View
219
Download
1
Category
Preview:
Citation preview
Hannes.Tammet@ut.eeLaboratory of Environmental Physics
Institute of Physics, University of Tartu
Quiet nucleation of atmospheric aerosol
and intermediate ions
Quiet nucleation of atmospheric aerosol
and intermediate ions
15th Finnish-Estonian air ion and atmospheric aerosol workshop
Hyytiälä 20110524
Sources of knowledge about growth and charging of nanoparticles
Kerminen, V.-M., and Kulmala, M.: Analytical formulae connecting the “real” and the “apparent” nucleation rate and the nuclei number concentration for atmospheric nucleation events, J. Aerosol Sci., 33, 609–622, 2002.
Tammet H. and Kulmala M.: Simulation tool for atmospheric aerosol nucleation bursts, J. Aerosol Sci., 36: 173–196, 2005.
Verheggen, B. and Mozurkewich, M.:An inverse modeling procedure to determine particle growth and nucleation rates from measured aerosol size distributions, Atmos. Chem. Phys., 6, 2927–2942, 2006.
Long quiet periods may happen between burst events. The particles of secondary aerosol are mortal and would disappear when no supply. How they are regenerated?
Many research papers are written about burst events of atmospheric aerosol nucleation. Not so much about nucleation during quiet periods between the burst events. Why?
A reason: concentration of intermediate ions sufficiently exceeds the noise level of common instrumentsonly during burst events.
Extra noise as in BSMA, lowest contour of 100 cm–3
Measurement with SIGMA, noise from BSMA
Extra noise as in BSMA, lowest contour of 20 cm–3
Measurement with SIGMA, noise from BSMA
Measurement with SIGMA, lowest contour of 20 cm–3
Measurement with SIGMA without extra noise
Low noise instrumentSIGMA:Tammet, H. (2011) Symmetric inclined grid
mobility analyzer for the measurement of charged clusters and fine nanoparticles in atmospheric air. Aerosol Sci. Technol., 45, 468–479. http://dx.doi.org/10.1080/02786826.2010.546818
Air inlet
Air outlet through multi-orifice plate
Repelling electrode
Attracting electrodes
Sheathair filter
Repelling electrode
Sheathair filter
Attracting electrodes
Repelling electrode
Shield electrode
Inlet gate
Air ion trajectory
Electrometric filter for
positive ionsFilter
batteries
Electrometric filter
for negative ionsFilter
batteries
Shield electrode
Repelling electrode
WORSE HALF OF MEASUREMENTS
BETTER HALF OF MEASUREMENTS
NOISE(10 min cycles)
Charged nanoparticles are air ions
Particles and cluster ions
Ion orparticle
Molecule orgrowth unit
Quantum retardation of sticking: internal enegy levels of a cluster will not be excited and the impact
is elastic-specular
Particle or molecular cluster ?
to grow, or not to grow ?
does not grow,molecules will bounce back
grows,molecules will
stick
1.5 or 1.6 nm
CLUSTER PARTICLE
Introduction to modeling
An aim is to make the mathematical model easy to understand. GDE is not used and equations will be derived from scratch.
Empiric information is coming from measurements of intermediate ions. Quiet periods are characterized by very low concentration of nanoparticles and nearly steady state of aerosol parameters. This allows to accept assumptions:
the size range is restricted with d = 1.5 – 7.5 nm,
the nanoparticles can be neutral or singly charged,
attachment flux of ions does not depend on polarity,
nanoparticle-nanoparticle coagulation is insignificant,
all processes are in the steady state.
Extra comment:
ccNcccI
NcccI00
0
0
Assumption: all surfaces are away
Law of balance: genesis = destruction
Flux of ionsto particles
Particle growth through a diameter margin
dd = GR(d) dt
do
d
J = GR n
Symbols:
diameter crossing rate,
– apparent nucleation rate, transit rate, cm–3s–1 dt
dNdJ )(
→ dN / dt = GR n dN = n dd = n GR dt
d – particle diameter (d = dp), nm,
ddddN
dn)(
)( density of concentration distribution, cm–3nm–1–
dtdd
dGR )( – growth rate, nm s–1,
N(d) – number concentration of particles in diameter
range of 0...d, cm–3,
(a well known equation)
NB: particle growth rate may essentially differ from the population growth rate.
c – concentration of small ions, cm–3
Particle growth through a diameter interval
da = d – h/2 db = d + h/2
Inflow Leakage Outflow
d
Extrasource
(analog: classic problem about water tank and pipes)
Steady state balance:
Inflow + Extrasource – Outflow – Leakage = 0or
Outflow = Inflow + Extrasource – Leakage
(GDE : Inflow + Extrasource – Outflow – Leakage = Increment)
Equation of steady state balance
Inflow J(da) = GR(da) n(da), Outflow J(db) = GR(db) n(db),
Leakage = , Extrasource = b
a
d
ddddndS )()(
b
a
d
ddddE )(
b
a
b
a
d
d
d
daabb dddndSdddEdndGRdndGR )()()()()()()(
General steady state balance equation (integral form):
da = d – h/2 db = d + h/2
Inflow Leakage Outflow
d
Extrasource
Outflow = Inflow + Extrasource – Leakage
dtddn
dndS
)()(
1)(
relative depletion rate or
sink of particles s–1,(incl. CoagS as a component)
– Charging state = CST
Comparison with Lehtinen et al. (2007)
b
a
b
a
d
d
d
daabb dddndSdddEdndGRdndGR )()()()()()()(
Balance equation:
Substitute GR n with J, assume E = 0,
consider da = const & db = argument:
d
constdddndSconstdJ )()()(
Equation (4) in Lehtinen et al. (2007): JGR
dCoagS
dddJ p
p
)(
Differences: different notations of sink and two simplifications
E = 0 & additional components of sink are neglected,
dependence of GR on d is not pointed out.
substitute n with J/GR:
)()(
)()(dJ
dGRdS
ddddJ )()(
)(dndS
ddddJ
calculate derivative:
Sink of nanoparticleson background aerosol
The background aerosol can be replaced with an amount of monodisperse particles in simple numerical models. The diameter of particles is assumed dbkg = 200 nm that is close to the maximum in the distribution of coagulation sink. The concentration Nbkg can be roughly estimated according to the sink of small ions. The coagulation sink is calculated as
Sbkg = K(d, dbkg) Nbkg
The coagulation coefficient K (d, dbkg) depends on the nanoparticle
charge and the sink could be specified according to the charge.
Notations: neutral nanoparticles – index 0, charged nanoparticles – index 1.
Sink of neutral nanoparticles Sbkg0 = K0(d, dbkg) Nbkg
Sink of charged nanoparticles Sbkg1 = K1(d, dbkg) Nbkg
Difference is small and neglecting of the charge would not induce large errors.
Charging and discharging of particles
0 +–
+
–
+
– 10
1 0
ion-to-neutral-particle attachment coefficient
(a special case of coagulation coefficient).
ion-to-opposite-charged-particle attachment coefficient
or the recombination coefficient
TWOTWOONEONE
Sink of nanoparticlesdue to the small air ions
When a neutral particle encounters a small air ion then it converts to a charged particle and number of neutral particles is decreased. We expect concentrations of positive and negative ions c equal and the sink is
Sion0 = 2 βo(d) c
A charged particle can be neutralized with an ion of opposite polarity. The sink of charged nanoparticles on small ions is
Sion1 = β1(d) c
Extrasource of nanoparticles
Some amount of neutral particles appear as a result of recombination the charged nanoparticles of the same size with small ions of opposite polarity:
E0(d) = 2 β1(d) c n1(d)
The ion attachment source of charged particles of one polarity is
E1(d) = β0(d) c n0(d)
E0 is usually a minor component in the balance of neutral particles while
E1 is an important component in the balance of charged particles.
If the rate ion-induced nucleation is zero, then all charged
nanoparticles are coming from the extrasource.
Numerical solving of balance equations
b
a
b
a
d
d
d
daabb dddndSdddEdndGRdndGR )()()()()()()(
babaabab
d
dddddddYdddY
b
a
where))(()(
2
)()()( ba
ab
dYdYdY
A small step can be made using the midpoint rule and few iterations:
)()()1 ab dYdY
ba dd )... 3, 2,
The first mean value theorem states for any continuous Y = Y(d):
da db da da dadb db
da da dadb db db
dStep by step:
GR or n can be computed step by step moving upwards or downwards
ab ddh )(11 bb dGRG )(00 aa dGRG Abbreviations:
, , , etc.
Itemized numerical model of steady state growth of nanometer particles
hncShcnnGnG abababbkgababaabb 000110000 )2(2
hncShcnnGnG abababbkgababaabb 111001111 )(
Equations:
Example of a specific problem:
Given – nucleation rates J0 and J1 or values of distribution functions
n0 and n1 at first diameter, and growth rates GR0 at all sizes.
Find – values of distribution functions n0 and n1 at all diameters.
),(),( 0110 ddKGddKG uu
Two degrees of freedom
Growth rates or values of a distribution function can be computed
step by step starting form four initial values of G0, G1, n0, and n1.
If the distribution of intermediate ions is measured then one initial
value (n1) is known. The ratio G0/G1 is always known and the
number of unknown initial values is reduced to two. These two
may be presented by G0 and n0 at some point or by any pair of
parameters that are unambigyosly related with G0 and n0.
Some examples of necessary initial information: growth rate at a certain size and a nucleation rate, growth rates at two different sizes, ratio of growth rates for two sizes and a nucleation rate. ratio of growth rates for two sizes
and value of n0 at a certain size.
Test datacharacteristic of quiet nucleation
Measurements with the SIGMA in the city of Tartu (April 2010 – February 2011) were sorted by the instrumental noise and the worse half of data was deleted. Next the data were sorted by concentration of intermediate ions and the half of measurements with high concentration was deleted. Remained 16240 five-minute records are expected to belong to the quiet phase of nucleation. 0
5
10
15
20
25
1.5 2.5 3.5 4.5 5.5 6.5
d : nm
dN1/dd : cm–3nm–1
(average of 16240 records of both + and – intermediate ions)
N
noise
OK
Fitting the measurements by means of the numerical model
J0 = 5.0 cm–3s–1, J1 = 0.00133 cm–3s–1,dbkg = 200 nm, Nbkg = 2224 cm–3.
nm Sbkg:1/h GR CST 1.5 7.38 1.26 0.4022.0 4.48 2.85 0.6862.5 3.11 3.74 0.6933.0 2.33 3.73 0.6793.5 1.82 3.55 0.6804.0 1.47 3.54 0.6934.5 1.22 3.55 0.7115.0 1.03 3.56 0.7515.5 0.88 3.59 0.7706.0 0.76 3.64 0.7906.5 0.67 3.70 0.809
0
5
10
15
20
25
1.5 2.5 3.5 4.5 5.5 6.5
Measurement
Model
d : nm
dN/dd : cm–3nm–1
(average of + and – ions)
Nbkg is estimated according to the small ion depletion. J0 and J1 are
chosen by method of trial and error.
NB: the method does not provide unambiguous results.
Alternative approach Use any numeric model of nanometer aerosol dynamics, decide steady state conditions, adjust growth parameters, and integrate over a long period at least of few hours
0
5
10
15
20
25
1.5 2.5 3.5 4.5 5.5 6.5
Measurement
Simulator
Example (simulation tool)J0= 13 cm-3s-1, J1 = 0.07 cm-3s-1
d = 1.5 2.5 4.5 6.5 nm GR = 0.8 3.6 3.5 3.8 nm/h
dN1/dd : cm–3nm–1
d : nm
Automated fitting of intermediate ion measurements
Given: measurements of intermediate ions n1 (d)
on a set of diameters (d1, d2,…, dm)
Assume and iterate 2…5 times: abab nnnn 1100 /
hncShncnGn
G abbkgabaab
b 11100111
1 )(1
11
00 ),(
),(G
ddK
ddKG
u
u
hncShcnGnG
n abbkgabaab
b 00011000
0 )2(21
2 ,
211
100
0ba
abba
ab
nnn
nnn
Fitting the measurements adjusting the growth rate
J0 = 5 cm–3s–1, J1 = 0.013 cm–3s–1,dbkg = 200 nm, Nbkg = 2224 cm–3.
nm Sb:1/h CST1.5 7.38 0.4012.0 4.48 0.6822.5 3.11 0.6863.0 2.33 0.6693.5 1.82 0.6684.0 1.47 0.6784.5 1.22 0.6925.0 1.03 0.7285.5 0.88 0.7426.0 0.76 0.7586.5 0.67 0.772 0
1
2
3
4
1.5 2.5 3.5 4.5 5.5 6.5
d : nm
GR : nm h–1
WARNING: the solution is ambiguous. Different
assumptions about
J0 and J1 are possible
0
1
2
3
4
5
6
1 2 3 4 5 6 7
d : nm
Est
imat
ed g
row
th r
ate,
nm
/h
J=1.5
J=2.3
J=3.5
J=5
J=6.2
J=8
J=9
J=10.2
J=11
Restrictions on the free parameters(when fitting the test distribution)
PRIOR INFORMATION?
ANALOG OFREGULARIZATION?
3 variants of GR0(d1)3 variants of J0(d1)
3 variants of GR0(d1)3 variants of J0(d1)
0.25
0.35
0.45
0.55
0.65
0.75
0 5 10 15
J 0 (1.5 nm) : cm-3s-1
J0(3nm)
G0(3nm)/10
Effect of guess about J0(1.5 nm)while required relation is GR0(3 nm) = GR0(7 nm)
(fitting the test distribution)
Sink, growth rate and transit rate compared with Lehtinen et al. (2007)
0
1
2
3
4
5
6
7
1.5 2.5 3.5 4.5 5.5 6.5
Sink:1/h
GR0:nm/h
J0, present model
J0, fixed KKL
J0, sliding KKL
d : nm
S : 1/h,GR0 : nm/h
J0(d) : cm–3s–1
Conclusions
SIGMA provides low-noise measurements of intermediate ions.
The integral equation of steady state balance derived in a straigth- forward way enables to design correct numerical algorithms with ease.
Measurement of intermediate ions is not sufficient to get unambiguous solution of balance equation. Additionally the values of two scalar parameters are required. Some combinations are: growth rate at a certain size and a value of n for neutral particles, growth rates at two different sizes, ratio of growth rates at two different sizes and a nucleation rate.
The nucleation of 3 nm neutral particles at Tartu about J = 0.5 cm–3s–1
is considerable contribution into the atmospheric aerosol generation.
The nucleation rate of 3 nm charged particles at Tartu about 0.002…0.005 cm–3s–1 indicates the minor contribution of ion-induced nucleation during periods of quiet nucleation.
The growth rate of fine nanometer particles during quiet phase of aerosol nucleation at Tartu is estimated about 3…9 nm/h.
for Attention
Thank YouThank You
Recommended