Lecture Ch. 5a. Macro-Thermodynamics. Water Saturation. Micro-Thermodynamics

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1 Lecture Ch. 5a Surface tension (Kelvin effect) Hygroscopic growth (subsaturated humidity) Saturation Chemical potential (Raoult effect) Nucleation Competition between surface and chemical effects Köhler curves Aerosol-cloud interactions Curry and Webster, Ch. 5 (skip 5.6, 5.7); also Pruppacher and Klett, Ch. 6 For Monday: Homework Problem 3 and 7 (Ch. 5) (to discuss) Wednesday, Oct. 27: Midterm Macro-Thermodynamics Hot air rises Rising air cools Cooled moist air saturates (Sub & Super)- saturated water vapor condenses Condensation liberates heat Water Saturation Saturation concentration of water over a flat water surface Seinfeld and Pandis, Fig N.B. Equilibrium is in but is NOT the same as steady state. Micro-Thermodynamics Saturation has the most possible dissolved species Equilibrium means two phases are balanced Supersaturated states are not stable Nucleation initiates a change of phase (from particle to droplet) Bohren,

2 Wikipedia, surface tension 10/20/09. Surface Thermodynamics Hygroscopic Growth of Particles Surfaces require energy to form Smaller particles have higher surface-to-volume ratios higher curvature Higher curvature requires more energy per mass S v,w e a,w = exp 4M wσ w / a e sat,w RTρ w D p Normalized diameter change (growth factor) of sulfate species Relative to particle size at 0% RH Seinfeld and Pandis, Fig Free Energy Equation Surface energy Free energy at constant T, P vapor pressure over a curved interface always exceeds that of the same substance over a flat surface vapor pressure of a liquid = energy necessary to separate a molecule from the attractive force of its neighbors curvature - increases the distance between a molecule and its neighbors so it has fewer neighbors -- therefore it is easier for molecules to break free for pure water Kelvin effects are important <0.05 µm diameter droplets Kelvin Equation Pw RH = sat P w 4M wσ w = xwγ w exp RTρwDp Ambient conditions RH relative humidity T temperature P w vapor pressure P w sat saturation pressure Particle composition x w mole fraction of water γ w activity coefficient for water σ w surface tension of solution ρ w density of aqueous solution M w molecular weight D p particle diameter 2

3 Raoult s Law Raoult s Law Chemical Potential From Maxwell s equations Integrating from vapor to liquid Measured Hygroscopic Growth Particle balance for levitating particles (Tang et al., 1987) Growth compensated by change in electric field Deliquescence occurs at transition from dry to wet Condensed Water Molecules Change in number of liquid molecules Seinfeld and Pandis, Fig

4 Critical Radius and Supersaturation Integrate then find maximum Cloud Droplet Nucleation particle activation - process by which droplets (several micron in size) are formed (or activated) from primarily submicron particles; also called heterogeneous nucleation or just nucleation by cloud physicists process illustrates the conditions required for growth to droplets the approach used assumes that this formation is an equilibrium process Köhler Curves Kelvin effect Köhler curves for sodium chloride and ammonium sulfate Dry diameters 0.05, 0.1, 0.5 µm Supersaturation of 1% is equivalent to 101% relative humidity Raoult effect Seinfeld and Pandis, Fig

5 7.1 Activation on Particles Soluble salts dissolve Kelvin effect Raoult effect S v,w = exp 2M wσ s / a RTρ w a υφ sm s M w / M s 4πa 3 3 ρ " s m s Activation of CCN to Droplets Variation of the equilibrium vapor pressure of an aqueous solution drop containing ammonium sulfate and insoluble material Initial dry particle diameter 0.1 µm Soluble mass fractions 0.2, 0.4, 0.6, 1.0 at 293K Seinfeld and Pandis, Fig Simulating Atmospheric Humidity using Molecular Dynamics Time = 2 ns Time = 5 ns NaCl solution reservoir Simulates a grand canonical (constant RH) ensemble Equilibrates with humid air Ambient pressure fixed by nitrogen molecules Lecture Ch. 5b Chapter 5, Problem 3 homework Kelvin effect Raoult effect Aerosol particles CCN Indirect effect Curry and Webster, Ch. 5 (skip 5.6, 5.7); also For Wednesday: Read Ch. 5 and current research. For Wednesday: Homework Problem 7, p. 158 (7d misprint) Bubbles Liquid (H 2 O/EtOH) supersaturated with vapor (CO 2 ) nucleates on salt to form bubbles Clouds Vapor (air) supersaturated with liquid (H 2 O) nucleates on particles to form droplets Chemical and Surface Effects Raoult effect Kelvin effect 5

6 Simplified Köhler Equation Kelvin effect Maximum ds/dr=0 Raoult effect Kelvin effect Raoult effect Critical Radius and Supersaturation S(r) =1+ a r b r 3 ds dr = a r + 3b 2 r ds dr = 0 = a r * + 3b 2 r * 4 ar * 2 = 3b r* = 3b a S* =1+ a r * b r * 3 =1+ a3 3b a 3 27b =1+ 4a3 27b Aerosol-Cloud Interactions Activation: Köhler 1921 (Aitken) CCN/Droplets: Twomey 1959 (Conover) Particle Growth: Hoppel 1986 (Frick) Precipitation Suppression: Albrecht 1989 (Rosenfeld, Ackerman, Ramanathan) Cloud Condensation Nuclei (CCN) cloud condensation nuclei - those particles which have large enough radii and enough solute content to activate to particles at a prescribed supersaturation in marine air, only 50% of all aerosol particles may be CCN for typical clouds, with supersaturations ~ 0.05%-0.5% 7.1 6

7 What is an Aerosol? Suspension of liquid or solid particles in a vapor phase Colloidal suspension that may be stable for <1 s or > 1 yr Particle Sources combustion incineration road dust power plants automobiles sea salt biogenic volcanoes Particle + Vapor = AEROSOL Cloud Condensation Nuclei Cloud Processing dn dlogd Diameter (µm) Diameter (µm) Diameter (µm) Size Range for Particle Sources Particle Type Size Range automotive emissions 0.01 µm to 1 µm bacteria 0.2 µm to 10+ µm Number Distributions vs. Population Distributions Human Population Age Distribution (Manhattan) Aerosol Particle Size Distribution (Manhattan) Population dn tobacco smoke 0.01 µm to 1 µm dlogd p viruses µm to 0.05 µm Age D p (µm) 7

8 Fine and Coarse Modes Fine Particles Coarse Particles Particle Size Distributions Number (dn/dlogd p ), cm -3 x10 3 Volume (dv/dlogd p ), µm 3 /cm Ultrafine Particles Nucleation Mode Condensation Submode Aitken Mode Accumulation Mode Droplet Submode Diameter (micrometers) Coarse Mode Number concentration Total number N Differential number n Mean size Geometric Arithmetic Number-based Mass-based Size variability Standard deviation σ Geometric standard deviation σ g D pg n(d p ) dn dlogd p σg D p (µm) Log-Normal Number Distributions Global Aerosol Distribution Cumulative Differential Cumulative Distribution (% less than D p ) % 50 D pg σ g Cumulative Number } 15.9% D p (µm) Cumulative Surface Cumulative Volume D pg n(d p ) dn dlogd p σ g D p (µm) Capaldo et al., Nature, 1999 How do Aerosols cool? Aerosol direct effects cause cooling by reflecting more light (e.g. smog). clear more reflection smoggy Aerosol indirect effects cause cooling by clouds that reflect more light (e.g. tracks). more reflection normal whiter Ship Tracks Coakley et al., Science,

9 Turkey Manitoba, Canada City Tracks South Australia Yellow indicates polluted clouds >>Polluted clouds cause cooling Rosenfeld, Science,

Critical Radius and Supersaturation. Condensed Water Molecules. Cloud Droplet Nucleation. Bubbles. Clouds. Change in number of liquid molecules

Condensed Water Molecules Change in number of liquid molecules Critical Radius and Supersaturation Integrate then find maximum Cloud Droplet Nucleation particle activation - process by which droplets (several