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

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

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

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

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

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

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

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

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

Formation of Cloud Droplets Nucleation Homogeneous Nucleation Heterogeneous Nucleation

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

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

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

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

Thermodynamics Reveiw Molecules are In motion

Thermodynamics Reveiw Collisions Molecules near surface gain velocity by collisions

Thermodynamics Reveiw Fast moving molecules leave the surface Evaporation

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

Thermodynamics Reveiw Slower molecules return to water surface Condensation

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

Thermodynamics Reveiw Net Evaporation Evaporation greater than condensation Air is subsaturated

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

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

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

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

Thermodynamics Reveiw Equilibrium Tair = Twater

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

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

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

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

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

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

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

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

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

Equilibrium Curve Assumed for flat water surface es Equilibrium Pressure Temperature

Equilibrium Curve Different for a water sphere

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

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

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

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

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

Surface Tension (s) Cut the drop in half!

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

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

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

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

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

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

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

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

Surface Tension (s) Small drop Big difference Po P

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

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

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

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

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

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

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)

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

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

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

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 >

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

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

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

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

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)

Critical Size Theory Observation Saturation ratio of 1.12 for a 0.01 mm droplet (SS = 12%) Observation Saturation ratios of 1.004 in cloud (SS = 0.4%)

Critical Size Homogeneous nucleation unlikely Aerosols important in cloud droplet formation

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

Heterogeneous Nucleation Aerosols Hydrophobic Water forms spherical drops on its surface

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

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

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)

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

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

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

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

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

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

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

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

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

Solute Effect Substitute into Raoult’s Formula

Solute Effect Simplify where

Solute Effect That was fun!!!!!!

Kelvin’s Formula Let’s rearrange Kelvin’s Formula where

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

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

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

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

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)

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)

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)

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)

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)

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)

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)

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)

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

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

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

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

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

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

Thermal Diffusion Chamber Temperature Gradient Linear From Top Plate To Bottom

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

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

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

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

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

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

Thermal Diffusion Chamber Repeat for different supersaturation Determine CCN spectra

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

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

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

Cloud Condensation Nuclei Mauna Loa, Hawaii

Cloud Condensation Nuclei Bondville, IL

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

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