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, or close enough together to look like a dye, or far enough apart for individual particles to be seen, the same three considerations must be made:

1. The particles must move accurately with the flow, must track the flow. This is not a problem with dyes; dye molecules generally move with the flow just fine, but particles are big enough that they may not follow when the flow turns quickly.
2. We want the particles to NOT disturb the flow.
3. We want the particles to show up – to have high visibility.

1: When will particles track well and be good tracers?

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 just yet. 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, with a bubble, maybe 1/1000 times less 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? Then we can figure out the motion, the acceleration. Back in the beginning of this Guidebook, we looked at forces that act on fluids and put them in two categories, body forces and surface forces. Here, gravity is the only body force, and we are neglecting that by looking only at the motion in the horizontal plane. Surface forces come from the surrounding fluid acting on the particle or bubble, and 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 big enough to be seen easily, pressure forces will also play a role.

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

Since both things 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 will accelerate slower than the fluid element, and so will lag the surrounding fluid. Conversely, in Figure 5, the bubble will be accelerated more quickly by the pressure gradient, and will move ahead through the neighboring fluid.

You may be thinking OK, where does this pressure gradient come from? Well, Newton’s first law says that to get a particle or fluid element or whatever to move 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 has to be a pressure gradient to create the curved streamline, with low pressure on the inside of the curve and high pressure on the outside. In the turning car in the video (Figure 3), the walls of the car push the air volume inside the car around the turn, and high pressure builds up on the walls doing the pushing. Now you have a pressure gradient pointing to the inside of the curve and that’s why the helium balloon leans into the curve. So which bubble path will you choose in Figure 2?

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

Rules of thumb:

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

Next consideration:

2: We want the particles to NOT disturb the flow.

Like with dyes, if we are injecting a flow seeded with particles into an unseeded flow, we’ll need to minimize differences between the seeded and unseeded flows: match 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, you’ve probably changed the basic properties of the fluid: density, viscosity, and those other thermodynamic properties. For example, water droplets that evaporate will cool a flow of air, which may change the trajectory of the flow. 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. Any floating particles on a liquid surface can have a big effect. Again, something to watch out for.

Chemical reactions

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

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, and drag the fluid along with them.

Particle-particle interaction

If the number density (number of particles per unit volume) is high enough, particles are more likely to interact with each other by collision or drag. This creates non-Newtonian effects. Newtonian fluids, i.e water, has 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 cling to each other and the fluid seems to be highly viscous, but when stirred slowly they can slide past each other and the fluid seems watery. 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.

3: High Visibility

Particles scatter light. ‘Scatter’ is a general term: in this context it means the sum of reflection, refraction, diffraction & 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 exactly happens depends on the size of the particle compared to the wavelength of the light that hits it, and whether the particle is transparent or reflective or neither. Let’s start with size.

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 and 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, depending on the shape of the particles, the index of refraction of the particle material, 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 6 shows a sketch of 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 in the rain at night you may have noticed that it’s easy to see raindrops in the headlights of oncoming cars (forward scatter) but harder to see raindrops in your own headlights (back scatter). Depending on the particle you may see one or more strong side lobes. It’s often at 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 limit is 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 as well as laser diode light sources that provide intense light. In the Mie regime the side lobes become smaller, while forward scatter is still stronger than back scatter.

Rayleigh

The Rayleigh regime includes scatter off molecules, including the components 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 the blue sky. Well, 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 in the atmosphere that will scatter the long wavelengths of yellow and red, leading to the warm colors of sunrise and sunset.

Particle Color

Scattering in the Rayleigh and Mie regimes is ‘elastic’, meaning that what light hits the particle sort of bounces off, unchanged in energy, so the color of the scattered light is the same as what hit the particle. Clouds in the sky are white because sunlight is white and atmospheric water is colorless; transparent. But solid particles often have color, absorbing most visible light and reflecting only the frequency of light corresponding to that color. Paint pigments are made of finely ground solids from various minerals, mostly. The smaller the particles, the more intense the color. The number density of particles in paint is also quite high. In contrast, particles used for seed in air are often made from transparent liquids, and have to be on the order of microns in size,   At the same time, particles of that size have poor light scattering efficiency, so the effect of color is reduced. An exception is colored smoke bombs, when the number density is high. The smoke is toxic at those high concentrations, however.

References