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Condensation

Condensation. Reading: Chap 13. In the continuum regime, diffusion theory is used. At steady state. Q: Is n d equal to n s ?. Rate of diffusional condensation. Q: How much is it?. Volume growth. Size growth. Q: How can the condensation rate be increased?

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Condensation

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  1. Condensation Reading: Chap 13 • In the continuum regime, diffusion theory is used. At steady state Q: Is nd equal to ns? Rate of diffusional condensation Q: How much is it? Volume growth Size growth Aerosol & Particulate Research Laboratory

  2. Q: How can the condensation rate be increased? Q: How does the growth rate depend on size? Implication? Ex: For dp = 0. 1 and 1 mm, calculate the new dp after 1 sec of water vapor condensation at 20 oC. • In the free molecular regime, the gas kinetic theory is applied Volume growth Size growth Aerosol & Particulate Research Laboratory

  3. Q: How does the growth rate depend on particle volume? Particle size? Implication? For the entire range (Sutugen, 1971) (Pratsinis, 1988) Kelvin effect Aerosol & Particulate Research Laboratory

  4. Log-Normal Model Free Molecular Continuum Pratsinis, S. J. Colloid & Interface Science, 124(2), 416-427. Aerosol & Particulate Research Laboratory

  5. Non-dimensionalize the equations Q: N(t)? dp(t)? sg(t)? S(t)? Assuming condensation only. Aerosol & Particulate Research Laboratory

  6. Asymptotic Behavior: after a long time For the Continuum regime Eliminating dt Integrating and noting that the initial values are very small Important!!!  s = ? Note Aerosol & Particulate Research Laboratory

  7. Condensation Characteristic Time Q: When? Constant Particle Size: Limited vapor with a high particle loading Q: Physical meaning? Constant Vapor Concentration: a small particle loading with unlimited vapor Q: When? Aerosol & Particulate Research Laboratory

  8. Characteristic time for simultaneous particle growth and vapor consumption Free Molecular regime (same for C+) Q: Physical meaning? Wu, C. Y. and Biswas, P., Aerosol Sci. Technol., 28:1-20, 1998 Aerosol & Particulate Research Laboratory

  9. Continuum regime (same for C+) Continuum Free Molecular Aerosol & Particulate Research Laboratory

  10. Free Molecular Regime Aerosol & Particulate Research Laboratory

  11. Comparison of the characteristic times Aerosol & Particulate Research Laboratory

  12. Condensation Nuclei Counter Q: How to measure N by light scattering intensity if dp is different? Q: Can we use CNC to measure dp? Q: What if we combine a DMA and a CNC? Aerosol & Particulate Research Laboratory

  13. Aerosol & Particulate Research Laboratory

  14. Effects of Temperature • Temperature at the surface may be different from that away from the surface • Droplet heating may take place due to the release of latent heat Q: What’s the resultant impact of latent heat on condensation? H: latent heat kv: thermal conductivity of the gas Dv: diffusion coefficient of the molecule Aerosol & Particulate Research Laboratory

  15. Empirical equation for temperature difference T1 in oC. Fuchs correction factor (necessary for small particles) Q: Resultant effect of Φon condensation? Aerosol & Particulate Research Laboratory

  16. Aerosol & Particulate Research Laboratory

  17. Condensation with Soluble Nuclei & Ions Saturation ratio for droplets containing dissolved materials m: mass of the dissolved salt i: number of ions each molecule of salt forms Mw: molecular weight of solvent (water) Ms: molecular weight of salt Aerosol & Particulate Research Laboratory

  18. Saturation ratio vs droplet size for 10-16 g NaCl (Solid sphere of 0.045 mm in diameter) Aerosol & Particulate Research Laboratory

  19. Relative humidify vs droplet size (a larger scale) Droplet formation & crystalization 10-14g Q: Implication? Aerosol & Particulate Research Laboratory

  20. Evaporation • The reverse process of particle growth though there is no ciritical size. • Droplet lifetime/drying time Q: Where is evaporation important? • For volatile materials, cooling of the droplet due to the latenet heat of evaporation needs to be considered. Droplet lifetime for dp > 1.0 mm Aerosol & Particulate Research Laboratory

  21. Aerosol & Particulate Research Laboratory

  22. Q: How can we control evaporation time? Aerosol & Particulate Research Laboratory

  23. Q: For a given aerosol system, what’s the effect of heating followed by cooling? Condensation Aerosol Generator Aerosol & Particulate Research Laboratory

  24. Reflection Aerosol & Particulate Research Laboratory

  25. Condensation Characteristic Time – Constant dp (continuum regime) (pressure-concentration conversion) Volume growth is Vapor concentration change is Aerosol & Particulate Research Laboratory

  26. Integrate both sides Initial condition The final solution is then Aerosol & Particulate Research Laboratory

  27. Condensation Characteristic Time – Constant C (continuum regime) (pressure-concentration conversion) Size growth Integrate both sides Aerosol & Particulate Research Laboratory

  28. Initial condition The final solution is then Aerosol & Particulate Research Laboratory

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