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Condensational Growth

r. Condensational Growth. Reading. Wallace & Hobbs pp 221 – 224. Condensational Growth. Objectives Be able to describe the factors that determine the condensational grow rate of a cloud droplet Be able to state the relationship between droplet size and growth rate

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Condensational Growth

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  1. r Condensational Growth

  2. Reading • Wallace & Hobbs • pp 221 – 224

  3. Condensational Growth • Objectives • Be able to describe the factors that determine the condensational grow rate of a cloud droplet • Be able to state the relationship between droplet size and growth rate • Be able to describe how ventilation effects influence growing cloud droplets

  4. Condensational Growth • Objectives • Be able to describe the initial growth of a cloud including typical supersaturation, height of maximum supersaturation, activated CCN and resulting cloud droplet spectrum

  5. Condensational Growth • How do droplets grow? t1 t2 t3

  6. Condensational Growth • Droplet gains water molecules

  7. Condensational Growth • Flux of water molecules towards droplet

  8. Condensational Growth • Equation of continuity • The net mass flux into the system equals the rate of increase of mass of the system rw= density of water vapor molecules rwV = mass flux of water molecules

  9. Condensational Growth • How do the molecules move towards the droplet? Kinetic Theory of Gases Flux Density – the net rate of transport per unit area

  10. Condensational Growth • Flux Density lw = molecular mean free path vw = mean molecular speed rw = density of water molecules

  11. Condensational Growth • Diffusional Coefficient Flux Density

  12. Condensational Growth • Flux density is the same as mass flux Substitute into or

  13. Condensational Growth • Diffusion Equation for Water Vapor • the change in water vapor density over time is a function of • Diffusion Coefficient • Distribution of water vapor

  14. Condensational Growth • Let’s solve this equation physically • Imagine a sphere around a growing droplet r Surface Area of Sphere = 4pr2

  15. Condensational Growth • Rate of droplet growth r m = mass of water

  16. Condensational Growth • Why is the drop growing? • Environmental water vapor density is greater than that at droplet surface r Water vapor gradient

  17. Condensational Growth • New equation for a growing droplet • Integrate vapor density adjacent to droplet surface r vapor density a great distance away from droplet

  18. Condensational Growth • Assuming the change in mass with time is independent of radius

  19. Condensational Growth • Substitute for the mass of water (assuming a spherical droplet) density of liquid water

  20. Condensational Growth

  21. Condensational Growth • Using the Ideal Gas Law Temperature at droplet surface Temperature far from droplet

  22. Condensational Growth • Assume temperature at droplet surface is same as environment

  23. Condensational Growth • Using the Ideal Gas Law again

  24. Condensational Growth Vapor pressure at droplet surface Vapor pressure far from droplet

  25. Condensational Growth • Vapor pressure at droplet surface depends on • Solute Effect • Surface Tension

  26. Condensational Growth .3 • Solute & Kelvin effects are small for droplets > 1mm Pure Water Supersaturation (%) .2 .1 100 95 Condensational Growth Relative Humidity (%) 90 10-16 g NaCl 10-14 g NaCl 10-13 g NaCl 10-15 g NaCl 85 80 10 .1 1 .01 Droplet Radius (mm)

  27. Condensational Growth • Vapor pressure at the droplet surface is approximately equal to that over a plane surface of water eo @ es

  28. Condensational Growth • If the vapor pressure at the droplet surface is not too different from the vapor pressure away from the drop

  29. Condensational Growth • Let’s review what’s happening • Environmental water vapor pressure is greater than that at droplet surface

  30. Condensational Growth • Supersaturation • Substitute into • Supersaturation here is a fraction rather than a percentage

  31. Condensational Growth • Rearranging and grouping terms Gl can be considered constant for a given environment at a fixed temperature where

  32. Condensational Growth • All that just to say.....

  33. Condensational Growth • Rate of Droplet Growth • Proportional to supersaturation • Bigger SS, grows faster

  34. Condensational Growth • Rate of Droplet Growth • Inversely proportional to droplet radius • Smaller radius, grows faster

  35. Condensational Growth • Ventilation Effects • Proportional to droplet terminal speed • Unimportant for growing droplets • Significant for falling raindrops

  36. A Cloud Story Written and Illustrated by Prof. Fred Remer

  37. Cloud Story • Once upon a time, there was a rising parcel of air • It had aerosols

  38. Cloud Story • As the parcel rose, it cooled adiabatically • It reached saturation with respect to liquid water RH = 100%

  39. Cloud Story • It kept rising! • Soon it was supersaturated! • The supersaturation increased at a rate proportional to the updraft velocity SS

  40. Cloud Story • The biggest (and most efficient) CCN were activated first

  41. Cloud Story • Maximum Supersaturation • Rate of condensation approaches rate of moisture supply SSmax

  42. Cloud Story • Maximum Supersaturation • Smallest cloud droplets are activated • Determines cloud droplet concentration SSmax

  43. Cloud Story • Maximum Supersaturation • Occurs within a few hundred meters of cloud base SSmax

  44. Cloud Story • Supersaturation begins to decrease • Rate of condensation greater than rate of moisture supply

  45. Cloud Story • Haze droplet begin to evaporate • Metastable droplets • Did not activate • Activated droplets grow

  46. Cloud Story • Smallest droplets grow fastest • Bigger droplets grow slower • Droplet spectrum becomes more uniform

  47. Condensational Growth • Monodisperse spectrum • Droplets grow to 10 mm after 5 min. • Slower growth at larger sizes

  48. Units: r [mm], n [liter-1], v [cm/s]

  49. Condensational Growth • Precipitation sized particles Large Cloud Droplet (50 mm) Small Raindrop (100 mm) Cloud Droplet (10 mm) Typical Raindrop (1000 mm)

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