Visualizing flow with particles can range from using fog machines to watching fallen leaves blowing in the wind. Whether the particles are liquid or solid, close enough together to look like a dye, or far enough apart for individual particles to be seen, the same three conditions are needed:

1. The particles must track the flow. This is not a problem with dyes; dye molecules generally move with the flow, but particles are big enough that they may not follow when the flow turns quickly.
2. The particles must NOT disturb the flow.
3. The particles need high visibility.

1: When will particles track the flow?

Consider a particle in a curved streamline as shown in Figure 1. Assume the particle is small but much denser than the fluid – maybe 4 times denser. Let’s say the curved flow is in the horizontal plane – in other words, don’t worry about gravity making the particle fall. Now, what will the particle path look like compared to the fluid path?

Possible choices: A) It will curve to the inside of the fluid streamline. B) It will track with the fluid. C) It will go straight along a tangent to the streamline. D) It will curve to the outside of the streamline. E) It will curve out away from the streamline.

 

 

 

 

 

Before we get to the answer, consider a different scenario: a bubble, one thousandth as dense, in a liquid. Figure 2 shows the same set of choices.

 

 

 

 

 

 

 

If you’re not sure, here’s a real-life example of the bubble in a more dense fluid (helium in air) :

Figure 3: How to get hit in the head by a helium balloon in a car.

Whaaa? The answer is not intuitive, but Newton’s Second Law (NSL) will help us out. For particles (or bubbles) to track with the surrounding fluid, they must accelerate the same as the neighboring fluid. NSL says that force = mass times acceleration. We have an idea of the relative masses. So what are the forces acting on our particle? With those, we can figure out the motion, the acceleration. Back in the beginning of this Guidebook, we put the forces that act on fluids in two categories: body forces and surface forces. Here, gravity is the sole body force, and we are neglecting it by looking only at motion in the horizontal plane. Surface forces come from the surrounding fluid acting on the particle or bubble, and they can be a combination of pressure (perpendicular to the surface) and shear (dragging along the surface). For very small particles, shear forces will dominate and will drag the particle along with the flow no matter what. But for slightly larger particles – particles that are big enough to be seen easily – pressure forces will also play a role.

 

 

Consider a particle in a pressure gradient, where the pressure on one side of the particle is higher than on the other, as shown in Figure 4. Imagine an equally-sized parcel of the surrounding fluid next to it.

Since both the particle and the fluid parcel are the same size and shape, they will experience the same net force from the pressure field. Newton’s second law says that, for the same force, the more massive particle accelerates slower than the fluid element, and so will lag the surrounding fluid. Conversely, in Figure 5, the bubble is accelerated more quickly by the pressure gradient, and will move ahead of the neighboring fluid.

You may be thinking: OK, where does this pressure gradient come from? Well, Newton’s first law says that to move a particle/fluid element/whatever off a straight line path, you have to exert a force on it. So, going back to Figures 1 and 2, we see that there must be a pressure gradient to create the curved streamline – with low pressure on the inside of the curve and high pressure on the outside. The heavier particle won’t be accelerated into the curve as much as the surrounding fluid, so which particle path will you choose?

In the turning car in the video (Figure 3), the walls of the car push the air inside the car around the turn, and high pressure builds up on the walls doing the pushing. That creates a pressure gradient pointing to the inside of the curve, and that’s why the helium balloon leans into the curve more than the surrounding air. So which bubble path will you choose in Figure 2?

Particle Motion Summary

Particles that are more dense than the surrounding fluid won’t be able to make the turn quite as sharply as the surrounding fluid.

Particles that are less dense than the surrounding fluid will turn more sharply than the surrounding fluid.

Rules of thumb:

• In water or other liquids, particles (of any density) sized 100 µm diameter or less will track most flows.
• In air, particles (of any density) sized 1 µm diameter or less will track most flows.

Next consideration:

2: How can the particles NOT disturb the flow?

As with dyes, injecting a particle-seeded flow into an unseeded flow requires minimizing differences between the two flows, matching: velocity, temperature, viscosity, density, etc. We’ll also want the particles themselves to not disturb the flow.

Soluble/evaporating particles

If the particles dissolve or evaporate in the flow, it’s probably changed the basic properties of the fluid: density, viscosity, and so on. For example, water droplets that evaporate will cool an air flow, which may change the flow’s trajectory. This may or may not be a problem in your flow, but it’s something to be aware of.

Surface tension:

There will be surface tension effects between particles and the flow, particularly in liquids. Floating particles on a liquid surface can have a big effect, sometimes called the “Cheerios Effect” when the particles clump together. Again, something to watch out for.

Chemical reactions

These can change your flow big time! For example, a flammable particle in a combusting flow can distort the flame region and add unwanted heat and exhaust products.

Increased density

Solid particles in air or water are much heavier than either fluid. Even if poor tracking isn’t an issue – say, in a slow flow – they will settle due to gravity, dragging fluid along with them.

Particle-particle interaction

If the number density (number of particles per unit volume) is high enough, particles will interact with each other through collision, drag or jamming. This creates non-Newtonian effects. Newtonian fluids (e.g., water) have a linear relationship between a shear force and how far the fluid will move in response to that shear in a certain amount of time. Linear means that if the force doubles, the distance traveled doubles. Non-Newtonian fluids behave differently . The classic example is oobleck, a mixture of corn starch and water. When sheared by stirring, the corn starch particles jam together, effectively turning the oobleck into a solid, but when stirred slowly, they can slide past each other and the oobleck remains a fluid . This means the force-displacement relationship is nonlinear, i.e. non-Newtonian. If the mixture is too dilute, the particles don’t interact and the effect is lost.

When oobleck is continually sheared by vibration, for example, you can get strange, creepy flows, as shown in Figure 6.

Figure 6: Instruction on how to make oobleck “dance” on a loudspeaker. Babble Dabble Do, 2020

3: How do we make the particles visible?

Particles scatter light. ‘Scatter’ is a general term: in this context it means the sum of reflection, refraction, diffraction, and absorption , i.e. ,pretty much everything that a particle can do to light. These terms were all defined back on the Dye Techniques 2 page. What happens depends on the size of the particle compared to the wavelength of the light that hits it, and whether the particle is transparent, reflective, or neither. This is a complex topic. The book by van de Hulst  from 1957 is a good place to start, but there are quite a few developments since then. For Flow Vis purposes let’s begin  with how particle size affects scattering.

Scattering Regimes

Particles for flow vis typically range from 100 µm (about the diameter of a human hair) to 1 µm (one micron) or less. Visible light wavelengths range from 1/3 to 3/4 µm.  So the largest useful particles are much larger than the wavelength of light; this is called the Fraunhofer scattering regime. If the particle size is on the order of the wavelength of light (between 1/10 and 10 times λ), then it’s in the Mie scattering regime. Particles smaller than 1/10 λ are in the Rayleigh scattering regime.

Fraunhofer

Scattering from the larger particles is complex and depends on the particle shape, the particles’ index of refraction, its absorption spectra, the incident light, and the viewing angle. Absorption and Scattering of Light by Small Particles, Bowren and Huffman, 1998 provides a detailed introduction but this area is changing rapidly, driven by solar cell and medical imaging technologies.

Figure 7 shows a scattering intensity plot for a large particle, with strong forward scatter (180 degrees from the incoming light), weaker back scatter, and several side lobes. The forward scatter is mostly from Fraunhofer diffraction around the particle. When driving through rain at night, you may have noticed that it’s easy to see raindrops in an oncoming car’s headlights (forward scatter) but harder to see raindrops in your own headlights (back scatter). Depending on the particle you use, you may see one or more strong side lobes – often around 120 ⁰ – but it’s worth varying your viewing angle to find the best scattering efficiency.

Mie

The Mie scattering regime includes particles at the small end of the useful range for flow visualization. This range is limited because the scattering efficiency drops rapidly for particles smaller than one micron. However, this range may be extended by new cameras with better low-light sensitivity and by laser diode light sources that provide intense light. In the Mie regime, the side lobes become smaller, while forward scatter  remains stronger than back scatter.

Rayleigh

The Rayleigh regime includes scatter off of molecules, including those of air. The scattering efficiency is quite low since particles much smaller than the wavelength have a hard time disrupting the wave, but you can see Rayleigh scattering from air in the focus region of a strong laser. You can also see it in the sky on any clear day. All air molecules – N₂, O₂ and CO₂ – are around about 1/3 micron in size, a little smaller than visible light wavelengths, but the blue wavelength comes closest at 0.45 µm. So with enough molecules and a strong light source (!) we get a blue sky. Violet is actually a shorter wavelength, but there is less of it in sunlight, and our eyes aren’t as sensitive to it, so we see the sky as blue. Rayleigh scattering is much less dependent on viewing angle than the other regimes, meaning it scatters in all directions, leading to the uniformity of the sky.  At dawn and dusk, when the sunlight passes through even more atmosphere, we can see the weaker interactions of air molecules with the longer wavelengths, plus the scatter from any particulate contaminants that scatter the long yellow and red wavelengths, leading to the warm colors of sunrise and sunset.

Particle Color

 

Scattering in the Rayleigh and Mie regimes is “elastic,” meaning that light hitting the particle bounces off, unchanged in energy, so the scattered light’s color is the same as what hit the particle. Clouds in the sky are white because sunlight is white and atmospheric water is colorless and transparent. But solid particles often have color, absorbing most visible light and reflecting only the light frequency corresponding to that color. For example, finely ground solids from various minerals are the main ingredient for most paint pigments. The smaller the particles, the more intense the color . The number density of particles in paint is also quite high. In contrast, seeding particles for air are often made from transparent liquids and are on the order of microns in size. Particles of that size have poor light scattering efficiency, so the effect of color is reduced. An exception is colored smoke bombs, when the particle number density is high. At those high concentrations, however, the smoke is toxic  . Figures 8 and 9 illustrate the use of smoke bombs to visualize wing tip vortexes. Notice how the smallest particles at the center of the vortex have no color.

Figure 9: This 29-second video taken in the 1970’s shows a C-5A aircraft undergoing a wing vortices test at NASA’s Langley Research Center, Hampton, VA. Published by NASA Armstrong Flight Research Center in 2017.

References