We started the overview by listing the choices, or steps to making a flow visualization:
- Flow phenomenon: Water boiling? Faucet dripping?
- Visualization technique: Add dye? See light distorted by air/water surface?
- Lighting: very important! Often the source of the worst visual problems.
- Visual acquisition: Still? Video? Stereo? Time lapse? High speed?
- Post processing: creating the final output. Editing, at least cropping the image and setting contrast.
We talked about framing the flow phenomenon as being the result of forces (surface, body, etc.) and keeping in mind “Why does it look like that?” For Choice 2 we saw how marked boundary techniques work, and we covered a little bit of Choice 3 – how to best light those kinds of scenes – at the same time. Now let’s talk about another big category of flow vis techniques:
Flow visualization techniques can be divided into three categories: A) marked boundary techniques, B) refractive index techniques, and C) particle tracking methods. We’ll look briefly at examples of each and how they work, and then come back to them in more depth in later sections.
A) Marked Boundary Techniques
Marked boundary techniques are used to visualize the boundary between two similar fluids, such as a jet of air from a fan contrasted with the rest of the air in a room. The idea is that one fluid is seeded with dye or particles which scatter or absorb light. The other fluid is transparent, not scattering or absorbing light. The boundary then can be seen between the two. In Figure 4, a jet of air coming out of a long slot (perpendicular to the page) carries stage fog and rolls up into a spiral, like a jelly roll, or a flat coil spring. A sheet of green laser light then slices through the roll, revealing the spiral. We can see the boundary between the green fog that came out of the slot, and the surrounding darkness, and little detail within the green or in the black. In this example, we are seeing light reflected off the fog aerosol. Contrast is heightened by keeping the rest of the room as dark as possible.
In contrast, Figure 6 shows a bright background, visible through the transparent medium, while the fluid marked with ink absorbs light. Shining additional light on this dark ink would not enhance the contrast, but adding light to just the backdrop would.
One more common example of the marked boundary technique is a flame (Figure 7). The yellow you see is soot glowing via black body radiation. The blue at the base is from intermediate combustion products, specifically C2 and CH molecules, that are excited and give off blue photons as they relax. Since the flame emits light, adding any light to the scene is likely to decrease contrast and make the flame less visible.
To conclude, marked or ‘seeded’ boundary techniques are characterized by dense seeding; within whatever has been used to mark the flow, you can’t see individual particles or molecules, you can only see the boundary between the marked fluid and the surrounding transparent fluid. This is a pretty easy technique to both create and understand.
Please choose environmentally benign materials such as food or personal care products. CU Boulder allows no chemicals to be poured down the drain, and the City of Boulder actually samples the CU sewers to make sure this rule is followed.
B) Refractive Index Techniques
First, what is the index of refraction?
Figure 1: Scale model of the Earth and the Moon, with a beam of light traveling between them at the speed of light. It takes approximately 1.26 seconds. By en:User:Cantus, CC BY-SA 3.0 <http://creativecommons.org/licenses/by-sa/3.0/>, via Wikimedia Commons
Maybe something to do with light bending? Maybe the speed of light? Read on!
The index of refraction (eta, η) is the speed of light in a vacuum (c) divided by the speed of light in whatever medium you are interested in (e.g., air, water, glass, plastic, etc.) : η = c / cmedium. So if the index of refraction is 2, then the speed of light in the medium is half the speed in vacuum. In air, light is hardly slowed at all, and η = 1.00029. In glass it’s slowed by 1/3 so η ≈ 1.5. In water and plexiglass η ≈ 1.3. Note that η is about the same in water and plexiglass, so it’s hard to see the interface between the two; a piece of plexi will almost look invisible underwater. There are some cool flow vis techniques that depend on this fact; we’ll cover them when we go over refractive index techniques in more depth later.
Normally, at the interface between media with different refractive indexes, light will bend according to Snell’s law: η1sin(θ1) = η2sin(θ2). The reason it bends has to do with the wavelength of the light, but we’ll get into that later too. For now, just trust that a light ray going from air into water or glass will take a nosedive as illustrated in Figure 2, and do the opposite coming out.
Examples of Refractive Index Techniques
There are quite a few flow vis methods that make use of how the index of refraction varies between materials (fluids and solids), and within materials at different temperatures. Some examples will be familiar, like how liquids in air can act like lenses (Figure 3), and soap bubbles and oil films change color. But there are less familiar techniques, as well, like schlieren, shadowgraphy, interferometry and holography.
Schlieren and shadowgraphy, for example, use the dependence of the refractive index on fluid density to show where there are temperature gradients in a transparent fluid. Schlieren has been used extensively during the pandemic to study the effect of masks on human exhalations, as shown in the video below.
Figure 4: Surgical masks can be effective at blocking aerosols from singing, depending on the fit and layers of material. Here vocalist Olivia Lerwick performs the same vocal exercise without a mask, and then with a three-ply mask. Schlieren imaging shows that her exhalation is blocked by the mask. A bit leaks out the top next to her nose, even though the nose band is fitted. Schlieren imaging was performed at the University of Colorado Boulder in July 2020 by Abhishek Kumar, Tehya Stockman and Jean Hertzberg. Other project personnel: Shelly Miller, Marina Vance, Darin Toohey, Sameer Patel.
Schlieren works by using a point (small) light source (small LEDs work great) and a lens or curved mirror to generate parallel, collimated light . Warmer gases deflect some of the light slightly. When the parallel light is brought back to a point by a matching lens or mirror, the deflected light misses the point (heh) and is blocked by a ‘knife’ or razor blade, as shown in Figure 5. The warm gas shows up in the camera image as dark regions. This isn’t the only way to set up a schlieren system but it’s the easiest to understand. Shadowgraphy works the same way, but without the razor blade. The warm gas area is still darker, but the deflected light shows up elsewhere in the image, decreasing the contrast.
Another type of refractive index technique is streaming birefringence . Micron sized mica flakes and a few other substances have two indices of refraction. As a result, when viewed through polarized light there are colored fringes that show regions of shear stress, as shown in Figure 6.
This type of visualization uses a ‘rheoscopic’, literally ‘current showing’, fluid that shows fluid flow throughout, and depends on the fluid motion; it won’t work in a stagnant flow. You may be familiar with some; pearlescent soaps and shampoos contain microscopic stearic acid crystals. The flow organizes the crystals to some extent, and various degrees of shinyness from the crystal orientation correlate to the flow state. It’s actually pretty easy to make your own rheoscopic fluid from a can of shaving cream .
C) Particle Tracking Techniques
When particles are dispersed throughout the flow, their motion can be detected in a couple of ways. The particles or ‘seed’ can be solids – such as aluminum or mica flakes used in water – or fluids – like tiny gas bubbles in water or liquid aerosols in air. The seeding can be similar to the larger markers used in boundary techniques, but with a much lower number density (particles per unit volume), so that individual particles can be seen.
Figure 8 is an example of a particle tracking image: a long exposure that shows pathlines, the trajectories that individual particles take. Pathlines are the same as streamlines and streaklines if the flow is steady (not changing in time), but are subtly different if the flow is unsteady, as it is in this case .
The techniques and examples we’ve seen so far are all qualitative. If the image can be analyzed to give numerical information about the flow, it becomes quantitative. One important quantitative flow vis technique is particle image velocimetry, or PIV. In PIV, the particles in the flow are typically illuminated by a thin sheet of laser light, in a flash, or a short exposure. The particles in such an image typically look like a starry night sky, as seen in the photo of a human cough , Figure 9. A second image taken a short time later shows that the particles have moved slightly. The motion is analyzed using a cross-correlation algorithm performed on small areas (windows) in the image, resulting in data, as shown in Figure 10. Each arrow represents the flow velocity vector computed at the base of the arrow, showing the direction and the speed of the flow there .
So that’s a quick overview of the basic flow vis techniques. Next we’ll address lighting, image acquisition and post-processing.