Particle Basics Flashcards
What is the mean free path (λ) of a gas (air)?
The average distance a molecule travels between collisions (air at STP = 66 nm)
What are 5 key pieces of info for describing particles?
- composition 2. avg. size 3. polydispersity 4. distribution shape 5. cumulative vs frequency
What particles will best scatter visible light and why?
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).
What is the fundamental issue with histograms?
The bar height depends on the bar width.
How to calculate the fraction of particles in a given range from the frequency size distribution?
df = f(dp)*ddp (the fraction of particles from dp to ddp)
What does the area under the curve of the frequency size distribution represent?
1
How to find the fraction of particles from size a to b from the frequency size distribution?
fab = integral of a to b [f(dp)ddp]
If only one size is used, fbb = 0 because the interval width is 0.
How can you calculate the arithmetic mean?
Add all the values together, divide by the number of values.
What is the median?
1/2 of particles are smaller and 1/2 are larger than the median size.
What is the mode?
Highest point of the frequency distribution.
What is the geometric mean? When would it be used?
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^.
What are the first 3 moments averages of the frequency distribution?
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)
How does the 95% interval differ from normal to lognormal distributions?
mean +/- 2σ vs exp(ln dg +/- 2ln σg) or [dg/σg^2, dg*σg^2]
What does σg = 1, 1.45 and 1.3 mean?
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.
What is Stokes diameter?
Particles which have a settling velocity and density as a sphere with this diameter.
What is Aerodynamic diameter
Particles which have the same settling velocity as a sphere with unit density (1g/cm3, i.e. water) and this diameter.
In general do irregularly shaped particles fall faster or slower than an equivalent sphere (dynamic shape factor > or < 1)?
Irregular particles fall slower (χ > 1).
What is the definition of the feret diameter?
Measure of a particle along two perpendicular length.s
What is the definition of the martin diameter?
Measure of particle length which bisects the projected area. (Splits the projected area into 2 equal parts).
What can fractal dimension (Df) tell us about particles?
Particle formation/growth mechanism.
Df and name of 6 common particle growth mechanisms?
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.
Describe nucleation/inception of particles.
atoms or molecules cluster together to a critical size to form a particle.
Describe condensation/surface growth of particles.
atoms or molecules adhere/bond to the surface of an existing particle thus increasing its size.
Describe evaporation of particles.
The opposite of condensation, individual atoms/molecules leave the surface of a particle reducing its size.
Describe flocculation/coalescence of particles
Two existing particles combine into one particle where they mix completely and form one new continuous particle (spherical).
Describe aggregation/sintering of particles.
Two existing particles chemically bond together at a point on their surfaces. You can still observe two distinct units but they cannot be separated.
Describe agglomeration of particles.
Two existing particles physically (weakly) bond together at a point on their surfaces. They can easily be separated and are distinct.
When are particles in the continuum, transition or free-molecule regime?
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.
What are the continuous, free molecular and transition regimes and why do they matter?
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.
What are the two possible mechanisms of particle formation in the gas phase? How do these mechanisms work?
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.
What is the minimum possible particle size (diameter) called? What equation determines this?
Critical size or Kelvin diameter, dictated by the Kelvin equation.
What is the Kelvin equation?
dp = 4σvl/(kBTlnS)
where σ = surface energy per unit area
vl = volume occupied by a molecule in the liquid phase
S = saturation ratio
What is a method of counting particles based on heterogeneous nucleation?
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.
What are possible mechanisms of particle growth in the gas phase?
Coagulation and condensation
What method of particle growth is best for attaining a monodisperse particle size distribution?
Condensation.
Give the basic equation for the change in particle concentration by Brownian coagulation of a monodisperse aerosol.
dn/dt = -1/2β(v1, v1)*n^2 where β = collision frequency
What is the GSD of the self-preserving size distribution?
~1.34
