Gas-To-Particle Conversion

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


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?


3


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?


5


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?


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


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)


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


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)


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


12

Saturation ratio vs dp

t = 0

dp*

?t = t1?

dp*


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


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


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


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?


17

Reflection


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


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

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Gas-To-Particle Conversion