# Progress Update

Ever wonder why the water coming out of a faucet doesn’t stay “smooth” as it goes rushing to the drain? Ever wonder why rain doesn’t come down from the sky in columns but rather, individual, separate droplets? Although witnessed for centuries, it wasn’t until 1878 that Lord Rayleigh was able to accurately identify a common household phenomena that all of us have noticed since we were children: appropriately coined, Rayleigh Plateau Instability. Although used in many different applications and extensively studied in the laboratory setting, this fluid instability has had little to no inexpensive, repeatable experimental setups that highlight the beautiful optical visualizations that can arise from it. This phenomenon has virtually no accessible and visually appealing demos for a young scientist’s first look at fluid mechanics. Since the Rayleigh-Plateau phenomena is ubiquitous, visually appealing, and demonstrative of fluid physics, the development of such a demo would be highly valuable for any student to gain a first look at the versatility of fluid mechanics.

To put it simply, Rayleigh-Plateau instability occurs in falling streams of fluid (i.e. water from a faucet or even rain) and describes how the stream, at some critical length, loses its cylindrical, “smooth” shape and breaks apart into individual droplets. Although the derivation is beyond the scope of this demo, this phenomena is mainly governed by surface tension, since liquids tend to minimize surface area in order to minimize their energy state. By knowing the relevant parameters of the fluid that we are working with, we will then be able to hypothesize at what length the stream will begin to break apart into its individual droplets. These scientific observations lead naturally into a lab experiment, where, perhaps, a student is working with an unknown fluid and it is up to the student to measure the critical length among other parameters in order to gain an understanding as to what liquid is being observed.

In our design process, we started with this problem: how do we make fluid mechanics engaging, accessible, and quantifiable for high school students? Fluid mechanics is often an intimidating and inaccessible field, especially when you’re just starting to learn calculus. To maximize appeal and approachability, we decided to research and design an in-class fluid mechanics demonstration and experiment that would allow students to understand a fluid phenomena they see everyday.

That’s why we picked the Rayleigh-Plateau Instability, described above, for the topic of our demonstration. Despite its intimidating name, it is a simple, common, and visually engaging phenomena that has a lot of exciting possibilities for flow visualization and data collection.

To start solving this design problem, we needed to do some research. We combed through academic papers on the instability to try to get a better understanding of the science behind it (Breslouer, 2010; Zeleny, 2014). Several of the sources we read helped us to get a functional understanding of the factors that affect the phenomenon. For instance, the greater the size of the hole the fluid exits from, the longer the fluid takes to break into droplets. Through this, we were able to make a digital model of the instability, which shows how the fluid stream changes (COMSOL Application Gallery).

Next, because no one in our literature review had developed an accessible and inexpensive way to observe this instability (Fragkopoulos et. al., 2015), we had to gauge whether it was even possible. We started by 3D printing our own nozzles, which we could use to test different fluids. However, we made the printing resolution too low and water leaked from multiple holes in the bases of the nozzles.

We still wanted to gather preliminary data, so we found clear plastic cups and drilled different-sized holes in the bottom. Then, we simply filled up the cups, held them above an empty an empty bin, and let the fluid drain from the holes. We also taped a meter-stick on the wall behind the cup. We wanted the fluid break down into droplets to be observable to the naked eye and quantifiable using a smartphone camera. This will help make our demonstration visually appealing and allow high school students to collect real data on the instability critical length.

We tested water, salt water, and glycerol, which is a very thick, viscous fluid. Water and salt water both developed observable droplet instability within half a meter. The difference in density between the salty and fresh water produced different critical lengths, which we were able to observe via individual frames from an iPhone video.

From this early data, we developed a plan for creating a modular and adaptable classroom demonstration. We sketched out a variety of designs and discussed what we liked and disliked about them, combining our best ideas into a design we wanted to prototype. We wanted the demo to be visible, easy to create, and to have options based on school budget. So, we picked a design that could be made from a variety of materials and that could be supplemented with additional features like strobe lights or a phone stand.

Then came time to prototype.

The basic structure consists of a pump that cycles water between the two plastic tubs. There is a 3D-printed nozzle in the top tub so the water pressure stays consistent throughout the experiment, but this nozzle could be switched out for others with different exit hole sizes. The top tub is supported by PVC pipes and a wooden backboard that has a scale (in cm) to help quantify the flow.

After building this prototype, a few things became apparent pretty quickly. It was difficult to keep the seal between the nozzle and the upper tank water tight and it was difficult to see the phenomenon clearly without an additional light source (like the phone flashlight used in the above video). For our initial prototype, we decided to scavenge for as many materials as possible both to save our budget for the final design but also to see if it was possible to build a functional demo with limited resources. We had hoped to use plexiglass to build platforms for the tubs, but the “plexiglass” we found turned out to be a different type of plastic and immediately melted in the laser cutter. We were able to use plywood, but noted that it blocked a lot more light and was more subject to warping when in contact with the demo fluid. Similarly, our nozzle did not create a watertight seal against the plastic tub, so we struggled to create a seal and keep the nozzle level. Moving forward, we want to focus on refining the demo parts so that they are easier to use and more consistent.

For future prototyping and testing, we’ve contacted two different high schools to gauge their interest and get feedback on ways to make this demonstration more useful to actual teachers. We’ll use their feedback to guide our implementation of various features and to design effective curricular resources, such as a lab report assignment and rubric. In addition, we plan to implement and test different ways to make the flow instability more visually exciting through effects like strobing light, projecting a cast shadow, and using a fluorescent fluid in a blacklight.

References

Breslouer, Oren. 2010 Rayleigh-Plateau instability: Falling Jet, Analysis and Applications. Princeton University, Complex Fluids Group.

Fragkopoulos, A. A., P. W. Ellis, and A. Fernandez-Nieves. 2015 Teaching Rayleigh-Plateau Instabilities in the Laboratory. EUROPEAN JOURNAL OF PHYSICS 36, 5.

Jet Instability – Moving Mesh. Stockholm, Sweden: COMSOL Application Gallery. Retrieved from https://www.comsol.com/model/jet-instability-8212-moving-mesh-4650

Zeleny, Enrique. 2014 Plateau-Rayleigh Instability in Water Stream. WOLFRAM Demonstrations Project.