1. Plot the settling velocity of a spherical particle, density = 1.5 g/cm³, on a log-log plot, for
particles ranging in size from 5 nm to 50 µm. Also, plot the settling time for particles in
the same size range from a height of 10 m.****
2. Estimate the stopping distance for particles 2.5 um, 1 um, 500 nm, and 100 nm diameter
particle with initial velocity of 30 m/s. Assume density of particle = 1.0 g/cm³.
3. Given the a-pinene volatility basis set discussed in class, estimate the aerosol formation
and gas-particle distribution (ξ₁) for each volatility bin from 1000 µg m³ of reacted a-
pinene.
4. Given the Volatility Basis Set given in class for Diesel Exhaust Particulate, estimate the
% contribution of each basis set bin to the final aerosol present for diesel exhaust
particulate in the tailpipe (10 000 µg m³), after dilution by 10 times (typical for some
source samplers) and after dilution by 1000 times (typical ambient dilution). (remember,
dilution allows for new equilibrium state (hint: gas-particle partitioning) to be
established; the only thing you know for sure is that a 10x dilution means 10x less total
hydrocarbon determined that was determined for the 10,000 µg m³ particle concentration
of diesel exhaust....)
****For this problem it is strongly recommended that you use excel, sheets, Matlab, C++, or
Python. To cover the wide range of sizes, either use increments of 1,2,5 and 10 or step
increments of 1.5x the size of the diameter.
Further, consider that if you wish to use Stokes Law to calculate drag, then you must
demonstrate that the flow over the particle created by the falling particle must be laminar. In air,
this means that the flow condition for laminar flow is Re <0.1 and Fdrag = 3nDpv/Cc. For 0.1<
Re <2, Fdrag is estimated using perturbation theory as Fdrag = 3πμDpv/C. * (1+(3/16)Re+
(9/160)Re*2ln(2Re)). For 2<Re<500, Fdrag = 3πµDpv/Cc * (1+0.15Re0.687). Re = pvD/μ.
Therefore, for Re < 0.1, you may use the terminal velocity determined in class but when Re >
0.1, you will have to use the approach from class but plug in appropriate drag force....
