major consequences, so evaluate when your design should be iterated or if it is sufficient for your purposes. Applying these lessons in my own work has helped me to successfully design and conduct many experiments.
