Microphysical Processes in the UTLS

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Transcript Microphysical Processes in the UTLS

Microphysical Processes in the UTLS
KEY 11
Klaus Gierens
Institut für Physik der Atmosphäre
DLR Oberpfaffenhofen
Recommended reading
1. Pruppacher and Klett, Microphysics of clouds and precipitation.
Contains almost everything.
2. Fletcher, Physics of Rainclouds (my favourite, albeit old).
3. Young, Microphysical Processes in Clouds.
4. Atkins, Physical Chemistry.
Contents
1. Classical nucleation theory (basics)
2. Koop’s theory of water activity controlled homogeneous freezing of
aqueous solution droplets
3. Some issues with Koop’s theory
4. Heterogeneous nucleation
5. Ice supersaturation within clouds
6. Volume vs. surface dominated homogeneous nucleation
Some outstanding problems
(see: Cantrell and Heymsfield, BAMS, June 2005)
1. Homogeneous nucleation
a) what role do collective fluctuations in water play?
b) is freezing only a function of the water activity?
c) what is the structure of the ice embryo and where does it form?
2. Heterogeneous nucleation
a) what are the most important properties of the heterogeneous
IN?
b) what are the mechanisms underlying contact and evaporation
nucleation?
c) what role do organic compounds play in ice nucleation?
Classical nucleation theory
G(T,RH)
r*
G(r) =  (4/3) r3 nLkT ln(e/e*) + 4r2
Classical nucleation theory
Number of critical nuclei: Boltzmann distribution
N(r*)=N0 exp(G(r*)/kT)
G(r*): energy required to form a critical nucleus:
G(r*) = 163/3(nLkT ln(e/e*)2 = (4/3) r*2
e*, e: saturation vapour pressure, actual vapour pressure
: surface tension or interfacial energy between droplet and vapour
nL: number concentration of water molecules in the liquid
r*: radius of a critical germ
Note the strong dependence on surface tension and temperature.
Classical nucleation theory, cont’d
Nucleation rate: rate at which critical germs are impinged by single
molecules (or larger clusters) to form supercritical clusters.
J = B N0 exp(G(r*)/kT),
where BN0 is of the order 1025 cm-3sec-1.
An accurate value of B is not really required since the process is
controlled totally by the exponential function.
Note the even stronger dependence of J on T!
Classical theory of homogeneous freezing
Similarly as before:
G(r*) = 16SL3/3[nSkT ln(1/awi)]2 = 16SL3/3(S T)2
with geometrical factor ,
entropy of fusion per unit volume of ice S
supercooling of the liquid T
awi=e*liq/e*ice.
Here B=(kt/h) exp(-g/kT) with activation energy g for self-diffusion,
hence
J  (nLkT/h) exp(-g/kT) exp (G(r*)/kT)
Supercooling and freezing of pure water
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Water can be cooled below its equilibrium melting point Tm.
Supercooled water is in a metastable state.
The maximum possible supercooling (Tf) can be achieved when the
water is free of any solid particles that can catalyse ice germ
formation.
At about Tf freezing happens as a kinetic (i.e. stochastic) nucleation
process, homogeneous nucleation.
Heterogeneous nucleation occurs at T>Tf, actual temperature
depends on properties of the solid particles.
Tf is a genuine property of the liquid water alone (not classically).
For pure water, arranged in µ-sized droplets, Tf is about 235 K.
When supercooled water is in equilibrium with its vapour, the
vapour must have 100 % RH (wrt liquid water).
Solution droplets have both lower Tm and lower Tf than pure water.
Concept of homogeneous nucleation in the UTLS
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pure water cannot exist at T<-38°C (supercooling limit)
ice formation via homogeneous freezing of solution droplets
foreign molecules (e.g. H2SO4) in the droplets impede formation of
ice lattice
... until droplets are grown to sufficient size in supersaturated air
(rarefies the foreign molecules)
hence solution droplets freeze at RHi>140% (this threshold
increasing with decreasing T)
freezing threshold independent of chemical composition of the
droplets
homogeneous nucleation is driven by thermodynamics
if homogeneous nucleation is the prevalent pathway to cirrus, then
high ice-supersaturation must exist in the clear and cloudy
atmosphere
Solutions – melting and freezing points
Rasmussen suggested a linear relation between melting point
depression and supercooling required for homogeneous nucleation of
aqueous solution droplets:
Tf =  Tm
Tf = Tf0–Tf
Tf0 is the supercooling limit of pure water (235 K),
Tm = Tm0–Tm
Tm0 = 273.15 K.
The constant  is independent of concentration, but depends on the
chemical composition of the solute;
 is an empirical constant and cannot be derived from first principles.
Classical treatment of solution freezing
Jsolution(T) = Jpure water(T+ Tf)
Water activity-based nucleation theory (1)
Koop, 2004
When melting and freezing temperatures of water and various aqueous
solutions are plotted vs. water activity, the data collapse on two single
curves, with little scatter in the case of the freezing temperature.
This implies that homogeneous freezing is independent of the chemical
nature of the solute.
Water activity-based nucleation theory (2)
aw
water activity aw:
saturation vapour pressure over solution
saturation vapour pressure over pure
water
the vapour pressure over the solution
equals that of pure ice at the melting
temperature Tm:
e*ice (Tm) = e*liq (Tm) aw or awi (Tm) = aw
Tf (aw) = Tm (aw -  aw)
 aw independent of chemistry.
 aw = 1 - awi (Tsc, max) = 0.305
The locus of the Tf curve is probably a determined by the
perturbation to the hydrogen bonding network induced by the foreign
molecules. (Koop 2004)
Water activity-based nucleation theory (3)
saturation vapour pressure over water
saturation vapour pressure over ice
e* liq (Tm) / e* ice (Tm)
(upper inverse aw scale)
melting curve (lower aw scale):
e*ice (Tm) / e*liq (Tm) = awi
freezing curve
critical supersaturation for homogeneous freezing
(upper inverse aw scale), red curve  blue curve:
e* liq (Tm) / e* ice (Tm)  aw (Tf)
Water activity-based nucleation theory (4)
water saturation
critical supersaturation
fit: Si,crit = 2.352 - 3.88310-3 T
J = 5.5 109 cm-3 s-1
e-folding freezing time 43 s for
1 µ droplets, or 1 s for 3.5 µ
droplets
Threshold supersaturation for homogeneous nucleation
increases with decreasing temperature
Why does water activity control hom. freezing ?
• Solutes affect the equilibrium and non-equilibrium properties of water
substance.
• Ice nucleation is affected by the solute molecules,
- increasing solute concentration  increasing supercooling
necessary for freezing.
• Peculiar properties of supercooled water
- interactions between water molecules via hygrogen bonds.
- nearly tetrahedal arrangement of the two H atoms and the two
free electron pairs around the central O atom
- preference of tetrahedral co-ordination in the local water
structure.
• Mechanical pressure and foreign (solute) molecules change the
preferred interatomic distances, hence the water structure.
How can the state of water’s hydrogen bonding network define the
locus of the Tf curve?
There are several theories:
1. Stability limit theory (Rasmussen and coworkers)
Proximity of the freezing curve to a postulated stability limit
bounding a region where isothermal compressibility is positive.
  ( lnV / p)T
2. The singularity-free scenario (Archer and Carter)
3. Existence of a second critical point (Baker and Baker)
Theory of the 2nd critical point
1. initiation of freezing in pure water
– liquid compressibility and density fluctuations reach maxima.
2. Temperature of the onset of freezing is an equilibrium property of
the liquid phase alone. (Remember strong influence of surface
tensions in classical theory. Not so here!)
3. Analytic model of liquid water: thermodynamic response functions
have extrema at atmospheric pressure and 235 K.
– predominance of weak H-bonds at higher temperatures
– predominance of strong H-bonds at lower temperatures
– locus of the extrema is a region of a significant change in the
character of the H-bonding network
– loci of the compressibility maxima and the freezing curve are
nearly the same at atmospheric pressures.
Heuristic argument and However…..
As T approaches Tf density fluctuations rise. So the probability rises to
find in the liquid regions where the density approaches that of ice.
However, as a function of T at atmospheric pressure the extrema of
compressibility etc. are much weaker then the sharpness of the
sudden increase of the freezing rate. This makes this explanation
somewhat unconvincing.
See Baker and Baker, GRL, 2004
test of Koop‘s theory in the AIDA cloud chamber
Good agreement between measurements and
model results show that Koop’s
parameterisation is able to predict correctly
homogeneous nucleation of H2SO4/H2O
solutions in the AIDA chamber.
Non-equilibrium effects lead to slightly higher
critical supersaturations as in Koop’s
equilibrium theory.
Haag et al., ACP, 2003
Some issues with Koop’s theory
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derivation of Tf(aw) needs assumption that aw does not depend on
temperature. This is indeed often the case above Tm where the
water activity can easily be measured.
Below Tm, aw must often be determined using models or
extrapolations.
For sulphuric acid, aw is nearly T-independent.
However, there are exceptions, e.g. ammonium nitrate NH4NO3.
- aw(NH4NO3) increases with decreasing T
- decreasing interaction of NH4NO3 with H2O at lower T
- more and more ion-ion recombination (NH4+ with NO3), which
makes it “invisible” for the water molecules.
- decreasing solubility of ammonium nitrate in water upon
cooling.
issues with Koop’s theory:
ammonium sulfate behaves differently
Koop et al. 2000
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Temperature (K)
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aw(ice)
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235
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215
205
195
1
0.9
0.8
0.7
0.6
0.5
0.4
Bertram et al. 2000emulsions
Prenni et al. 2000AFTIR 100%
Chelf and Martin
2000-AFTIR onset
Cziczo and Abbatt
1999-AFTIR onset
Hung et al. 2002AFTIR 50%
Chen et al. 2000CFDC, F = 0.001
Chen et al. 2000CFDC, F = 0.01
Mangold et al. 2004AIDA (my guess)
Water activity aw
from Paul DeMott
measurements of very large supersaturation, influence of organics?
no organics
with organics
Jensen et al., ACP, 2005,
report on measurements of
very large supersaturations in
very cold air, Si being much
larger than Si,crit
De Mott et al., PNAS, 2003
Kärcher & Koop, 2005, show that
organic material within the
solution droplets is able to impede
nucleation such that the peak
supersaturation can be much
higher than Si,crit
200 K
215 K
230 K
possible impedence of freezing by organic materials or
surfactants
Kärcher &
Koop, 2005
• At a certain temperature it needs a certain activity for freezing (big dots).
• Different solutions reach that activity at different solute mass fractions (W).
• Solutions containing organics generally have higher solute mass fractions
than inorganic solutions when the critical activity is reached.
• This implies
- less water,
- smaller particle volume (1/W),
- smaller freezing nucleation rates.
freezing temperature and nucleation rates
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Koop’s theory is able to predict freezing temperatures or critical
supersaturation for homogeneous freezing.
it is not able to predict freezing rates.
Freezing rates are parameterised in Koop’s paper as a function of
awawi.
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In the classical theory it is relatively straightforward to envisage
- critical germ
- attack frequency by single molecules
-  nucleation rate.
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The notion of an ice germ does not exist in Koop’s theory.
Hence difficult to see how a nucleation rate could be derived within
the framework of this theory.
heterogeneous nucleation
Classical framework:
Energy for germ formation (contact angle )
G(het) = G(hom) × f(cos ) with 0  f(cos )  1
 G(het)  G(hom),
i.e.
lower critical supersaturation or higher critical temperatures (less
supercooling) for heterogeneous nucleation.
heterogeneous nucleation
Water activity based framework:
Zuberi at al. 2002:
it may be possible to compute freezing temperatures for solution
droplets with insoluble inclusions in a way analogous to the
description of homogeneous nucleation by Koop et al. 2000.
However, the scatter in the measured freezing temperature in the
aw-T diagram is large and the fit is not perfect.
It could be that such an analogy is indeed there, but if there is not a
single value of aw (a single value of maximum supercooling of
pure water drops with insoluble inclusions) such an analogy does
not help much.
Measurements of het. freezing in the AIDA chamber
The AIDA chamber at
IMK in Karlsruhe is a
large (84 m3) cloud
chamber. Freezing is
initiated by quasiadiabatic expansion.
Ice crystals appear
and start to grow as
soon as the critical
supersaturation
characteristic for the
IN is reached.
Different species
have different
thresholds.
See Stefanie Schlicht’s poster!
observations of nucleation thresholds in data of RHi
ambient RHi
in cloud RHi
Haag and
Kärcher, 2003
onset of heterogeneous freezing
onset of homogeneous freezing
Ice supersaturation within clouds
The usual thinking is that after a (short) while the relative humidity in a
cloud should approach saturation. However, this while, the so-called
relaxation time, can last very long, depending on temperature and
crystal number concentration.
 g= [(4/3) N D(T,p)]-1
When the updraught goes on after cloud formation, saturation is not
reached because of the ongoing decrease of the saturation pressure.
Instead a residual supersaturation of a few percent will be the stable
situation.
sasympt.= g/(u g)
with updraft time scale u= (Rv cp T2) / (Lgw), provided u > g
Sometimes the relaxation time is longer than other relevant time scales
within a cloud, e.g. the sedimentation time scale. Then saturation
will never be reached within a cloud.
Ni = 5L-1, w = 4.5 cm/s, RHihet = 130 %
Time (min)
Ice supersaturation within clouds – examples
Comstock et al. (ARM data)
Ovarlez et al. (INCA data)
All CRYSTAL-FACE RHi within clouds:
Physical-chemical effects may also cause persistent supersaturation
within clouds, e.g. Delta-ice or cubic ice.
Mean RHi
binned by T:
open circles.
13 July 2002
contrail:
triangles.
19 July 2002
contrail:
diamonds.
(taken from
Figure 1 of:
R. S. Gao et
al., Science,
2004)
From R.
Herman,
2004
Where does homogeneous nucleation occur?
Drop Volume or Surface?
Traditionally the homogeneous nucleation process is described as a
process that occurs somewhere in the bulk of the droplet that then
freezes completely.
 Freezing rate is then proportional to the droplet volume
 Freezing of an ensemble obeys:
P{unfrozen at time t} = exp(-JVt) with [J] = cm-3s-1
Djikaev et al. (JPCA, 2002) and Tabazadeh et al. (PNAS, 2002) have
found indications and given arguments that homogeneous
nucleation (germ formation) should instead proceed close to the
droplet surface.
wetting criterion
Condition: at least one facet of the crystal is only partly wetted by liquid
water (could be valid for the ice-water system).
vs vl < ls
surface energies extrapolated to T= 40°C
vs = 102 to 111 mJ/m2
vl  87 mJ/m2
ls = 15 to 25 mJ/m2
Hence vs vl is approximately in the range 15 to 26 mJ/m2.
The surface energies are only measured for systems with macroscopic
dimensions, not for the small clusters containing only some tens of
molecules.
If homogeneous nucleation is a surface process, freezing experiments with
droplets in oil-emulsions can be affected by the oil.
Is this also relevant for droplets in an atmospheric environment?
Tabazadeh et al., PNAS, 2002
Duft and Leisner (ACP, 2004):
Test of the surface nucleation
hypothesis using an electrodynamic
droplet levitation apparatus.
• droplets of 19 and 49 µm radius
have the same (volume-)
nucleation rates.
• At least for such large droplets
freezing seems to occur
preferentially in the bulk.
• Relevant for freezing of droplets in
Cb or fog.
• Experiments do not exclude that in
sub-micron droplets ice germs
form preferentially at the surface.