Formation of Cloud Droplets

1
Formation of Cloud Droplets
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 Raoults 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
• Dont 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
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 gt Equilibrium

es
e gt es
e
Pressure
Temperature
31
Supersaturation

• Water Vapor Pressure gt Equilibrium

Net Condensation
es
e gt es
e
Pressure
Temperature
32
Equilibrium

• Water Vapor Pressure Equilibrium

Condensation Evaporation
es
e es
Pressure
e
Temperature
33
Subsaturation

• Water Vapor Pressure lt Equilibrium

es
Net Evaporation
Pressure
e lt es
e
Temperature
34
Subsaturation

• Water Vapor Pressure lt Equilibrium

es
Net Evaporation
Pressure
e lt es
e
Temperature
35
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)

• Lets derive an expression for the difference in
  pressure bewteen 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
• 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
Kelvins 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 of Environment
Vapor Pressure Over a Curved Surface

62
Saturation Ratio

• The ratio e/es determines if a droplet grows,
  evaporates, or is at equilibrium

e
Saturation Ratio
es (saturation)
63
Supersaturation

• The ambient water vapor in excess of saturation
• Usually expressed in percentage

Saturation Vapor Pressure Over a Plane Surface
Vapor Pressure of Environment
e
gt
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
• Smaller Than Critical Size
• Large Surface Tension
• Vapor pressure of droplet is high
• Evaporates

es
ec
ec
ec
66
Critical Size

• Metastable Equilibrium
• Larger Than Critical Size
• Small Surface Tension
• Vapor pressure of droplet is low
• Condensational Growth

ec
ec
ec
es
67
Critical Size

• Rearrange Kelvins Formula

rc critical radius S ec/es
68
Critical Size

• Critical Radius vs. Saturation Ratio

1.12
12
1.10
10
1.08
8
Supersaturation ()
Saturation Ratio
1.06
6
T 5oC
1.04
4
1.02
2
1.00
.01
.1
1
10
Droplet Radius (mm)
69
Critical Size

• Theory
• Saturation ratio of 1.12 for a .01 mm droplet (SS
  12)
• Observation
• Saturation ratios of 1.004 in cloud (SS .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
8
Supersaturation ()
Saturation Ratio
1.06
6
1.04
4
T 5oC
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
Pure Water Droplet
Solution Droplet
79
Solute Effect

• Saturation vapor pressure is proportional to
  number of water molecules on droplet surface

e
e
e
e
Pure Water Droplet
Solution Droplet
80
Solute Effect

• Fractional decrease in vapor pressure

e
e
Pure Water Droplet
Solution Droplet
no number of kilomoles of water n number of
kilomoles of solute
where
Raoults Formula
81
Solute Effect

• For dilute solutions

no number of kilomoles of water n number of
kilomoles of solute

• So

82
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 Raoults Formula

86
Solute Effect

• Simplify

where
87
Solute Effect

• That was fun!!!!!!

88
Kelvins Formula

• Lets rearrange Kelvins Formula

where
89
Kohler Curve

• Lets combine the Solute Effect and Kelvins
  Formula

Solute Effect
Kelvins 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
93
Kohler Curve
.3

• Solute Effect
• Small radii
• Surface Tesion
• Larger Radii

Pure Water
Supersaturation ()
.2
Solute Effect
.1
100
Surface Tension
95
Relative Humidity ()
90
10-15 g NaCl
85
80
10
.1
1
.01
Droplet Radius (mm)
94
Kohler Curve
.3

• Deliquesce
• To become liquid by absorbing water from the air
• RH lt 100

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

• Haze Droplets
• In stable equilibrium
• RH lt 100
• Visibility

Pure Water
Supersaturation ()
.2
Haze
.1
100
95
Relative Humidity ()
90
10-15 g NaCl
85
80
10
.1
1
.01
Droplet Radius (mm)
96
Kohler Curve
.3

• Critical Radius
• In metastable equilibrium
• Critical Supersaturation
• Evaporating droplets grow back

Pure Water
Supersaturation ()
Critical Radius
.2
.1
100
95
Relative Humidity ()
90
10-15 g NaCl
85
80
10
.1
1
.01
Droplet Radius (mm)
97
Kohler Curve
.3

• Critical Radius
• Exceed Critical Supersaturation
• Droplets grow by condensation
• Saturation exceeds that which is required

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

• Critical Radius
• Exceed Critical Supersaturation
• Droplets have been activated

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

• Aerosol Spectra
• Different Critical Radii
• Different Critical Supersaturations

Pure Water
Supersaturation ()
.2
.1
100
95
Relative Humidity ()
90
10-15 g NaCl
10-14 g NaCl
10-13 g NaCl
10-16 g NaCl
85
80
10
.1
1
.01
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
T2
T1

• Top Plate Warm Moist (T2)
• Bottom Plate Cold Moist (T1)
• Temperature Gradient

107
Thermal Diffusion Chamber
T2
T1

• Temperature Gradient Linear From Top Plate To
  Bottom

108
Thermal Diffusion Chamber

• Ambient vapor pressure is linear from top to
  bottom

109
Thermal Diffusion Chamber

• Saturation vapor pressure is a curve

110
Thermal Diffusion Chamber

• Supersaturation exists between top and bottom

111
Thermal Diffusion Chamber
T2
T1

• 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

116
Cloud Condensation Nuclei

• Geographic Distribution
• Continental Air Mass
• Diurnal Variation
• Min. _at_ 6 AM
• Max. _at_ 6 PM

117
Cloud Condensation Nuclei

• Geographic Distribution
• Maritime Air Mass
• Lower Concentration
• Total Concentrations 100 cm-3 at Ocean Surface
• Constant with Height

118
Cloud Condensation Nuclei

• Mauna Loa, Hawaii

119
Cloud Condensation Nuclei

• Bondville, IL

120
Cloud Condensation Nuclei

• Sources
• Land Surface
• Sea Salt
• Diamters gt 1 mm
• Gas to Particle Conversion

121
Cloud Condensation Nuclei

• Large Nuclei
• .1 to 1 mm
• Primary Composition
• Sulfates
• Sulfuric Acid
• Salts
• Ammonium Sulfate