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HW4-6130-Solution

# HW4-6130-Solution - Homework IV Coagulation Nucleation...

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Homework IV Coagulation, Nucleation & Condensation (due April 02, 200) 1. In an experiment using cadmium oxide smoke, the particle concentration was recorded as follows: Time from Start (min) Number conc. (#/cm 3 X 10 -6 ) 8 0.92 24 0.47 43 0.33 62 0.24 84 0.21 It is argued that the major mechanism in this system was Brownian coagulation only. Determine the coagulation constant from these data and compare with theory for monodisperse aerosols. (10%) Sol> The graph shows a strong linear correlation (K 0 =8.2×10 -10 cm 3 /s) and a good assumption of the aerosol as nearly monodisperse. The theoretical value is K 0 =3.0×10 -10 cm 3 /s. If the particle follows the theory of monodisperse, the Cc might be 2.7 and the particle size is around 0.1μm.

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2. A log-normal aerosol model (BIMODALM.EXE) has been developed to help you understand the dynamic behavior of aerosols undergoing coagulation and/or condensation. Instruction of how to run the program is provided in “README.TXT” and “INPUT HELP.DOC” . Use it to study the following scenarios: (a) coagulation only run for a total time of 10 s (which is equal to the product of time step (dt) and total number of steps (IT)); (b) condensation only run for a total time of 1×10 -2 s. Use the default values specified in INPUT and choose the uni-modal option. However, for each scenario, choose two g s (1 and 2). Plot the number concentration (N), particle diameter (d g ), geometric standard deviation ( g ) and saturation ratio (S) as a function of time for each scenario. In addition, plot particle size distributions at the beginning and at the end of each scenario. Report your observation and explain why it is so. (20%) Sol> Change of number concentration: condensation doesn't change the number of particles while coagulation quickly reduces number concentration of particles.
Change of MMD: for coagulation, when s g is greater, dg increases faster because large particles serve as sites and small particles can quickly attack the sites due to diffusion. For condensation, difference is not significant. Change of s g : for all cases, the final trend is going to constant because small particles all go to larger particles and particle size difference becomes smaller and smaller until almost no difference. For coagulation, when s g =1,

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