EAS 6795 Atmospheric Aerosols

Homework Assignment 5, Evaporation/Condensation

1.  Given the following aerosol size distribution (attached) calculate the H2SO4 characteristic lifetime if it is lost only by particle scavenging. Use the Fuchs Sutugin transition regime mass transport equation.

·  ambient temperature is 20°C, pressure 1 atm

·  ambient RH is 80% leading to a H2SO4 weight % of 25.9 resulting in a H2SO4 molecule plus its associated water having a density of 1.194 g cm-3 and volume of 5.53x10-22 cm3

·  the H2SO4 diffusivity in air is 0.08 cm2 s-1

·  no evaporation from particle

Solve the problem twice, assuming the H2SO4 accommodation coefficient is 0.5 and then 1.0

2. For the same conditions calculate the H2SO4 characteristic lifetime assuming free molecular transport with accommodation coefficient of 1 and no evaporation. Compare this to the “actual” lifetime determined above. Which is larger? The cause for this difference is sometimes referred to as “diffusional resistance”.

3. Calculate the growth rate of a 2-µm diameter droplet of pure water in an environment with 2% supersaturation at an ambient T of 20°C. Neglect non –continuum effects (eg, Fuchs Sutugin correction) and droplet heating. Prove any assumptions you make are correct.

Dp, nm / dN/dlogdp, cm^-3 / Dp, nm / dN/dlogdp, cm^-3
18.79 / 448.66 / 167.2 / 196.36
20.04 / 483.96 / 178.3 / 169.93
21.37 / 531.22 / 190.1 / 144.98
22.79 / 593.82 / 202.8 / 128.15
24.3 / 655.73 / 216.2 / 116.35
25.91 / 726.41 / 230.6 / 104.37
27.63 / 820.5 / 245.9 / 91.643
29.47 / 882.32 / 262.2 / 82.325
31.43 / 918.58 / 279.6 / 81.907
33.51 / 965.59 / 298.2 / 78.491
35.74 / 959.26 / 318 / 69.801
38.11 / 868.31 / 339.1 / 60.654
40.64 / 785.03 / 361.6 / 55.006
43.34 / 705.61 / 385.6 / 52.77
46.22 / 577.52 / 411.3 / 50.393
49.29 / 458.89 / 438.6 / 48.291
52.56 / 365.92 / 467.7 / 37.978
56.05 / 307.59 / 498.7 / 31.101
59.77 / 270.51 / 531.9 / 30.702
63.74 / 241.24
67.97 / 223.02
72.49 / 222.63
77.3 / 229.67
82.43 / 237.82
87.91 / 245.24
93.74 / 258.71
99.97 / 276.36
106.6 / 286.3
113.7 / 285.32
121.2 / 283.85
129.3 / 282.13
137.9 / 264.91
147 / 237.95
156.8 / 216.57