Now we will consider Brownian motion, which leads to diffusion.
So far we have been discussing large particles, like the green 10 micrometer particle shown on the right hand side of the slide.
Very different forces are important for small particles that approach the size of gas molecules,
like the red 5 nanometer particle shown in the slide.
These particles randomly jitter because of the bombardment of gas molecules.
This movement is called Brownian motion and is important for particles smaller than about 100 nanometers.
Brownian motion leads to diffusion, which is the net movement of particles away from where they started.
Brownian motion is characterized by the diffusion coefficient, capital D.
Shown in the equation in the yellow box, the diffusion coefficient is directly proportional
to the fluid temperature and inversely proportional to particle diameter
So, if the particle temperature increases, gas molecules move faster, and the diffusion coefficient becomes larger,
and the particle will jitter more.
Unlike other forces that we have seen so far, Brownian motion is inversely proportional to particle diameter.
Thus, this equation tells us that smaller particles will jitter more due to Brownian motion than larger ones.
Brownian motion causes particles to be displaced.
Consider for example, if we line up a bunch of particles at time zero and then allowed them to randomly jitter.
After some time, these particles become displaced away from the center, randomly moving in any direction.
The net displacement can be expressed as the root mean square displacement,
which is simply the square root of 2 times the diffusion coefficient times time
Shown in the table at the lower right, a small particle, like a 5 nanometer particle,
will have a large diffusion coefficient, and therefore a large displacement due to diffusion,
whereas a larger particle, say 300 nanometers, will have negligible displacement.
If we look at this equation, the more time that we give diffusion, the more displacement we will have.
To get a better feeling for how particle size dictates what forces are important,
let’s compare how far a silica particle moves in 1 minute due to Brownian motion and gravity settling.
Again, I show particle diameter in micrometers and in nanometers in the first two columns.
Then I provide displacement in one minute due to Brownian motion in Column 3, and that due to gravity settling in Column 4.
Finally, in the rightmost column, I show the ratio of these displacements that due to Brownian motion divided by that due to gravity settling.
The force of gravity dominates for particles larger than 1 micrometer,
whereas the Brownian motion dominates for particles smaller than 100 nanometers.
For a 10 nanometer sized particle, Brownian motion causes 424 times more displacement than gravity.
However, the distance moved in one minute is still very small – 0.002 meters or 2 millimeters.
To put things in further perspective, we need to change the scale of things that we are considering.
So here, for this plot, on the y-axis, I show the distance the particle is displaced in 1 minute, but instead of showing this data in meters,
I show it in micrometers. The x-axis is particle diameter that we are familiar with.
For perspective, I add that the mean diameter of a human alveolus is 200 micrometers.
Again we can see that, for particles smaller than 100 nanometers, diffusion dominates over gravity settling.
These particles, if allowed to stay in the alveolar region for one minute,
will likely be displaced a sufficient distance to hit the wall of the human alveolus.
Diffusion can be used to remove small particles by passing a particle-laden airstream through a screen.
Brownian motion causes the smallest particles, say with a diameter of 10 nanometers, to jitter more than medium-sized particles,
say 100 nanometers sized particles.
The smallest particles, therefore, have a higher probability of hitting and collecting on the screen, having a high collection efficiency.
In contrast, the medium-sized particles tend to follow the airflow, pass through the screen with low collection efficiency.
In my laboratory, we have used a combination of inertial devices and diffusion screens to develop
what we call the personal nanoparticle respiratory deposition sampler, or NRD sampler.
The motivation for this work was to measure nanoparticle exposures separately from larger particles in a workplace,
because sometimes nanoparticles have more biological activity than other airborne particles, even if they are made from the same material.
In this device, particles enter a respirable cyclone, which removes the largest dust, nominally that larger than 4 micrometers,
and may cause downstream components to fail.
An impactor then removes particles larger than 300 nanometers, leaving only the smallest particles airborne.
Then a series of diffusion screens collect nanoparticles with an efficiency that mimics deposition in the human respiratory system.
These nanoparticles can then be analyzed separately from other airborne particles.
The entire sampler can be worn on the lapel and works with traditional belt-mounted air sampling
pumps, and analysis can be done by traditional analytical chemistry methods.