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2. Formation of Cloud droplets. 2.1 General aspects. 2.2 The curvature effect. 2.3 The solute effect. 2.4 Atmospheric aerosols and CCN. 2.1 General Aspects. * Phase changes of water. vapor ---- liquid. liquid ---- solid. vapor ---- solid. * Nucleation processes.

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2. Formation of Cloud droplets

2.1 General aspects

2.2 The curvature effect

2.3 The solute effect

2.4 Atmospheric aerosols and CCN


2.1 General Aspects

* Phase changes of water

vapor ---- liquid

liquid ---- solid

vapor ---- solid

* Nucleation processes

Homogeneous: droplets form in a pure environment

Heterogeneous: droplets form on nuclei

* Supersaturation: the excess of relative humidity

over the equilibrium value of 100%


2.2 The Curvature Effect

  • Surface tension
    • Work per unit area necessary to increase the surface area.
    • Process stores potential energy in the surface.
    • Units: J/m2 or N/m.
    • For water ~ 7.5x10-2 N/m at meteorological temps.
  • Vapor pressure
    • The pressure on a liquid or solid surface due to the partial pressure of the molecules of that substance in the gas phase which surrounds the surface.



Curved Surface

  • Surface energy of a curved surface
    • equilibrium vapor pressure.
    • rate of evaporation from droplets.
  • Surface tension
    • droplet tends to assume a minimum area to volume ratio.
    • Lowest possible surface potential energy state.
  • Curvature
    • Increased vapor pressure at equilibrium compared with a flat surface.

Pure Water

  • Nucleation
    • Depends on partial pressure of water vapor in the surroundings.
    • Determines the rate which water molecules impinge upon the drops.
  • Evaporation
    • Temperature of droplet and surface tension.
    • Surface molecules must obtain enough energy to overcome the binding forces.


  • Condensation and evaporation take place at the same rate.
  • Vapor pressure = saturation vapor pressure.
  • Equilibrium vapor pressure over a droplets surface.
  • Kelvin or Curvature effect
    • Enhanced equilibrium vapor pressure over curved surfaces, such as drops.

Droplet Growth

  • Net rate of growth depends on vapor deficit
    • e - es(r) = vapor deficit where e is ambient vapor pressure.
    • e - es(r) < 0 Decay
    • e - es(r) > 0 Growth
    • e - es(r) = 0 Critical size.

Critical radius

  • High supersaturation is required for very small droplets to be stable.
  • Unstable drops will evaporate.

Homogeneous nucleation

  • Droplets of critical size are formed by random collisions.
  • What if they capture another drop?
    • Drop becomes supercritical.
    • es(r) decreases.
    • Rate of growth increases.
    • Drop grows spontaneously!
  • Homogenous nucleation does not take place in the atmosphere.
    • Supersaturation rarely exceeds 1 or 2 percent.

2.3 The Solute Effect

  • Cloud drops form on aerosols
    • condensation nuclei or hygroscopic nuclei
  • Rate of formation is determined by the number of these nuclei present.
  • Nuclei keep supersaturation from exceeding a few percent.

* Radius smaller than r*

  • Solution term dominates.
  • Very small solution drops are in equilibrium with vapor at RH < 100%.
  • If RH increases, drop will grow until equilibrium is again reached.
    • This continues up the curve beyond 100% RH.
  • Once S* is reached, the droplets have critical radius r*.

Up to r* the droplet is in stable equilibrium with its environment.

  • Any change in S causes the drop to grow until equilibrium is once again reached.
  • Haze particle.

* Radius equal to or larger than r*

  • When r=r*, condensation nuclei
  • is said to be “activated”.
  • If S goes beyond S*, the droplet grows beyond r*.
  • Vapor begins to diffuse to the droplet and it will continue to grow without the further increase in S.
  • Any change in S causes droplet to grow or evaporate, but r deviates from r*.

Droplet will continue to grow to cloud drop size if S remains above the curve.

  • Actual clouds
    • Growth does not continue indefinitely
    • Too many drops present and competition for water vapor.
    • S tends to lower once condensation becomes more rapid than the production of supersaturation.

2.4 Atmospheric Aerosol and CCN

  • 75% of total mass from natural or anthropogenic sources
    • Wind-generated dust (20%)
    • Sea spray (40%)
    • Forest fires (10%)
    • Combustion and other industry (5%)
  • 25% of total mass from conversion of gaseous constituents to small particles by photochemical and other chemical processes.
    • SO2, NO2, Olefins, NH3

Categorized according to their affinity for water.

  • Hydrophobic
    • Nucleation is difficult and requires even higher super-saturation.
  • Neutral
    • Same supersaturation as homogeneous nucleation.
  • Hygroscopic
    • Much lower supersaturation required.

Hygroscopic nuclei

  • A non-volatile dissolved substance tends to lower the equilibrium pressure of a liquid.
  • When solute is added, solute molecules replace liquid molecules at the surface.
  • If vapor pressure of solute is less than that of the solvent, the vapor pressure is reduced.
  • A solution droplet can be in equilibrium at a much lower supersaturation than a pure water droplet of the same size.

Nuclei Formation

  • Condensation of gases
    • Spherical
  • Disintegration of liquids or solids.
    • Crystals, fibers, agglomerates, irregular fragments.
  • Equivalent spherical diameter
    • Diameter of sphere having same volume as the aerosol particle.

Nuclei Size

  • Size: 10-3m to 10m in diameter.
    • Salt, dust, combustion particles.
  • D > 2m Giant aerosols
  • 0.2m < D < 2m Large aerosols
  • D < 0.2m Aitken particles
    • Overwhelming majority.

Cloud Condensation Nuclei (CCN):

The nuclei activated at supersaturations less

than a few per cent (S < 1.02) are called CCN.


Meteorology 342

  • Homework (2)
  • Problem 6.4
  • Problem 6.10