Tyler L’Hotta

Dr. Jean Hertzberg

Flow Visualization 5151-002

22 September 2024

Get Wet | Cappuccino Waterfalls

                A morning coffee on its own is unassuming; the details hidden within the favorite libation of many reveal the key to unraveling the underlying phenomenon that shape our world. I set out to capture the complex fluid flows I see through the ice laden glass that brings light to my mornings. Plopping a dose of espresso into frothy milk has the potential to produce small whispers of coffee enriched flow that drizzle down the inside of the glass as water may trickle down a rock face.

                Creating the foundations of the set, a room temperature 250 ml glass with high transparency and minimal features was filled just under halfway with crescent shaped ice cubes. 50 ml of 4 °C creamer, Chobani Sweet Cream, was combined with 150 ml of whole milk, at the same temperature, and frothed in a Keurig Standalone Frother on the cold setting. 28 ml of espresso was prepared from whole beans, brewed at 8bar for 29 seconds, giving a firm crema at a temperature of 90 °C. The frothed product was added to the glass 8 cm above the top of the glass, and sat for six seconds before the espresso was added 3 cm above the top of the foam, directly in the center of the rim.

                The primary driving forces behind the fluid flow relate directly to the kinetic energy imparted with to the system by pouring in the espresso, the temperature gradient providing movement once the espresso has been poured, and finally the difference in density between the frothed mixture, and the coffee beneath.

The density and viscosity were found from a paper, “The experimental data on the density, viscosity, and boiling temperature of the coffee extract” published by A P Khomyakov, S V Mordanov and T V Khomyakova, from the department of chemical plant machinery and equipment, Institute of Chemical Engineering, Ural Federal University, Ekaterinburg, Russia. I extracted the exact figures used based on a high temperature, high dry substance mass fraction datapoint. The speed and distance were found by measuring the movement of espresso in a given frame found to be 2 centimeters over 1/60^th of a second.

                The secondary fluid flow was the phenomenon which I wished to capture, the small trails of white fluid falling from the frothed foam cap:

My initial thought behind this flow was that it was similar to the Guinness beer phenomenon. After reading a paper from the Nature Scientific Reports, Watamura et al., 2019, that outlines the gravity current instability behind the famous flow, I found that it is unlikely to be related. The flow I observe occurs after the beverage has reached steady state just after the RT mixing, and upon closer inspection, the flows do not seem to include bubbles from the froth. Instead, I believe that as the foam decays at nucleation sites across the interface, the comparatively warmer suspended milk and creamer droplets begin to cool and sink into the iced coffee-milk mixture beneath them, forming small trails with minimal disturbances, suggesting laminar flow, especially regarding the slow movement of 0.6cm in 1/60^th of a second. The greatest contrast between the freshly fallen froth and the coffee below is seen just below the interface, with dilution occurring further down the flow.

                Regarding the methods of visualization, the only controlled aspects of the scene were lighting and background: no alterations were made to the fluid itself to enhance visibility. The background was selected as a black fluid tolerant tablecloth that could withstand a spill without altering the appearance of the fabric, steamed and hung such that it produced no creases that may be visible in the final filming. The scene was recorded in the long hours of the evening such that no external light came through windows; the only source was a singular 5500 K spotlight bulb. The color temperature was selected to be neutral between warm and cool colors. The spotlight was aimed such that it minimized glare on the glass.

                The raw video itself was shot at 3840×2160 at 60 frames per second on a Samsung S24+. The quality and framerate were a balance between the highest quality, 8K, and the highest framerate 120 fps, available to me. I utilized my phone’s telephoto, 3x optical zoom, lens at a distance of 40cm from the glass with the intention of obscuring the reflection of the phone in the glass, while letting the glass completely fill the image with a field of view of 3.5”x6.22”. I started with minimizing the ISO to its lowest setting, 50, in an attempt to reduce noise in my dark background. I then set the shutter speed to 1/60 to achieve the exposure I desired. In the editing of the video, I was paywall limited to 1920×1080 30fps in Microsoft Clipchamp, which I found rather disheartening. I chose to only increase the contrast and saturation of the clip by a few points to give the background an inky black appearance against the beverage. I enjoy the visual feeling of the glass existing alone in space, I feel that it helps focus the mind on the flow at hand.

Before	After

After reflecting upon the video, I find myself genuinely pleased with the intricate flow patterns captured in my morning brew. The interplay of colors against the glass background evokes a sense of wonder. However, to delve deeper into the specific flow phenomena that intrigue me, I intend to reshoot using the standard 1x optical zoom lens at a much closer range. My aim is to reveal the subtle waterfalls with greater clarity, seeking a more concrete understanding than my initial observations provided. Given the relatively slow nature of these flows, I plan to record in 8K at 30fps for greater fidelity of the smallest details. Investing in the premium post-processing software will ensure the quality aligns with my camera’s capabilities. Remarkably, I am content with the existing setup, lighting, and camera settings. Sometimes, consistency yields the most satisfying results. In the editing process, I envision retaining the captivating shot of milk and espresso being poured. However, I’ll strategically introduce a glimpse of the desired flow at the video’s outset, drawing viewers into the narrative before culminating with the mesmerizing waterfalls.

References

Andrew W. Cook and David Youngs (2009) Rayleigh-Taylor instability and mixing. Scholarpedia, 4(2):6092.

A P Khomyakov et al 2020 IOP Conf. Ser.: Earth Environ. Sci. 548 022040

GuideRealm. “How To Extract Frames From A Video – Full Guide.” YouTube, YouTube, 13 Sept. 2023, www.youtube.com/watch?v=seUvEd-UtxA.

Sharp, Nicole. “Rayleigh-Taylor Instability.” YouTube, YouTube, 17 Nov. 2014, www.youtube.com/watch?v=bW4526vHnY0.

Watamura, T., Iwatsubo, F., Sugiyama, K. et al. Bubble cascade in Guinness beer is caused by gravity current instability. Sci Rep 9, 5718 (2019). https://doi.org/10.1038/s41598-019-42094-0