0. The polymath source for aerosol reactor is here.
1. Review the description of the aerosol reactor on page 1. Assume the inlet gaseous stream is always saturated with Al vapor. The entering concentration of Al molecules is 2.64 ´ 1022 molecules/kg of gas.
a) For a cooling rate of 500 K/s and an initial temperature
of 1600°C, plot particle diameter, (dp) nucleation rate, 
, and 
, condensation rate, 
and 
, molecule concentrations (nm) and
(nms), saturation ratio, S, molecules per nuclei, (n*), gas velocity, (U), gas
density, (rg), number of particles,
(N), and flocculation rate 
as a function of
time (moving with the fluid) and of distance down the reactor.
b) Determine the number of particles, Al concentration and particle diameter in the exit stream as a function of cooling rate between 50°C/s and 1500°C/s for an initial temperature of 1600°C.
c) Determine the number of particles, Al concentration and particle diameter in the exit stream as a function of pressure between 0.1 atm and 20 atm for an initial temperature of 1600°C and cooling rate 500°C/s.
d) Determine the number of particles, Al concentration and particle diameter in the exit stream as a function of initial temperature between 1500°C and 1800°C for 1 atm pressure cooling rate 1000 K/s.
e) For a cooling rate of 500 K/s find the relationship between inlet temperature and pressure.
f) Explore the problem to see the effect of the various
operational variables. on dp, 
,
, 
, etc. Write a paragraph describing
operation of an APFR and how to vary the particle sizes.
e.g. 
for which dp = 500 nm.
The Polymath program is shown in the appendix.
2) It is proposed to replace the carrier gas by helium.
a) What changes do you need to make in the polymath code given in the CD and in the appendix? Before carrying out any computer runs, discuss qualitatively what differences using Helium rather than Argon. Assume the gas enters the reactor saturated with Aluminum.
b) Compare your plots (He versus Ar) of the number of Al particles as a function of time. Explain the shape of the plots. Print out your Polymath code and plot.
c) How does the final value of dp compare with that when the carrier gas was Argon? Explain.
d) Compare the time at which the rate of nucleation reaches a peak in the two cases [carrier gas = Ar and He]. Explain the comparison.
For parts (b) and (c), write down or sketch the results as appropriate.
Data for a He molecule:
Mass = 6.64 ´ 10–27 kg
Volume = 1.33 ´ 10–29 m3
Surface area = 2.72 ´ 10–19 m2
Bulk density = 0.164 kg/ m3, at normal temperature (25°C) and pressure (1 atm)
3) What additional equations will be needed in the flame pyrolysis model? Write down as many as you can. Explain qualitatively any differences you expect.
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