Relative Humidity Supersaturation Formation of Cloud Droplets Prof

Relative Humidity (%) Supersaturation (%) Formation of Cloud Droplets Prof. Fred Remer University of North Dakota . 3 Pure Water . 2. 1 100 95 10 -15 g Na. Cl 90 85 80. 01 . 1 1 Droplet Radius (mm) 10

Reading • Wallace & Hobbs – pp 209 – 215 • Bohren & Albrecht – pp 252 – 256 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

Formation of Cloud Droplets • Nucleation – Homogeneous Nucleation – Heterogeneous Nucleation Prof. Fred Remer University of North Dakota

Homogeneous Nucleation • The formation of droplets from vapor in a pure environment Prof. Fred Remer University of North Dakota

Homogeneous Nucleation • Chance collisions of water molecule • Ability to remain together • Depends on supersaturation Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Molecules in liquid water attract each other • Like to be in between other water molecules Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Molecules at surface have more energy • Don’t need to be surrounded by other molecules Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Molecules are In motion Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Collisions • Molecules near surface gain velocity by collisions Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Fast moving molecules leave the surface • Evaporation Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Soon, there are many water molecules in the air Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Slower molecules return to water surface • Condensation Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Net Evaporation – Number leaving water surface is greater than the number returning Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Net Evaporation – Evaporation greater than condensation – Air is subsaturated Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Molecules leave the water surface at a constant rate • Depends on temperature of liquid Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Molecules return to the surface at a variable rate • Depends on mass of water molecules in air Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Rate at which molecule return increases with time – Evaporation continues to pump moisture into air – Water vapor increases with time Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Eventually, equal rates of condensation and evaporation • Air is saturated • Equilibrium Prof. Fred Remer University of North Dakota

Thermodynamics Reveiw • Equilibrium – Tair = Twater Prof. Fred Remer University of North Dakota

Thermodynamics Review • What if? – Cool the temperature of liquid water – Fewer molecules leave the water surface Prof. Fred Remer University of North Dakota

Thermodynamics Review • Net Condensation – More molecules returning to the water surface than leaving – Air is supersaturated Prof. Fred Remer University of North Dakota

Water at Equilibrium • Equilibrium Curve Rate of Condendation = Rate of Evaporation Pressure Equilibrium Temperature Prof. Fred Remer University of North Dakota es es = water vapor pressure at equilibrium (saturation)

Supersaturation • Water Vapor Pressure > Equilibrium Pressure es e > es e Temperature Prof. Fred Remer University of North Dakota

Supersaturation Pressure • Water Vapor Pressure > Equilibrium e Net Condensation es e > es Temperature Prof. Fred Remer University of North Dakota

Equilibrium • Water Vapor Pressure = Equilibrium Pressure Condensation = Evaporation es e = es e Temperature Prof. Fred Remer University of North Dakota

Subsaturation • Water Vapor Pressure < Equilibrium Pressure Net Evaporation e e < es Temperature Prof. Fred Remer University of North Dakota es

Subsaturation • Water Vapor Pressure < Equilibrium Pressure Net Evaporation e e < es Temperature Prof. Fred Remer University of North Dakota es

Equilibrium • Water Vapor Pressure = Equilibrium Pressure Condensation = Evaporation es e = es e Temperature Prof. Fred Remer University of North Dakota

Equilibrium Curve • Assumed for flat water surface Pressure Equilibrium Temperature Prof. Fred Remer University of North Dakota es

Equilibrium Curve • Different for a water sphere Prof. Fred Remer University of North Dakota

Water Sphere • Water molecules at surface have higher potential energy • Molecular attraction is pulling them to center Prof. Fred Remer University of North Dakota

Surface Tension (s) • The surface potential energy per unit area of surface Prof. Fred Remer University of North Dakota

Surface Tension (s) • The surface energy is contained in a layer a few molecules deep Prof. Fred Remer University of North Dakota

Surface Tension (s) • Pressure inside the drop is greater than the pressure outside (due to surface tension) Prof. Fred Remer University of North Dakota Po P

Surface Tension (s) • Let’s derive an expression for the difference in pressure bewteen inside & outside! Prof. Fred Remer University of North Dakota Po P

Surface Tension (s) • Cut the drop in half! Prof. Fred Remer University of North Dakota

Surface Tension (s) • Determine the balance of force for the drop Prof. Fred Remer University of North Dakota

Surface Tension (s) • Force acting to the right – Outside Pressure • Force per unit area • Acts as if force is applied to circle area Prof. Fred Remer University of North Dakota Po

Surface Tension (s) • Force acting to the right – Outside Pressure Prof. Fred Remer University of North Dakota Po

Surface Tension (s) • Force acting to the right – Surface Tension • At periphery – Energy per area, or – Force per length Prof. Fred Remer University of North Dakota

Surface Tension (s) • Force acting to the right – Surface Tension Prof. Fred Remer University of North Dakota

Surface Tension (s) • Forces acting to the left Po – Internal Pressure P Prof. Fred Remer University of North Dakota

Surface Tension (s) • Balance of Forces – Outside Pressure – Surface Tension – Internal Pressure Po P Prof. Fred Remer University of North Dakota

Surface Tension (s) • Difference between internal & external pressure due to surface tension Po P Prof. Fred Remer University of North Dakota

Surface Tension (s) • Small drop – Big difference Po P Prof. Fred Remer University of North Dakota

Equilibrium Vapor Pressure Over a Curved Surface • An amazing discovery! • …but what does that have to do with the growth of cloud drops? Prof. Fred Remer University of North Dakota

Equilibrium Vapor Pressure Over a Curved Surface • The surface energy affects the equilibrium vapor pressure Prof. Fred Remer University of North Dakota

Equilibrium Vapor Pressure Over a Curved Surface • At Equilibrium ec = PExternal ec = vapor pressure over a curved surface Prof. Fred Remer University of North Dakota

Equilibrium Vapor Pressure Over a Curved Surface • Not the same as the equilibrium vapor pressure over a plane surface es Prof. Fred Remer University of North Dakota ec

Equilibrium Vapor Pressure Over a Curved Surface • What is the vapor pressure over a curved surface? • Must add correction factor to es Prof. Fred Remer University of North Dakota ec

Equilibrium Vapor Pressure Over a Curved Surface • It depends on – Surface tension – Temperature of drop – Density of water Prof. Fred Remer University of North Dakota 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. 5 x 10 -2 N m-1) Prof. Fred Remer University of North Dakota r = radius of droplet (m) Rv = gas constant for water vapor (461 J K-1 kg-1) r. L = density of water (1 x 103 kg m-3)

Equilibrium Vapor Pressure Over a Plane Surface • Magnus Formula – An approximation es = equilibrium vapor pressure (in mb) T = temperature (in K) Prof. Fred Remer University of North Dakota

Equilibrium Vapor Pressure Over a Curved Surface • Ambient Vapor Pressure (e) Vapor Pressure Over a Curved = Pressure of Environment Surface Prof. Fred Remer University of North Dakota e

Saturation Ratio • The ratio e/es determines if a droplet grows, evaporates, or is at equilibrium Saturation Ratio es (saturation) Prof. Fred Remer University of North Dakota e

Supersaturation • The ambient water vapor in excess of saturation • Usually expressed in percentage Saturation Vapor Pressure of > Over a Plane Environment Surface Prof. Fred Remer University of North Dakota 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) • Metastable state Prof. Fred Remer University of North Dakota ec

Critical Size • Metastable Equilibrium – Smaller Than Critical Size • Large Surface Tension • Vapor pressure of droplet is high es • Evaporates ec Prof. Fred Remer University of North Dakota ec ec

Critical Size • Metastable Equilibrium – Larger Than Critical Size • Small Surface Tension • Vapor pressure of droplet is low • Condensational Growth ec ec ec es Prof. Fred Remer University of North Dakota

Critical Size • Rearrange Kelvin’s Formula rc = critical radius S = ec/es Prof. Fred Remer University of North Dakota

Critical Size 1. 12 12 1. 10 10 1. 08 8 1. 06 6 1. 04 1. 02 1. 00. 01 Prof. Fred Remer University of North Dakota 4 T = 5 o. C 2. 1 1 Droplet Radius (mm) 10 Supersaturation (%) Saturation Ratio • Critical Radius vs. Saturation Ratio

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%) Prof. Fred Remer University of North Dakota

Critical Size • Homogeneous nucleation unlikely • Aerosols important in cloud droplet formation Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation • The formation of a cloud droplet by condensation of water vapor on an aerosol Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation • Aerosols – Hydrophobic • Water forms spherical drops on its surface Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation • Aerosols – Hydrophobic • Water forms spherical drops on its surface – Wettable (Neutral) • Allows water to spread out on it Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation • Wettable Aerosols – Droplet formation requires lower saturation ratios due to their size Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation 1. 12 12 1. 10 10 1. 08 8 1. 06 6 1. 04 1. 02 1. 00. 01 Prof. Fred Remer University of North Dakota 4 T = 5 o. C 2. 1 1 Droplet Radius (mm) 10 Supersaturation (%) Saturation Ratio • Example -. 3 mm aerosol ~ SS. 4%

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 Prof. Fred Remer University of North Dakota

Heterogeneous Nucleation • Hygroscopic Aerosols – Droplet formation requires much lower saturation ratios due to solute effect Prof. Fred Remer University of North Dakota

Solute Effect • Saturation vapor pressure over a solution droplet is less than that over pure water of the same size e’ Solution Droplet Prof. Fred Remer University of North Dakota e Pure Water Droplet

Solute Effect • Saturation vapor pressure is proportional to number of water molecules on droplet surface e’ e Solution Droplet Prof. Fred Remer University of North Dakota e e Pure Water Droplet

Solute Effect • Fractional decrease in vapor pressure e e’ Solution Droplet no = number of kilomoles of water where Prof. Fred Remer University of North Dakota Pure Water Droplet n = number of kilomoles of solute Raoult’s Formula

Solute Effect • For dilute solutions no = number of kilomoles of water n = number of kilomoles of solute • So Prof. Fred Remer University of North Dakota ~ ~

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 = # of ions Prof. Fred Remer University of North Dakota i =2 for Na. Cl (sodium chloride) & (NH 4)2 SO 4 (ammonium sulfate)

Solute Effect • Volume of solution droplet • Mass of solution droplet m’ = mass of solution droplet r’ = density of solution droplet Prof. Fred Remer University of North Dakota

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 Prof. Fred Remer University of North Dakota

Solute Effect • Substitute into Raoult’s Formula Prof. Fred Remer University of North Dakota

Solute Effect • Simplify where Prof. Fred Remer University of North Dakota

Solute Effect • That was fun!!!!!! Prof. Fred Remer University of North Dakota

Kelvin’s Formula • Let’s rearrange Kelvin’s Formula where Prof. Fred Remer University of North Dakota

Kohler Curve • Let’s combine the Solute Effect and Kelvin’s Formula Solute Effect Prof. Fred Remer University of North Dakota Kelvin’s Formula

Kohler Curve • This equation describes the saturation ratio (or relative humidity) adjacent to a drop of radius r Prof. Fred Remer University of North Dakota

Kohler Curve • Plot of relative humidity vs. droplet radius is known as a Kohler Curve Prof. Fred Remer University of North Dakota

Relative Humidity (%) Supersaturation (%) Kohler Curve Prof. Fred Remer University of North Dakota . 3 Pure Water . 2 . 1 100 95 10 -15 g Na. Cl 90 85 80. 01 . 1 1 Droplet Radius (mm) 10

– Small radii • Surface Tesion – Larger Radii Prof. Fred Remer University of North Dakota Relative Humidity (%) • Solute Effect Supersaturation (%) Kohler Curve. 3 Pure Water . 2 . 1 Solute Effect 100 Surface Tension 95 90 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

– To become liquid by absorbing water from the air – RH < 100% Prof. Fred Remer University of North Dakota Relative Humidity (%) • Deliquesce Supersaturation (%) Kohler Curve. 3 Pure Water . 2 . 1 100 95 90 Deliquesce 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

– In stable equilibrium – RH < 100% – Visibility Prof. Fred Remer University of North Dakota Relative Humidity (%) • Haze Droplets Supersaturation (%) Kohler Curve. 3. 2 Pure Water Haze . 1 100 95 90 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

– In metastable equilibrium – Critical Supersaturation • Evaporating droplets grow back Prof. Fred Remer University of North Dakota Relative Humidity (%) • Critical Radius Supersaturation (%) Kohler Curve. 3. 2 Pure Water Critical Radius . 1 100 95 90 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

– Exceed Critical Supersaturation • Droplets grow by condensation • Saturation exceeds that which is required Prof. Fred Remer University of North Dakota Relative Humidity (%) • Critical Radius Supersaturation (%) Kohler Curve. 3. 2 Pure Water Critical Radius . 1 100 95 90 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

– Exceed Critical Supersaturation • Droplets have been activated Prof. Fred Remer University of North Dakota Relative Humidity (%) • Critical Radius Supersaturation (%) Kohler Curve. 3. 2 Pure Water Critical Radius . 1 100 95 90 85 80. 01 10 -15 g Na. Cl. 1 1 Droplet Radius (mm) 10

• Droplets have been activated Prof. Fred Remer University of North Dakota . 3. 2 Pure Water Critical Supersaturation . 1 100 95 90 85 80. 01 10 -15 g Na. Cl – Exceed Critical Supersaturation Relative Humidity (%) • Critical Radius Supersaturation (%) Kohler Curve . 1 Critical Radius 1 Droplet Radius (mm) 10

Prof. Fred Remer University of North Dakota . 3 Pure Water . 2 . 1 85 80. 01 . 1 10 -13 g Na. Cl 90 10 -14 g Na. Cl 95 10 -15 g Na. Cl 100 10 -16 g Na. Cl – Different Critical Radii – Different Critical Supersaturations Relative Humidity (%) • Aerosol Spectra Supersaturation (%) Kohler Curve 1 Droplet Radius (mm) 10

Cloud Condensation Nuclei • Aerosols which serve as nuclei upon which water vapor condenses Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Aerosols will deliquesce at lower supersaturations if – Larger Particles – Hygroscopic Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Small fraction of aerosols become CCN – Continental Air • 1% – Maritime Air • 10 – 20% Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Mixed Nuclei – Most CCN are a mixture of soluble and insoluble components Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber • Device to measure the number of CCN in a sample of air Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber T 2 T 1 • Top Plate Warm & Moist (T 2) • Bottom Plate Cold & Moist (T 1) • Temperature Gradient Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber T 2 T 1 • Temperature Gradient Linear From Top Plate To Bottom Prof. Fred Remer University of North Dakota

Vapor Pressure Thermal Diffusion Chamber es top es bottom T 1 T 2 Temperature • Ambient vapor pressure is linear from top to bottom Prof. Fred Remer University of North Dakota

Vapor Pressure Thermal Diffusion Chamber es es top es bottom T 1 T 2 Temperature • Saturation vapor pressure is a curve Prof. Fred Remer University of North Dakota

Vapor Pressure Thermal Diffusion Chamber es es top es bottom T 1 T 2 Temperature • Supersaturation exists between top and bottom Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber T 2 T 1 • Supersaturation can be adjusted by changing T 1 or T 2 Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber • Air sample is introduced to the chamber • Condensation occurs in the supersaturated air Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber • Concentration of activated CCN is determined by counting droplets in a volume Prof. Fred Remer University of North Dakota

Thermal Diffusion Chamber • Repeat for different supersaturation • Determine CCN spectra Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Geographic Distribution • Higher Concentration – Total Concentrations ~ 500 cm-3 at Surface • Decreases with Height – Factor of 5 from surface to 5 km Prof. Fred Remer University of North Dakota 1000 CCN (cm-3) – Continental Air Mass Continental Air 100 10 . 1 1. 0 10 Supersaturation (%)

Cloud Condensation Nuclei • Geographic Distribution • Diurnal Variation – Min. @ 6 AM – Max. @ 6 PM 1000 CCN (cm-3) – Continental Air Mass Continental Air 100 10 . 1 1. 0 10 Supersaturation (%) Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Geographic Distribution • Lower Concentration – Total Concentrations ~ 100 cm-3 at Ocean Surface • Constant with Height Prof. Fred Remer University of North Dakota 1000 CCN (cm-3) – Maritime Air Mass Continental Air 100 10 Marine Air. 1 1. 0 10 Supersaturation (%)

Cloud Condensation Nuclei • Mauna Loa, Hawaii Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Bondville, IL Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Sources – Land Surface – Sea Salt • Diamters > 1 mm – Gas to Particle Conversion Prof. Fred Remer University of North Dakota

Cloud Condensation Nuclei • Large Nuclei –. 1 to 1 mm • Primary Composition – Sulfates • Sulfuric Acid • Salts – Ammonium Sulfate Prof. Fred Remer University of North Dakota