1. Formation of Cloud Droplets
Droplet Radius (mm)
Relative Humidity (%)
Supersaturation (%) 80 85 90 95
100 .1 .2 .3
.01 1 10
Pure
Water
10-15 g NaCl

2. Reading
Wallace & Hobbs
pp 209 – 215
Bohren & Albrecht
pp 252 – 256

3. Objectives
Be able to identify the factor that determines the rate of evaporation from a water surface
Be able to identify the factor that determines the rate of condensation of water molecules on a water surface
Be able to draw a curve that shows the relationship between temperature and water vapor pressure at equilibrium for a flat water surface

4. Objectives
Be able to show supersaturated and subsaturated conditions on an equilibrium curve
Be able to draw a balance of force diagram for a water droplet
Be able to calculate the equilibrium water vapor pressure for a flat water surface
Be able to calculate the equilibrium water vapor pressure for a curved water surface

5. Objectives Be able to define saturation ratio and supersaturation
Be able to calculate saturation ratio and supersaturation of the air
Be able to calculate the critical size of a droplet given a saturation ratio
Be able to distinguish between heterogeneous and homogeneous nucleation

6. Objectives
Be able to list the three different types of aerosols that may act as cloud nuclei
Be able to describe the characteristics of each type of aerosol that may act as a cloud nuclei
Be able to describe the change in saturation vapor pressure as a result of solute effect

7. Objectives
Be able to calculate the fractional change in saturation vapor pressure using Raoult’s formula
Be able to pat your head and tummy simultaneously while whistling “Livin’ La Vida Loca”
Be able to identify areas on the Kohler curve that are influenced by solute and curvature effect

8. Objectives Be able to define deliquesce
Be able to determine critical radius on a Kohler curve
Be able to determine critical supersaturation on a Kohler curve
Be able to state the condition of a water droplet based on supersaturation on a Kohler curve

9. Objectives
Be able to describe the operation of a thermal diffusion chamber
Be able to compare CCN spectra for maritime and continental locations
Be able to list the sources for CCN

10. Formation of Cloud Droplets
Nucleation
Homogeneous Nucleation
Heterogeneous Nucleation

11. Homogeneous Nucleation
The formation of droplets from vapor in a pure environment

12. Homogeneous Nucleation
Chance collisions of water molecule
Ability to remain together
Depends on supersaturation

13. Thermodynamics Reveiw
Molecules in liquid water attract each other
Like to be in between other water molecules

14. Thermodynamics Reveiw
Molecules at surface have more energy
Don’t need to be surrounded by other molecules

15. Thermodynamics Reveiw
Molecules are In motion

16. Thermodynamics Reveiw
Collisions
Molecules near surface gain velocity by collisions

17. Thermodynamics Reveiw
Fast moving molecules leave the surface
Evaporation

18. Thermodynamics Reveiw
Soon, there are many water molecules in the air

19. Thermodynamics Reveiw
Slower molecules return to water surface
Condensation

20. Thermodynamics Reveiw
Net Evaporation
Number leaving water surface is greater than the number returning

21. Thermodynamics Reveiw
Net Evaporation
Evaporation greater than condensation
Air is subsaturated

22. Thermodynamics Reveiw
Molecules leave the water surface at a constant rate
Depends on temperature of liquid

23. Thermodynamics Reveiw
Molecules return to the surface at a variable rate
Depends on mass of water molecules in air

24. Thermodynamics Reveiw
Rate at which molecule return increases with time
Evaporation continues to pump moisture into air
Water vapor increases with time

25. Thermodynamics Reveiw
Eventually, equal rates of condensation and evaporation
Air is saturated
Equilibrium

26. Thermodynamics Reveiw
Equilibrium
Tair = Twater

27. Thermodynamics Review
What if?
Cool the temperature of liquid water
Fewer molecules leave the water surface

28. Thermodynamics Review
Net Condensation
More molecules returning to the water surface than leaving
Air is supersaturated

29. Rate of Condendation = Rate of Evaporation
Water at Equilibrium
Equilibrium Curve
Rate of Condendation = Rate of Evaporation es
Equilibrium
es = water vapor pressure at equilibrium (saturation)
Pressure
Temperature

30. Supersaturation Water Vapor Pressure > Equilibrium es e > es e
Temperature

31. Supersaturation Water Vapor Pressure > Equilibrium Net Condensation
e > es e
Pressure
Temperature

32. Condensation = Evaporation
Equilibrium
Water Vapor Pressure = Equilibrium
Condensation = Evaporation es
e = es
Pressure e
Temperature

33. Subsaturation Water Vapor Pressure < Equilibrium es Net Evaporation
e < es e
Temperature

34. Subsaturation Water Vapor Pressure < Equilibrium es Net Evaporation
e < es e
Temperature

35. Condensation = Evaporation
Equilibrium
Water Vapor Pressure = Equilibrium
Condensation = Evaporation es
e = es
Pressure e
Temperature

36. Equilibrium Curve Assumed for flat water surface es Equilibrium
Pressure
Temperature

37. Equilibrium Curve
Different for a water sphere

38. Water Sphere Water molecules at surface have higher potential energy
Molecular attraction is pulling them to center

39. Surface Tension (s)
The surface potential energy per unit area of surface

40. Surface Tension (s)
The surface energy is contained in a layer a few molecules deep

41. Surface Tension (s)
Pressure inside the drop is greater than the pressure outside (due to surface tension) Po P

42. Surface Tension (s)
Let’s derive an expression for the difference in pressure between inside & outside! Po P

43. Surface Tension (s)
Cut the drop in half!

44. Surface Tension (s)
Determine the balance of force for the drop

45. Surface Tension (s) Force acting to the right Outside Pressure Po
Force per unit area
Acts as if force is applied to circle area Po

46. Surface Tension (s)
Force acting to the right
Outside Pressure Po

47. Surface Tension (s) Force acting to the right Surface Tension
At periphery
Energy per area, or
Force per length

48. Surface Tension (s)
Force acting to the right
Surface Tension

49. Surface Tension (s)
Forces acting to the left
Internal Pressure Po P

50. Surface Tension (s) Balance of Forces Outside Pressure Surface Tension
Internal Pressure Po P

51. Surface Tension (s)
Difference between internal & external pressure due to surface tension Po P

52. Surface Tension (s)
Small drop
Big difference Po P

53. Equilibrium Vapor Pressure Over a Curved Surface
An amazing discovery!
…but what does that have to do with the growth of cloud drops?

54. Equilibrium Vapor Pressure Over a Curved Surface
The surface energy affects the equilibrium vapor pressure

55. Equilibrium Vapor Pressure Over a Curved Surface
At Equilibrium
PExternal
ec = PExternal
ec = vapor pressure over a curved surface

56. Equilibrium Vapor Pressure Over a Curved Surface
Not the same as the equilibrium vapor pressure over a plane surface ec es

57. Equilibrium Vapor Pressure Over a Curved Surface
What is the vapor pressure over a curved surface?
Must add correction factor to es ec

58. Equilibrium Vapor Pressure Over a Curved Surface
It depends on
Surface tension
Temperature of drop
Density of water ec

59. Kelvin’s Formula
ec = saturation vapor pressure over a curved surface (Pa)
es = saturation vapor pressure over a plane surface (Pa)
s = surface tension of water (7.5x10-2 N m-1)
r = radius of droplet (m)
Rv = gas constant for water vapor (461 J K-1 kg-1)
rL = density of water
(1x103 kg m-3)

60. Equilibrium Vapor Pressure Over a Plane Surface
Magnus Formula
An approximation
es = equilibrium vapor pressure (in mb)
T = temperature (in K)

61. Equilibrium Vapor Pressure Over a Curved Surface
Ambient Vapor Pressure (e) e
Vapor Pressure Over a Curved Surface
Vapor Pressure of Environment =

62. Saturation Ratio
The ratio e/es determines if a droplet grows, evaporates, or is at equilibrium e
Saturation Ratio
es (saturation)

63. Supersaturation e The ambient water vapor in excess of saturation
Usually expressed in percentage
Saturation Vapor Pressure Over a Plane Surface
Vapor Pressure of Environment e
>

64. Critical Size
Radius at which the vapor pressure for the droplet is equal to the vapor pressure of the air (for a particular temperature) ec
Metastable state

65. Critical Size Metastable Equilibrium es ec ec ec
Smaller Than Critical Size
Large Surface Tension
Vapor pressure of droplet is high
Evaporates es ec ec ec

66. Critical Size Metastable Equilibrium ec ec ec es
Larger Than Critical Size
Small Surface Tension
Vapor pressure of droplet is low
Condensational Growth ec ec ec es

67. Critical Size Rearrange Kelvin’s Formula rc = critical radius
S = ec/es

68. Critical Size Critical Radius vs. Saturation Ratio Supersaturation (%)
1.12 12
1.10 10
1.08
Supersaturation (%) 8
Saturation Ratio
1.06 6
1.04
T = 5oC 4
1.02 2
1.00
.01 .1 1 10
Droplet Radius (mm)

69. Critical Size Theory Observation
Saturation ratio of 1.12 for a 0.01 mm droplet (SS = 12%)
Observation
Saturation ratios of in cloud (SS = 0.4%)

70. Critical Size Homogeneous nucleation unlikely
Aerosols important in cloud droplet formation

71. Heterogeneous Nucleation
The formation of a cloud droplet by condensation of water vapor on an aerosol

72. Heterogeneous Nucleation
Aerosols
Hydrophobic
Water forms spherical drops on its surface

73. Heterogeneous Nucleation
Aerosols
Hydrophobic
Water forms spherical drops on its surface
Wettable (Neutral)
Allows water to spread out on it

74. Heterogeneous Nucleation
Wettable Aerosols
Droplet formation requires lower saturation ratios due to their size

75. Heterogeneous Nucleation
Example - .3 mm aerosol ~ SS .4%
1.12 12
1.10 10
1.08
Supersaturation (%) 8
Saturation Ratio
1.06 6
1.04
T = 5oC 4
1.02 2
1.00
.01 .1 1 10
Droplet Radius (mm)

76. Heterogeneous Nucleation
Aerosols
Hydrophobic
Water forms spherical drops on its surface
Wettable (Neutral)
Allows water to spread out on it
Hygroscopic
Have affinity for water
Soluble

77. Heterogeneous Nucleation
Hygroscopic Aerosols
Droplet formation requires much lower saturation ratios due to solute effect

78. Solute Effect
Saturation vapor pressure over a solution droplet is less than that over pure water of the same size e e’
Solution Droplet
Pure Water Droplet

79. Solute Effect
Saturation vapor pressure is proportional to number of water molecules on droplet surface e e’ e e
Solution Droplet
Pure Water Droplet

80. Solute Effect Fractional decrease in vapor pressure e e’
Solution Droplet
Pure Water Droplet
no = number of kilomoles of water
n = number of kilomoles of solute
where
Raoult’s
Formula

81. Solute Effect For dilute solutions So
no = number of kilomoles of water
n = number of kilomoles of solute So ~ ~

82. for NaCl (sodium chloride) & (NH4)2SO4 (ammonium sulfate)
Solute Effect
Number of kilomoles of solute
m = mass of solute
Ms = molecular weight of solute
Solute may dissociate into ions
Effective number of kilomoles of solute
i = 2
for NaCl (sodium chloride)
& (NH4)2SO4 (ammonium sulfate)
i = # of ions

83. Solute Effect Volume of solution droplet Mass of solution droplet
m’ = mass of solution droplet
r’ = density of solution droplet

84. Solute Effect Number of kilomoles of water
m’ = mass of solution droplet
r’ = density of solution droplet
m = mass of solute
Mw = molecular weight of water

85. Solute Effect
Substitute into Raoult’s Formula

86. Solute Effect
Simplify
where

87. Solute Effect
That was fun!!!!!!

88. Kelvin’s Formula
Let’s rearrange Kelvin’s Formula
where

89. Kohler Curve Let’s combine the Solute Effect and Kelvin’s Formula

90. Kohler Curve
This equation describes the saturation ratio (or relative humidity) adjacent to a drop of radius r

91. Kohler Curve
Plot of relative humidity vs. droplet radius is known as a Kohler Curve

92. Kohler Curve Pure Water 10-15 g NaCl Droplet Radius (mm) .3
Relative Humidity (%)
Supersaturation (%) 80 85 90 95
100 .1 .2 .3
.01 1 10
Pure
Water
10-15 g NaCl

93. Kohler Curve Solute Effect Surface Tesion Small radii Larger Radii.3
Solute Effect
Small radii
Surface Tesion
Larger Radii
Pure
Water
Supersaturation (%) .2
Solute
Effect .1
100
Surface
Tension 95
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

94. Kohler Curve Deliquesce.3
Deliquesce
To become liquid by absorbing water from the air
RH < 100%
Pure
Water
Supersaturation (%) .2 .1
100 95
Deliquesce
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

95. Kohler Curve Haze Droplets In stable equilibrium RH < 100%.3
Haze Droplets
In stable equilibrium
RH < 100%
Visibility
Pure
Water
Supersaturation (%) .2
Haze .1
100 95
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

96. Kohler Curve Critical Radius In metastable equilibrium.3
Critical Radius
In metastable equilibrium
Critical Supersaturation
Evaporating droplets grow back
Pure
Water
Supersaturation (%) .2
Critical
Radius .1
100 95
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

97. Kohler Curve Critical Radius Exceed Critical Supersaturation.3
Critical Radius
Exceed Critical Supersaturation
Droplets grow by condensation
Saturation exceeds that which is required
Pure
Water
Supersaturation (%) .2
Critical
Radius .1
100 95
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

98. Kohler Curve Critical Radius Exceed Critical Supersaturation.3
Critical Radius
Exceed Critical Supersaturation
Droplets have been activated
Pure
Water
Supersaturation (%) .2
Critical
Radius .1
100 95
Relative Humidity (%) 90 85
10-15 g NaCl 80
.01 .1 1 10
Droplet Radius (mm)

99. Kohler Curve Critical Radius Exceed Critical Supersaturation.3
Critical Radius
Exceed Critical Supersaturation
Droplets have been activated
Pure
Water
Supersaturation (%) .2
Critical
Supersaturation .1
100 95
Relative Humidity (%) 90
10-15 g NaCl
Critical
Radius 85 80
.01 .1 1 10
Droplet Radius (mm)

100. Kohler Curve Aerosol Spectra Different Critical Radii.3
Aerosol Spectra
Different Critical Radii
Different Critical Supersaturations
Pure
Water
Supersaturation (%) .2 .1
100 95
Relative Humidity (%) 90
10-16 g NaCl
10-15 g NaCl
10-14 g NaCl
10-13 g NaCl 85 80
.01 .1 1 10
Droplet Radius (mm)

101. Cloud Condensation Nuclei
Aerosols which serve as nuclei upon which water vapor condenses

102. Cloud Condensation Nuclei
Aerosols will deliquesce at lower supersaturations if
Larger Particles
Hygroscopic

103. Cloud Condensation Nuclei
Small fraction of aerosols become CCN
Continental Air 1%
Maritime Air
10 – 20%

104. Cloud Condensation Nuclei
Mixed Nuclei
Most CCN are a mixture of soluble and insoluble components

105. Thermal Diffusion Chamber
Device to measure the number of CCN in a sample of air

106. Thermal Diffusion Chamber
Top Plate Warm & Moist (T2)
Bottom Plate Cold & Moist (T1)
Temperature Gradient

107. Thermal Diffusion Chamber
Temperature Gradient Linear From Top Plate To Bottom

108. Thermal Diffusion Chamber
Temperature
Vapor Pressure
es bottom es
top T2 T1
Ambient vapor pressure is linear from top to bottom

109. Thermal Diffusion Chamber
Temperature
Vapor Pressure
es bottom es
top T2 T1
Saturation vapor pressure is a curve

110. Thermal Diffusion Chamber
Temperature
Vapor Pressure
es bottom es
top T2 T1
Supersaturation exists between top and bottom

111. Thermal Diffusion Chamber
Supersaturation can be adjusted by changing T1 or T2

112. Thermal Diffusion Chamber
Air sample is introduced to the chamber
Condensation occurs in the supersaturated air

113. Thermal Diffusion Chamber
Concentration of activated CCN is determined by counting droplets in a volume

114. Thermal Diffusion Chamber
Repeat for different supersaturation
Determine CCN spectra

115. Cloud Condensation Nuclei
Geographic Distribution
Continental Air Mass
Higher Concentration
Total Concentrations ~ 500 cm-3 at Surface
Decreases with Height
Factor of 5 from surface to 5 km
Supersaturation (%)
Continental Air
CCN (cm-3) .1
1.0 10
100
1000

116. Cloud Condensation Nuclei
Geographic Distribution
Continental Air Mass
Diurnal Variation
6 AM
6 PM
Supersaturation (%)
Continental Air
CCN (cm-3) .1
1.0 10
100
1000

117. Cloud Condensation Nuclei
Geographic Distribution
Maritime Air Mass
Lower Concentration
Total Concentrations ~ 100 cm-3 at Ocean Surface
Constant with Height
Supersaturation (%)
Continental Air
Marine Air
CCN (cm-3) .1
1.0 10
100
1000

118. Cloud Condensation Nuclei
Mauna Loa, Hawaii

119. Cloud Condensation Nuclei
Bondville, IL

120. Cloud Condensation Nuclei
Sources
Land Surface
Sea Salt
Diamters > 1 mm
Gas to Particle Conversion

121. Cloud Condensation Nuclei
Large Nuclei
.1 to 1 mm
Primary Composition
Sulfates
Sulfuric Acid
Salts
Ammonium Sulfate