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MicrophysicsTom Peter, ETH Zurich
• Observations• Modelling
1
• Modelling
Thermo-dynamics
AerosolsClouds
Kinetics
Aerosol and Cloud Processes
IN snowice
evaporationdetrainment
nucleation
coagulation
melting
2
precipitation
CCN
H2O molecules
rain
cloud drops
activation
aqueousaerosols
scavenging
Precipitation staircase
Prerequisites for cloud formation:• water• low T• supersaturation• Cloud Condensation Nuclei (CCN)
or Ice Nuclei (IN)
3
Particle size distributions:The result of the interplay of thermodynamics andkinetics in response to outer forcings ( T, hνννν , g)
4
Size distribution of cloud particles near the top of young continental
cumuli (Hobbs et al., 1980)
Size distribution of aerosol particles from photooxidaton of a methylcyclohexane-propane-NOx mixture (Seinfeld,1994)
Example of instrument:
Optical particle counter (OPC):
- “White light counter”- Aerosol forward scattering single particle counter- Mie theory to determine aerosol size [Mie, 1908]- Scattered light amplified by photomultiplier tube
5
- Scattered light amplified by photomultiplier tube- Pulse height detection- Prior to each flight calibration with polystyrene
latex spheres
All OPC channels measure particles larger than a certain size
),,(),,(),,(log
),,(log
trxnrtrxdr
dnrtrx
rd
dntrx
Dd
dnr
rrrr ≡==
The differential particle size distribution
6
7
Size distribution of stratospheric aerosols
Diffusional growth: OCS → SO2 → H2SO4 → aerosolox ox cond
8
Size distribution of stratospheric aerosols
Diffusional growth: OCS → SO2 → H2SO4 → aerosolox ox cond
9Thomason and Peter, 2006
Size distribution of stratospheric aerosols
Diffusional growth: OCS → SO2 → H2SO4 → aerosolox ox cond
Background mode
Volcanic mode: Pinatubo, 15°N, June 1991: coagulation of freshly nucleated with largest background particles
10
103
104
105
106
dN/d
(logD
) (
cm-3)
Size distribution in and around Zürich:smallest particles are 10 times more abundant in the citycompared to the country side and 100 times more abundant duirng the day than in the night
11Bukowiecki et al., 2002
10 100 1000 1000010-2
10-1
100
101
102
Urban Area: (Downtown Zürich)
Day (SMPS) Night (SMPS) Day (OPC) Night (OPC)
dN/d
(logD
) (
cm
Dp (nm)10 100 1000 10000
Rural Region:(Zürcher Oberland)
Day (SMPS) Night (SMPS) Day (OPC) Night (OPC)
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
12
Clouds
How far do we get with thermodynamics in explaining
cloud formation?
Cloud droplet formationA fierce competition without which precipitation would be massively impeded!
What decides whether the aerosolparticle stays an aerosol particleor becomes a cloud droplet?Köhler Theory
13
RH↑
water moleculeaerosol particle (e.g. NH4
+/SO42--/H2O solution)
diluted aerosol particlecloud droplet
3 big names: Raoult, Kelvin, Köhler
� Raoult’s law (1870)small droplets have higher solute concentrations (salts, acids) and this reduces the H2O vapor pressure� advantage for small droplets
� Kelvin effect (1879)
14
� Kelvin effect (1879)small droplets have a higher H2O vapor pressure(curvature effect)� disadvantage for small droplets
� Köhler equation (1921)balance between Kelvin and Raoult terms� quantitative understanding
Clapeyron’s equation(applies to any phase transition of a pure substance)
∆Vm dp = ∆Sm dT ∆Sm = change of molar entropy during phase transition∆Vm = change of molar volume during phase transition
Clausius-Clapeyron equation(valid for solid-gas and liquid-gas phase transitions)
Gibbs free energy: ∆Gvap = µdn = ∆Hvap - T∆Svap = 0 ∆Hvap: molar enthalpy change during vaporization
15
∆Hvap: molar enthalpy change during vaporization
� ∆Svap = ∆Hvap/T at equilibrium of two phases
���� ����
����
assumes ∆Hvap to be T-independent
dTRT
∆Hlnpd
pdp
2vap==
−−=
01
vap
0 T1
T1
R
∆H
pp(T)
ln
2vap
vap
vap
RT
p∆H
T∆V
∆H
dTdp ==
Vapor pressure of liquid water and ice
300
400
500
600
700
800
900
1000P
ress
ure
(Pa)
over waterover ice
16
Murphy & Koop 2005, Q. J. R. Meteorol. Soc. 131, 15 39–1565:
p over water in Pa:ln(pwater) ≈ 54.842763− 6763.22/T − 4.210 ln(T) + 0.000367T+ tanh{0.0415(T − 218.8)}
× (53.878− 1331.22/T− 9.44523 ln(T) + 0.014025T)
p over ice in Pa:ln(pice) = 9.550426 − 5723.265/T + 3.53068 ln(T) − 0.00728332T ; T > 110 K
0
100
200
200 210 220 230 240 250 260 270 280
Temperature / K
Vapor pressure of liquid mixtures: Raoult’s law
Mixture of two liquids A und B:
pA = xA pA*, pB = xB pB*
P = pA +pB
P = total pressurep = partial pressurep* = pressure of pure substance
pB*
17
p* = pressure of pure substance
x = mole fraction:
n = mole number∑
=i
11 n
nx
pA*
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1
Vap
or p
ress
ure
(mm
Hg
)
abs VP
VP etOH
VP H2O
Water / ethanol – mixtures at 25.13 °°°°C
total vapor pressure P
partial vapor pressure of etOH = C2H5OH
partial vapor pressure of H2O
Measurement of the vapor-liquid-equilibrium (VLE) ofethanol (etOH) / water mixtures
18
0
1
2
3
4
5
6
7
8
9
0 0.2 0.4 0.6 0.8 1x(etoh)
activ
ity c
oeffi
cien
ts
UNIFAC: g(etOH)
UNIFAC: g(H2O)
VLE g(etoh)
VLE g(h2o)
x(etoh)
γ(etOH) from UNIFAC model calculation
γ(H2O) from UNIFAC model calculation
γ(etOH) from VLE data
γ(H2O) from VLE data
Activity coefficients γ of ethanol / watermixtures
Kelvin effect
rpa
pi
Work required to increase the surface area A of the liquid-vapor interface:dW = σdAσ = surface tensionA = 4πr2 = surface area
dW = σdA4πr2 (p – p ) = A dp = σ d(4π r2) = 8π r σdr
19
� pi = pa + 2 σ / r Laplace equation (valid for bubble or droplet)
4πr2 (pi – pa) = A dp = σ d(4π r2) = 8π r σdr
Chemical potential depends on pressure: (∂µ/∂p)T = Vm,
Vm: molar volume
� Vm,l dpl = Vm,g dpg =
What is the influence of the higher pressure inside a curved surface on the vapor pressure of a droplet?
µg
µl
In equilibrium: µg = µl and dµg = dµl
gg
dpp
RT
∆pRT
VdpV
RTdp
plm,
∆p*p
llm,
p
g ≈= ∫∫+11
⇒
20
For curved surfaces: ∆p = 2σ /r
p(∞) = vapor pressure over flat surface, r = ptcl radius, R = gas constant, Vm.l = liquid molar volume, e.g. of H2O, σ = surface tension
Kelvin Equation/rRTV2 lm,e)p(p(r) σ×∞=
RT
∆pV
)p(p(r) lm,=
∞ln
∆pRT
dpVRT
dpp )p(
llm,)p(
gg
≈= ∫∫∞∞
⇒
⇒
Köhler theory = Raoult’s law + Kelvin Effect
×∞=
×∞+
=
×∞=
×∞=
1e)(p(r)p
e)(pnn
n(r)p
e)(px(r)p
e)p((r)p
/rRTV2
/rRTV2w
sw
ww
/rRTV2www
/rRTV2w
lm,
lm,
wm,
wm,
σ
σ
σ
σ
21
The last two steps assume the solution to be dilute, and make a Taylor expansion; pw(∞) = H2O vapor pressure over pure liquid bulk water, σ = surface tension of solution, r = particle radius, Vm.w = liquid molar volume of H2O, ns = molar density of solute
−×∞≈
×∞+
≈
×∞−+
=
3
23
3
4
32exp
)(4311
)/3(411
πr
Vn
rRT
V)(p(r)p
e)(pπr/Vn
(r)p
e)(pVnπr/Vn
(r)p
wm,swm,ww
/rRTVw
wm,sw
/rRTV2w
sswm,sw
wm,
lm,
σ
σ
σ
Köhler theory
−×∞≈ 3
p
wm,s
p
wm,wpw
πD
Vn
RTD
V)(p)(Dp
64exp
σ
Köhler curves for a NaCl particle with a dry diameter of 50 nm
1.004
1.005
22
pw(∞) = H2O vapor pressure over pure liquid bulk water, σ = surface tension of solution, Dp = particle radius, Vm.w = liquid molar volume of H2O, ns = molar density of solute
0.995
0.996
0.997
0.998
0.999
1
1.001
1.002
1.003
1.004
0 1 2 3 4 5
wet diameter, µm
Kelvin term
Raoult term
Köhler curve
p w(r
)/p w
(∞)
0.1
0.2
0.3
0.4
sup
ers
atu
ratio
n, %
Köhler curves for NaCl particles of different dry diameters
−≈
∞= 3
p
wm,s
p
wm,
w
pww
πD
Vn
RTD
V
)(p
)(DpS
64exp
σ
Köhler curves for particles (with dry dia-meters of 100 nm) of different compositions
0.1
0.2
0.3
0.4
sup
ersa
tura
tion
, %
23
-0.3
-0.2
-0.1
0
0.1
0 1 2 3 4 5
wet diameter, µm
sup
ers
atu
ratio
n, %
NaCl 50 nm
NaCl 100 nm
NaCl 200 nm
The Köhler curve describes the equilibrium vapor pre ssure of a droplet with a specified dry diameter as it takes up or los es water.
-0.3
-0.2
-0.1
0
0.1
0 1 2 3 4 5
wet diameter, µm
sup
ersa
tura
tion
, %
NaClAS, full dissociationglycerol1,2-hexanediol
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
24
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
25
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
26
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = = 14300 14300 ppmppm= = 11..43 43 %%
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
27
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 2000 cmcm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
28
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
29
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
30
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
31
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = = 14300 14300 ppmppm= = 11..43 43 %%
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
32
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 2000 cmcm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
33
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
34
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
35
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
36
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = = 14300 14300 ppmppm= = 11..43 43 %%
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
37
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 2000 cmcm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
38
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
39
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
40
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
41
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = = 14300 14300 ppmppm= = 11..43 43 %%
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
42
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 2000 cmcm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
43
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Mass balance:
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
44
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
45
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
46
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
47
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
48
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
49
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
50
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
51
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
52
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
53
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
54
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
55
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
56
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
57
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
58
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
59
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
60
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Adiabatic cooling of an air parcelAdiabatic cooling of an air parcel701.57 hPa 701.57 hPa �������� 700.00 hPa700.00 hPa
280.18 K 280.18 K �������� 280.00 K280.00 K(Lift of ~17 m)(Lift of ~17 m)
� The minority has the “size ad-vantage”. But whether it loses
χχχχχχχχtottot = 14300 = 14300 ppmppm= 1.43 %= 1.43 %
MonodisperseMonodisperse salt salt particles:particles:
Number density: Number density:
For everyone who has will begiven more, and he will have an abundance. Whoever does not have, even what he has will betaken from him.
Denn wer hat, dem wird gegeben, und er wird im Überfluss haben; wer aber
61
33
)()()(34
−==⇒
−==
wvapw
vapw
totw
vapw
w
w
totwww r
r
Tp
NkT
Tp
p
Tp
pSkT
rNnkTnp
υπ
whether it loses or wins the battle depends on the cooling rate, i.e. on kinetics.
Mass balance:
Number density: Number density: 2000 cm2000 cm --33
Salt mass:Salt mass:22××××××××1010--1616gg ((NHNH44))22SOSO44
Minority withMinority with22××××××××1010--1515gg ((NHNH44))22SOSO44
Überfluss haben; wer aber nicht hat, dem wird auch noch weggenommen, was er hat.
Car à celui qui a, on donnera, et il aura encore davantage; mais à celui qui n'a pas, on ôtera même ce qu'il a.
(Mt 25,29)
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
62
Clouds
How far do we get with thermodynamics in explaining
cloud formation?
3 Types of Polar Stratospheric Clouds (PSCs)
(1) Ice (2) NAT (nitic acid trihydrate
= HNO3 ⋅⋅⋅⋅ 3H2O, crystalline)(3) STS (supercooled ternary
solutions, H2SO4/HNO3/H2O)
Lidar observations
63
Lidar observationsPSCs over the Norwegian Alps Wirth et al. (1994)
Hanson and Mauersberger (1986):
Mass spectrometric measurements Formation of NAT PSCs
64
Carslaw et al. (1994):
Thermodynamic modeling of STS (supercooled ternarysolutions, H2SO4/HNO3/H2O)
65
Thermodynamics of Electrolytes. I. Theoretical Basis and General Equations
Kenneth S. Pitzer, J. Phys. Chem., 77, 268 - 277, 1973:
66
Pitzer Ion-Interaction Model:
long range ionic short range short range neglectinteraction potential 2-body interactions 3-body interactions higher order( I = ion strength) of species (i, j, k, w) of species (i, j, k, w) terms
Activities:
.....11
)( 2∑ ∑ +++=ij ijk
kjiijkw
jiijw
w
ex
nnnn
nnn
IfnRTG µλ
ii n
GRT
a∂∂×= 1
ln
67
Theoretical decription for f(I): Debye-Hückel theory (1928)
Data used to parameterize the ineraction potentials λij , µijk :
(1) pvap measurements: for water
for solutes, e.g. HCl ↔ H+ + Cl-
(2) Electromotive force measurements:
(3) Enthalpy measurements: (4) Measurements of heat capacities.(5) Measurements of solubilities.(6) Measurements of dissociation coefficients
)ln(ClH −+×+= aa
RTF
EE 0
)/()/(
TTG
H1∂
∆∂=∆
wwwww n
GRT
aapp∂∂×=×= 10 ln;
iH nG
RTa
K
aap
∂∂×== −+ 1
HClClH
HCl ln;
Pitzer Ion-Interaction Model:
Activities:
pvap for H2O
∑ ∑++=ij ijk
kjiijkw
jiijw
w
ex
nnnn
nnn
IfnRTG µλ 2
11)(
ii n
GRT
a∂∂×= 1
ln
G∂1
68
�
pvap for HNO3
�
wwwww n
GRT
aapp∂∂×=×= 10 ln;
iH nG
RTa
K
aap
∂∂×==
+ 1ln; H
HH 3
-3
3 NO
NON
O
Alti
tude
[km
]S
urfa
ce a
rea
cm3 ]
Ice
Ice
Bac
ksca
tter
Rat
io
Bac
ksca
tter
Rat
io
Box modeling of PSCs
(a) Lidar backscatter ratio
(b) Backscatter along trajectory of ice, NAT and STSRed: measured, black: calc.
(c) Calculated surface area densities
69
Sur
face
are
a [ µµ µµ
m2 /
cmM
ixin
g R
atio
[p
pbv]
Time [h]
Distance [km]
densities
(d) Calculated chemical effects, mainly due to HCl + ClONO2 → Cl2 + HNO3
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Deliquescence of aerosols
70
Clouds
How far do we get with thermodynamics in explaining
cloud formation?
Deliquescence RH of organic mixtures
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
Eutonic mixtures:
M2: malic + malonic
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
Eutonic mixtures:
M2: malic + malonic
M3: malic + malonic + maleic
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
Eutonic mixtures:
M2: malic + malonic
M3: malic + malonic + maleic
M4: malic + malonic + maleic + glutaric
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
Eutonic mixtures:
M2: malic + malonic
M3: malic + malonic + maleic
M4: malic + malonic + maleic + glutaric
M5: malic + malonic + maleic + glutaric + methylsuccinic
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
Eutonic mixtures:
M2: malic + malonic
M3: malic + malonic + maleic
M4: malic + malonic + maleic + glutaric
M5: malic + malonic + maleic + glutaric + methylsuccinic
T = 25°C Marcolli et al. (2004)
Deliquescence RH of organic mixtures
The more complex the solution the lower its deliquescence (and hence
Eutonic mixtures:
M2: malic + malonic
M3: malic + malonic + maleic
M4: malic + malonic + maleic + glutaric
M5: malic + malonic + maleic + glutaric + methylsuccinic
T = 25°C Marcolli et al. (2004)
lower its deliquescence (and hence efflorescence) RH (entropic effect). Aerosols with such complex com-positions stay liquid to very low RH
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Deliquescence of aerosols
Homogeneous nucleation of water droplets
78
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
NucleationFormation of a critical cluster from a sequence of bimolecular additions:
A + A ↔↔↔↔ A2
A2 + A ↔↔↔↔ A3
…Ai-1 + A ↔↔↔↔ Ai (critical cluster)
- supersaturation: necessary but not sufficient- need to form new surface (Kelvin equation)
Clathrate structure
79
- need to form new surface (Kelvin equation)- need to overcome energy barrier by a critical cluster
What energy is needed to form a critical cluster?What is the size of the critical cluster?
Excess free energy for cluster formation: ∆G = ∆GS + ∆GV
∆GS > 0 � excess free energy required to form cluster surface (expense) ∆GV < 0 � excess free energy released from volume transformation (gain)
Ice –Ih structure(Hale & Plummer, 1974)
Nucleation: Classical Theory – a poor man’s approach
where
∞=−=
)p(p
kTlnµµµ lg∆
µνπσπ
µσ
∆−=
∆−=∆+∆=∆
m
vs
rr
nA
GGG
34
43
2
∆G
∆Gcrit
- G∆ V ∆GS
rcrit
80
� Critical radius:
� Critical energy (barrier): Assumptions?
∆µ
σνr mc
2=
( )222
23
2
23
2
23
2
23
)(/ln(3
16)(3
16
)(332
)(16
∞=
∆=
∆−
∆=∆
ppTk
vv
vvG
mm
mmcrit
πσµ
πσµ
πσµ
πσ
∆ ∆G + GS V
rcrit
Obtain prefactor K from kinetic collision frequency:
mm : molecular massNv : vapor concentration
If we assume an Arrhenius reaction velocity equation commonly used for the rate of a thermally activated process, the rate of nucleation, J, is given as:
SNv
mK vm
m
22/12
=
πσ
( )
∞−=
∆−= 222
23
)(/ln(3
16expexp
ppTk
vK
kTG
KJ mcrit πσ
81
Nv : vapor concentrationSmm π
Example: critical radius, number, and nucleation rate for water droplets at 298 K
p/p(∞) rc (Å) ic J (cm-3s-1)
1 ∞ ∞ - ∞
2 15.1 482 1.3 x 10-47
3 9.5 121 8.9 x 10-4
4 7.6 60 6.4 x 10+7
5 6.5 39 3.8 x 10+11
σ = 0.072 N/m ; νm = 2.99 x 10-29 m3 ; mm =2.99 x 10-26 kg
Experiments on homogeneous nucleation from vapors b y a nucleation pulse method
82
• Premixed vapor and carrier gas (Xe, Kr, Ar, Ne or He)
• Expansion is held for texp (a few ms)
• Small recompression to quench further nucleation� nuclei can grow into droplets of observable size (µm)
• Number density C of the droplets obtained from scattered light� J = C / texp Wagner & Strey, JPC 1983
Strey et al., JPC, 1994
83Strey et al., JPC, 1994, 98, 7748 – 7758.
Homogeneous nucleation exp.:
ptot and scattered light flux, θ = 15°
Significant light scattering occurs only after the nucleation pulse
Nucleation pulse:
Obtain experimental pressure drop ∆pexpt and duration ∆texpt of the nucleation pulse
Homogeneous nucleation rates for water: gas-to-liqu id and liquid-to-solid
84
Nucleation rate measurements and classical (Becker-Döring) theory (Viisanen et al., J. Chem. Phys., 1993).
Solid lines belong to solid points.
Variation of the rate of homogeneous ice nucleation in supercooled water (from Pruppacher and Klett, Kluwer, 1997).
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosols
85
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
A quantitative thermodynamic ice freezing theory Koop et al., Nature 2000
Unifies freezing nucleation temperatures and rates for 18 different aqueous solutions:
H2SO4
HNO
Homogeneous ice nucleation
86
H2SO4
HNO3
HNO3/H2SO4
NH4HSO4
(NH4)2SO4
NH4F
LiCl
NaCl
KCl
NH4Cl
CaCl2MnCl2
Ca(NO3)2H2O2
urea
ethylene
glycol
glucose Relative humidity
∆aw
∆aw
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
87
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
separation
Deliquescence/efflorescence of aerosol particles
88
Electrodynamic particle trap
� store single micron-sized particle� air flow with controlled RH (5-95 %)� air flow with controlled T (160-310 K)� multiple spectroscopic analysis methods
Efflorescence measurements
� here (NH4)2SO4 (sulfate) particle� also NH4HSO4 (bisulfate)� and (NH4)3H(SO4)2 (letovicite)
hysteresis(measured in trap)
Trajectory-based global analysis (Colberg et al., 2003):left: full account for hysteresisright: allow efflorescence w/o supersaturation
O/H/SO/HSONH 22444
−−+
89
Thermodynamic properties of aerosols• evidence for prevalence of liquid organic aerosols• evidence for liquid-liquid phase separations
90
Raman microscope:
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
91
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
Heterogeneous nucleation of ice on mineral dust
Heterogeneous nucleation on Arizona test dust (ATD):A first active-site-attribution approach
Hea
t flo
w (a
.u.)
1 wt% ATD
DSC expt on emulsified aqueous suspension of ATD (1 wt%)
Marcolli et al., ACP, 2007.
92
230 235 240 245 250 255 260
Temperature (K)
Hea
t flo
w (a
.u.)
Homogeneousfreezing of dust-
free droplets
Hetero-geneous
freezing on ATD
(a) DSC experiments on an emulsified ATD suspension �
(b) Assuming all ATD particles to have the same active site(c) Attributing stochastically a single active site per ATD ptcl(d) Active site distribution on each ATD particleMore realistic dusts than ATD: Pinti et al.
Where does mineral dust come from?
93
Location of preferential dust sources
W. African
Bodélé
Taklamakan
Gobi
94
Percentage of model grid box that is a preferential dust source, calculated from the extent of potential lake areas, excluding areas of actual lakes [Tegen et al., 2003, Quat. Sci. Rev].
Bodélé
Lagrangian tracing of RH ice
RHice,Lagr > 100 %
RHwater,Lagr < 100 %
“cold cirrus”T = -40°C
“warm thin cirrus”
altitude
9595
Transported specific humidity (Q) at beginning of each trajectory (t = 0)No condensation and mixing � trace Q only up to RHw ≤ 100%Checked ECMWF’s T(t = 0) and Q(t = 0) are realistic
T < 0°C
Q (t = 0)
distance
40
60
80
100
120
140
160
180
200
avgdry wet
RH
ice
[%] Liquid Liquid
water water cloudcloud
MPCMPC
MPCMPC’’
Warm thin
cirrus
Cold thin
cirrus
ClasscalClasscalcirruscirrus Mixed phase Mixed phase
cloudscloudsClassical Classical
cirruscirrus’’
Cloud formation processes200
150
100
50
96
210 220 230 240 250 260 270 280 2900
20
40 avgdry wet
Temperature [K]220 230 240 250 260 270 280 290
# sa
tura
ting
traj
ecto
ries
[K-1
] 0
2000
1000
0210
Distribution of trajectories from Taklamakan
10
12
14
16
18Mixed phase
clouds
Results by Cloud Type%
of a
ll tr
ajec
tory
poi
nts
(1.7
Mio
in e
ach
regi
on)
Dust gets
Potentially big effect
herenegligible
97
0
2
4
6
8
10
Classical cirrus
Cold thin cirrrus
Liquid water clouds
Warm thin cirrrus
% o
f all
traj
ecto
ry p
oint
s (1
.7 M
io in
eac
h re
gion
)
No effect on cold cirrus
Do “warm thin cirrus” exist at all?
Dust gets into cirrus
only via MPC Affects cloud
properties and precip.?
negligible
40
60
80
100
120
140
160
180
200
avgdry wet
RH
ice
[%] Liquid Liquid
water water cloudcloud
MPCMPC
MPCMPC’’
Warm thin cirrus
Cold thin cirrus
Classical Classical cirruscirrus Mixed phase Mixed phase
cloudscloudsClassical Classical cirruscirrus’’
Cloud formation processes200
150
100
50?!AIDA chamber
experiments[Möhler et al., 2006]↑↑↑↑ Saharan
IN efficiency drops by > 1 order of magnitude upon coating with 1-10 nm of H 2SO4, (NH4)2SO4, C2H4(COOH)2[Wex et al., 2009]
CFDC measure-ments[Salam et al., 2006]
Thermal dif-fusion chamber[Schaller & Fukuta, 1979]↑↑↑↑ kaolinite
AIDA warm measurements [Field et al., 2006]
Saharan
?!Microscope cold stage [Roberts & Hallett, 1968]
Montmorillonite
98
210 220 230 240 250 260 270 280 2900
20
40 avgdry wet
Temperature [K]220 230 240 250 260 270 280 290
# sa
tura
ting
traj
ecto
ries
[K-1
]
0
2000
1000
0
210
Distribution of trajectories from Taklamakan
↑↑↑↑ Saharan↑↑↑↑ Taklimakan↓↓↓↓ ATD
↑↑↑↑ kaolinite↓↓↓↓ montmorillon.
↑↑↑↑ kaolinite– local soil↓↓↓↓ silver iodide
SaharanAsian
Montmorillonite↑↑↑↑ unprocessed↓↓↓↓ preactivated
� Availability of bare dust for cold cirrus is negligible� Mineral dust unlikely competitor to homogeneous nucleation� Availability for mixed-phase clouds higher from Asian deserts
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
99
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
Heterogeneous nucleation of ice on mineral dust
Diffusion growth of droplet or ice particle
Diffusion Growth of Flat Surface or Water Droplet
1-D 3-D
(1) Continuity equationn = H2O molecule number density (in the gas phase)j = molecules per area per time = molecular flux
=∂
∂t
txn ),(
100
(2) Fick’s LawDiffusive flux of molecules is a result of number density gradients:(diffusion coefficient [D] = cm2 s-1) j =
(3) Diffusion EquationCombine (1) and (2) :
∂t
The droplet growth problem:
r = radial coordinatea = droplet radiusn = number density of H2O moleculesn∞ = number density far from dropletna = number density just above
= droplet surface
Transform from Cartesian coordinates to spherical c oordinates:
101
(e.g. formulae in Jackson’sbook on electrodynamics)
The droplet growth problem is in good approximation spherically symmetric. Therefore, the diffusion of H2O molecules towards a small water droplet of radius a can be described by the radial diffusion equation:
where Dg is the diffusion constant of H2O molecules in air.
n)(rrr
DnDtn
2
2
g2
g ∂∂×=∇=
∂∂ 1
Task: For stationary conditions (∂/∂t = 0), derive n from this equation.
Need two boundary conditions:n(r → ∞) = n∞ = const far awayn(r → a) = na = const above droplet surface.
n)(rrr
DnDtn
2
2
g2
g ∂∂×=∇=
∂∂ 1
102
2)()(and)()(ra
nnDrn
Drjnr
nnrn gg ∞∞∞ −=∂∂−=+−= aa
a
Interpretation:
• p∞ = n∞ kT is the H2O partial pressure.• pa = na kT is the H2O vapor pressure. • (na – n∞) < 0 � water uptake• (na – n∞) > 0 � water loss• (na – n∞) = 0 � equilibrium
Droplet growth:
103
S = droplet surface areaN = # H2O molecules in dropletV = droplet volumeVm = H2O molecular volume
)( ∞−−= nna
DV
dtda
ag
m
Growth/evaporation law for a droplet
⇒⇒⇒⇒
pa = na kT is the H2O vapor pressure
But there is a serious problem with our solution:
⇒⇒
104
⇒⇒⇒⇒ Violation of flux limitation
This result diverges for . But this is physical non-sense!
The flux cannot become arbitrarily large but is limited by molecular bombardment.
Continuum Theory Molecular Theorydiffusion equation statistical thermodynamics
In mathematical terms, we need to change our boundary condition:
Need a flux boundary condition, not a concentration boundary condition!
Molecular bombardment on surface: (v = mean molecular thermal velocity)
⇒⇒⇒⇒ Hertz-KnudsenEquation
nvj41=
)(4
!1
)()( avapag nnva
nnDaj −=−= ∞α
105
v = mean molecular thermal velocityα = mass accommodation coefficient
� 1 - α is the fraction of colliding molecules that is reflected by surface
From this equation determine na :
No divergence!Finite growth andevaporation rates!
Dg =
)/4(1 vaD
nn
a
DV
dtda
g
vapgm α+
−×−= ∞
=+
−×−= ∞nnD
Vda vapg
m αλ
106
=+
×−=aa
Vdt m αλ /1
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
107
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
Heterogeneous nucleation of ice on mineral dust
Diffusion growth of droplet or ice particle
Microphysics and micrometeorological interplay
Importance of meso-scale temperature fluctuations for ice
nucleation
0 10 20 30time (hours)
0.8
0.4
frac
tion
of o
ccur
renc
e
MASP (0.3-40 µm)
T (K)
245
240
235
108
SUCCESS campaign, cirrus cloud at ~ 7 km altitude
time (hours)0
0.8
0.4
0
0.0001 0.01 0 100 10000
frac
tion
of o
ccur
renc
e
Model
0.0001 0.01 0 100 10000ice particle number density (cm-3)
Hoyle et al. (JAS, 2005)
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
109
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
Heterogeneous nucleation of ice on mineral dust
Diffusion growth of droplet or ice particle
Microphysics and micrometeorological interplay
Glass formation
Example:
H2O uptake impedance of glassy aerosols: sucrose particle
deli-que-scence
no efflorescence
impeded H2O uptake
Particle mass(UDC signal)
110
particle at 291 K
(5-day experiment, each leg ~ 1 day)
RMSD (intensity)
crystal
crystal (aspherical)
droplet or glass bead (perfectly spherical)
Light scattering
Thermo-dynamics
AerosolsClouds
Kinetics
Formation of water clouds
Formation of Polar Stratospheric Clouds
Homogeneous nucleation of water droplets
Homogeneous nucleation of ice in aqueous solutionsDeliquescence of
aerosolsHom. efflorescence and liquid-liquid separation
111
Clouds
How far do we get with thermodynamics in explaining
cloud formation?When do we need a kinetic
treatment?
Heterogeneous nucleation of ice on mineral dust
Diffusion growth of droplet or ice particle
Microphysics and micrometeorological interplay
Glass formation
Combined frost point / backscatter measurements
Very last slide:
Low clouds, cirrus and stratospheric aerosol above Zurich, 16 September 2009
112
Highlight:New Instrument development
COBALDLightweightBackscatter Sonde
Feature Specification Remark
wavelengths 455 nm & 870 nm color index 1-15
Backscatter 104 from unperturbed dynamic range stratosph. aerosol to
thick anvil outflowthick anvil outflow
time resolution 1 s 0.05-3 s selectable
dimensions 17 × 14 × 12 cm3 incl. 3 cm insulation
total weight 540 g suited for piggyback
power supply 8 × LR61 (1.5V AA) for > 3 h of operation2 × 6LR61 (9V)
data interface 19.2 kbit/s, settings for SRS-C34,logic level RS232 adaptable to telemetry
altitude range ground to > 30 km cp. weather sondes
More on this: Cirisan et al., future work
Aerosol and Cloud Processes
INsnow
ice
evaporation
detrainmentnucleation
coagulation
melting
precipitation
CCN
H2O molecules
rain
cloud drops
activation
aqueous
aerosols
scavenging
Thanks!
115
Last slide:The differential particle size distribution
and its corresponding transport equation:
),,(),,(log
trxnrtrxrd
dnr
rr ≡
116
),)(,(),,())(,(
),,(),,(),(
),,(
),,(),,(),,(),,(),,(
3/1333/133
0
0
2
trrxntrxnrrrKrd
trxntrxnrrKrd
trxJ
trxnDtrxrnv
trxzn
vtrxnvtrxtn
rr
r
rr
nuc
rrrrr
srr
′−′′−′′+
′′′−
=
∇+∂
∂+∂∂+∇⋅+
∂∂
∫
∫∞
rr
rr
r
rrrrrr
aerosol
What decides whether the aerosolparticle stays an aerosol particle
water moleculeaerosol particle (e.g. NH4
+/SO42--/H2O solution)
diluted aerosol particlecloud droplet
moister
117cloud droplet
particle stays an aerosol particleor becomes a cloud droplet?
� Köhler Theory
moister
Cloud droplet formationA fierce competition without which precipitation would be massively impeded!
What decides whether the aerosolparticle stays an aerosol particleor becomes a cloud droplet?Köhler Theory
118
cooling
water moleculeaerosol particle (e.g. NH4
+/SO42--/H2O solution)
diluted aerosol particlecloud droplet
Different pathways for ice nucleation, e.g.:
Homogeneous nucleation of solution droplets
Heterogeneous nucleation on solid particles
119
Cloud condensation nucleiinsoluble aerosol
120
Depending on surface, composition,temperature, relative humidity ...
Hier Colberg
Hoyle paper
Do we need a kinetic treatment for H2o transport
121
treatment for H2o transport in strat?
Raoult lived when?
Snowwhite / Cobald