Particle Basics

Question 1

What is the mean free path (λ) of a gas (air)?

Answer 1

The average distance a molecule travels between collisions (air at STP = 66 nm)

Question 2

What are 5 key pieces of info for describing particles?

Answer 2

1. composition 2. avg. size 3. polydispersity 4. distribution shape 5. cumulative vs frequency

Question 3

What particles will best scatter visible light and why?

Answer 3

380 - 700 nm particles because light is scattered most by particles in the size range corresponding to the wavelength of light (380 - 700 for visible light).

Question 4

What is the fundamental issue with histograms?

Answer 4

The bar height depends on the bar width.

Question 5

How to calculate the fraction of particles in a given range from the frequency size distribution?

Answer 5

df = f(dp)*ddp (the fraction of particles from dp to ddp)

Question 6

What does the area under the curve of the frequency size distribution represent?

Answer 6

1

Question 7

How to find the fraction of particles from size a to b from the frequency size distribution?

Answer 7

fab = integral of a to b [f(dp)ddp]

If only one size is used, fbb = 0 because the interval width is 0.

Question 8

How can you calculate the arithmetic mean?

Answer 8

Add all the values together, divide by the number of values.

Question 9

What is the median?

Answer 9

1/2 of particles are smaller and 1/2 are larger than the median size.

Question 10

What is the mode?

Answer 10

Highest point of the frequency distribution.

Question 11

What is the geometric mean? When would it be used?

Answer 11

Used when there is a lognormal distribution. Calculated as the arithmetic mean would be calculated but values (diameter) are converted to ln space for calculations then converted back to real space with e^.

Question 12

What are the first 3 moments averages of the frequency distribution?

Answer 12

1st: mean diameter
2nd: diameter of average surface area (or avg. settling velocity)
3rd: diameter of average mass

dp = (sum(n*d^p)/N)^(1/p)

Question 13

How does the 95% interval differ from normal to lognormal distributions?

Answer 13

mean +/- 2σ vs exp(ln dg +/- 2ln σg) or [dg/σg^2, dg*σg^2]

Question 14

What does σg = 1, 1.45 and 1.3 mean?

Answer 14

σg = 1: monodisperse
σg = 1.45: self-preserving number size distribution for brownian coagulation
σg = 1.3: self-preserving volume (mass) size distribution for brownian coagulation.

Question 15

What is Stokes diameter?

Answer 15

Particles which have a settling velocity and density as a sphere with this diameter.

Question 16

What is Aerodynamic diameter

Answer 16

Particles which have the same settling velocity as a sphere with unit density (1g/cm3, i.e. water) and this diameter.

Question 17

In general do irregularly shaped particles fall faster or slower than an equivalent sphere (dynamic shape factor > or < 1)?

Answer 17

Irregular particles fall slower (χ > 1).

Question 18

What is the definition of the feret diameter?

Answer 18

Measure of a particle along two perpendicular length.s

Question 19

What is the definition of the martin diameter?

Answer 19

Measure of particle length which bisects the projected area. (Splits the projected area into 2 equal parts).

Question 20

What can fractal dimension (Df) tell us about particles?

Answer 20

Particle formation/growth mechanism.

Question 21

Df and name of 6 common particle growth mechanisms?

Answer 21

Monomer cluster: “Eden” Df = 3.00, “Vold” Df = 3.00, “Witten-Sander” Df = 2.50
Cluster-cluster: “RLCA” Df = 2.09, “Sutherland” Df = 1.95, “DLCA” Df = 1.80.
Reaction-limited, ballistic, diffusion-limited.

Question 22

Describe nucleation/inception of particles.

Answer 22

atoms or molecules cluster together to a critical size to form a particle.

Question 23

Describe condensation/surface growth of particles.

Answer 23

atoms or molecules adhere/bond to the surface of an existing particle thus increasing its size.

Question 24

Describe evaporation of particles.

Answer 24

The opposite of condensation, individual atoms/molecules leave the surface of a particle reducing its size.

Question 25

Describe flocculation/coalescence of particles

Answer 25

Two existing particles combine into one particle where they mix completely and form one new continuous particle (spherical).

Question 26

Describe aggregation/sintering of particles.

Answer 26

Two existing particles chemically bond together at a point on their surfaces. You can still observe two distinct units but they cannot be separated.

Question 27

Describe agglomeration of particles.

Answer 27

Two existing particles physically (weakly) bond together at a point on their surfaces. They can easily be separated and are distinct.

Question 28

When are particles in the continuum, transition or free-molecule regime?

Answer 28

When particles are much larger (d > 10λ) than the mean free path of the gas they are in the continuum regime. Much smaller (d < 10λ) and they are in the free-molecule regime. In between transition regime.

Question 29

What are the continuous, free molecular and transition regimes and why do they matter?

Answer 29

In the continuous regime diffusion is the main driver while in the free molecular regime particle/molecule collisions are the main drivers. Different physics govern these two types of particle interactions requiring us to differentiate. The transition regime is where the two extremes mix resulting in mixed physics.

Question 30

What are the two possible mechanisms of particle formation in the gas phase? How do these mechanisms work?

Answer 30

Heterogeneous and homogeneous nucleation. Homogeneous = concentration of molecules is high enough that molecules can come together on their own. Heterogeneous = a different species acts as an impurity for other gas phase molecules to condense onto and form into a particle.

Question 31

What is the minimum possible particle size (diameter) called? What equation determines this?

Answer 31

Critical size or Kelvin diameter, dictated by the Kelvin equation.

Question 32

What is the Kelvin equation?

Answer 32

dp = 4σvl/(kBTlnS)
where σ = surface energy per unit area
vl = volume occupied by a molecule in the liquid phase
S = saturation ratio

Question 33

What is a method of counting particles based on heterogeneous nucleation?

Answer 33

Condensation particle counter. Takes particles which are typically too small to be counted using an optical sensor and uses heterogeneous nucleation to grow the particles to sizes which can be optically detected. On the order of micrometers.

Question 34

What are possible mechanisms of particle growth in the gas phase?

Answer 34

Coagulation and condensation

Question 35

What method of particle growth is best for attaining a monodisperse particle size distribution?

Answer 35

Condensation.

Question 36

Give the basic equation for the change in particle concentration by Brownian coagulation of a monodisperse aerosol.

Answer 36

dn/dt = -1/2β(v1, v1)*n^2 where β = collision frequency

Question 37

What is the GSD of the self-preserving size distribution?

Answer 37

~1.34