gas-to-particle conversion
DESCRIPTION
Gas-To-Particle Conversion. Reading: Chap 13.5. Q: What’s the interaction between gas molecules and particles? . Activated Carbon. VOC. Water droplet. Water vapor. Q: Examples?. ==> Condensation. Q: How do we have the first particle for vapor condensation?. ==> Nucleation. Q: Examples?. - PowerPoint PPT PresentationTRANSCRIPT
04/22/2023Aerosol & Particulate Research Laboratory
1
Gas-To-Particle ConversionQ: What’s the interaction between gas molecules and particles?
VOC
Water vapor
Activated Carbon
Water droplet
Q: How do we have the first particle for vapor condensation?
==>Condensation
==>NucleationQ: Examples?
Q: Examples?
Reading: Chap 13.5
04/22/2023Aerosol & Particulate Research Laboratory
2
Vapor Pressure
The pressure required to maintain a vapor in equilibrium with the condensed vapor (liquid or solid) with a flat surface at a specified temperature
TCBATPv
)(log Pv in mmHg and T in oC (if Table 9.2 is used)
(Saturation) Vapor PressureTime to reach equilibrium
How does vapor pressure change if the temperature increases?
04/22/2023Aerosol & Particulate Research Laboratory
3
04/22/2023Aerosol & Particulate Research Laboratory
4
What is the vapor pressure of water at 20 oC? If the measurement is conducted on Mars (the atmospheric pressure is about 0.006 atm), what will be the value?
04/22/2023Aerosol & Particulate Research Laboratory
5
04/22/2023Aerosol & Particulate Research Laboratory
6
Partial Pressure: the pressure that a gas (or vapor) in a mixture of gases would exert if it were to occupy the entire volume occupied by the mixture
TAA PyP
)100( )(
SRHTP
PSv
A
Supersaturation: S > 1 (RH > 100%)
Saturation Ratio (or relative humidity for water)
Q: After a rain at dusk, the temperature starts to drop. How do PV and PA change correspondingly? How about S? Can you predict the weather at dawn?
1 mole of O2 @ 1 atm
4 moles of N2
Q: How much is PO2?
Adiabatic Expansion, Mixing, Cooling, Speciation change by Gas Phase Reaction
Q: What would happen if S > 1?Q: When does it happen for S > 1?
04/22/2023Aerosol & Particulate Research Laboratory
7
Adiabatic ExpansionAn expansion allowing no heat input from the surroundings
1
2
1
1
2
TT 1
1
2
1
2
TT
pp Constp
Q: Saturated water vapor @ 20 oC (p = 17.6 mmHg) expands 20%. Calculate the new saturation ratio. Ps @ 0 oC = 4.7 mmHg, = 1.38.
Example: Cloud formation, smoke generated in the neck of a wine bottle
04/22/2023Aerosol & Particulate Research Laboratory
8
Kelvin Effect
vaporpuresystemembryos GGG
Change in Gibbs free energy accompanying the formation of a single droplet of pure material A of radius Rp
NT: # of moleculesN: # of vapor moleculesNl: # of liquid molecules
23
2
2
43
44
4
pll
ppll
Tpll
RggR
RggN
gNRgNgNG
g: Gibbs free energy of a molecule in the vapor phasegl: Gibbs free energy of a molecule in the liquid phasel: volume of one liquid molecule: surface tensionRp: particle radius
A system moves toward a lower energy state whenever possible.
(initial)(final)
04/22/2023Aerosol & Particulate Research Laboratory
9
dpp
kTggd
dpggddpggd
sdTdpdg
l
l
ll
23
4ln3
4 p
l
p RSkTR
G
SkTppkTgg
A
Al lnln 0
Q: How do we determinethe critical size?
Q: How does G change as Rp increases?
= 0 at constant T
04/22/2023Aerosol & Particulate Research Laboratory
10
)(4exp4exp ** SKkTdRTd
MWpp
Rp
l
ps
0,
pTpRG
SkTR l
p ln2*
3
23*
ln332
SkTN l
l
(Kelvin Equation)
Maximizing the G
(Critical radius)
(Critical Number)
22*
ln2
34
34*
SkTRG l
p (Max G)
The partial pressure of vapor at the surface of a small droplet is greater than the saturation vapor pressure defined for a flat surface
Q: Calculate Rp* and Nl* for water at 273 K, S = 2 ( = 75.6 dynes/cm)
(Kevin Ratio)
04/22/2023Aerosol & Particulate Research Laboratory
11
T=273 Ka T=298 Kb
S Rp* (Å) Nl* Rp* (Å) Nl*1 2 17.3 726 15.1 4823 10.9 182 9.5 1214 8.7 91 7.6 605 7.5 58 6.5 39
a = 75.6 dyne/cm; l= 2.99X10-23 cm3/moleculeb = 72 dyne/cm; l= 2.99X10-23 cm3/molecule
Critical number and Radius for water droplets
Equilibrium vapor pressure over a pure water dropletsfor various dp at T = 298 K
04/22/2023Aerosol & Particulate Research Laboratory
12
Saturation ratio vs dp
t = 0
dp*
?t = t1?
dp*
04/22/2023Aerosol & Particulate Research Laboratory
13
Homogeneous Nucleation• Nucleation of vapor on embryos comprised of vapor
molecules in the absence of foreign substances
Equilibrium Cluster DistributionFor a fluid at equilibrium, the concentration of clusters obeys a Boltzmann distribution
)/exp(1 kTGNN eNl
23
23
1 )(ln)(316exp*
SkTNN le
N l
Nl: number of molecules in the clusterN1: number of gas molecules
04/22/2023Aerosol & Particulate Research Laboratory
14
23
23
1
3/23/2
1
1
**
ln316exp
22
2
SkTN
kTkTmp
NNNaJ
lll
le
l
kTmpcNkTbN l
1
1
3/4*
24
9/2
Flux of monomer
Equilibrium # of critical sizeSurface area
energy Thermalenergy Surface
Classical Nucleation Rate
)3/43( 3llb
m1: mass of one moleculep1: gas pressure
04/22/2023Aerosol & Particulate Research Laboratory
15
Critical cluster size and droplet current for homogeneous nucleation of water at 293 K
*lNlo
g J
Critical saturation ratio set at J = 1 #/cm3.s
04/22/2023Aerosol & Particulate Research Laboratory
16
Self-Consistent Kinetic Theory
Girshick, S. L. and Chiu, C. P. J. Chem. Phys., 93(2), 1990, 1273-1277.
Q: What if Nl = 1?
)/lnexp( 3/21 kTbNSNNN ll
eNl
Classical
kTNbSNNN lleNl
/1ln1exp 3/21 Kinetic
classicalkinetic JSkTa
J
1exp Toluene
Q: What is the physical meaning of for a very small cluster?
04/22/2023Aerosol & Particulate Research Laboratory
17
Reflection
04/22/2023Aerosol & Particulate Research Laboratory
18
Adiabatic Expansion
)constant a(
C
pressureconstat at heat specific: gas, idealan For
lumeconstat voat heat specific: 0
heat : adiabatic,When enthalpy :
energy internal : amics thermodynof lawFirst
CC
dhdTCdudT
C
Cpd
dpdudhdq
qhdpdhdqupddudq
p
p
p
υ
dpp
dCC
dudh
pddp p
04/22/2023Aerosol & Particulate Research Laboratory
19
)1/(
1
2
1
2
2
1
11
22
1
2
1
1
2
22
11
1
2
2
1
1
2
//
//
law, gas ideal theUsing
constantor
sides,both Integrate
TT
pp
pp
pTpT
TT
TT
ppp