2. Formation of Cloud droplets

2.2 The curvature effect

2.3 The solute effect

2.4 Atmospheric aerosols and CCN

2.1 General aspects

* Phase changes of water

* Nucleation processes

Heterogeneous: droplets form on nuclei

Homogeneous: droplets form in a pure environment

vapor ---- liquid

liquid ---- solid

vapor ---- solid

* Supersaturation: the excess of relative humidity over the equilibrium value of 100%

2.1 General Aspects

• 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.

2.2 The Curvature Effect

e

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.

Equilibrium• 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.

• High supersaturation is required for very small droplets to be stable.

• Unstable drops will evaporate.

Critical radius

STRr

Lvc ln

2

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.

• 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.

2.3 The Solute Effect

• 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*.

* Radius smaller than 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.

• 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*.

* Radius equal to or larger than r*

• When r=r*, condensation nuclei is said to be “activated”.

• 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.

• 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

2.4 Atmospheric Aerosol and CCN

• 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: 10-3m to 10m in diameter.– Salt, dust, combustion particles.

• D > 2m Giant aerosols

• 0.2m < D < 2m Large aerosols

• D < 0.2m Aitken particles– Overwhelming majority.

Cloud Condensation Nuclei (CCN):

The nuclei activated at supersaturations lessthan a few per cent (S < 1.02) are called CCN.

* The size distribution

Meteorology 342 Homework (2)

1. Problem 6.4

2. Problem 6.10