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May the force be with the particles!

Q: Difference between impaction and electrostatic collection in terms of forces acting on the system?

Reading: Chap15

Electrical Migration

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Millikan Experiment

(Robert Millikan, US, 1868-1953)Nobel Laureate, 1923

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• Coulomb’s law

• Units (esu)

• Electric Field

221

rqqKF EE

xW

qFE E

q = ne (e: unit charge)

Statcoulomb (stC): the charge that causes a repulsive force of 1 dyne when 2 equal charges are separated by 1 cm (3.3310-10C)Unit charge: 4.8 10-10stC (1.610-19C)

Electrostatic Force

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Electrical Mobility• Terminal velocity in an electrical field

qEBd

qECVp

cTE

3

c

TEp

CVd

qE3

(force balance)

qBd

qCE

VZp

cTE 3

(for Re < 1)

Charging MechanismsFlame ChargingStatic Electrification: Electrolytic charging, Spray electrification, Contact chargingDiffusion ChargingField Charging

Q: physical meaning?

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Diffusion Charging• Random collisions between ions and particles

– No external electrical field needed; independent of materials

kTtNecd

ekTd

q iipp

2

1ln2

2

Total charge

Q: Does q depend on time? on composition? on size?

STP) @ cm/s 10(2.4

speed lion thermamean 4

ic

Ni: ion concentration

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Field Charging• Bombardment of ions in the

presence of a strong field

4

23 2

ps

Edq

Saturation charge

Q: Is the charging rate dependent on particle size? On field strength?

tNtNEd

qi

ip

i

i2

eZ 1eZ

4

23

Charges by field charging

Zi: ion mobility (450 cm2/stVs): dielectric constant

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Positive Corona Negative Corona+ - -

- +

-

-

-

+

+

+

- +

electron molecule particleCollection Plate Collection PlateElectrode Electrode

Step 1

+ -

+Step 2

+ -+Step 3

+

+

-Step 4

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1 2 3

(28) (24) (12)

1 2 3

Turbulent Flow with Lateral Mixing ModelElectrostatic Precipitator

Three assumptions:

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Electrostatic Precipitator• Deutsch-Anderson Equation

RdtV

RdtRV

NdN TETE 22

2

)2exp()(

0 RtV

NtN TE

QRLVPE

QLRt

tLRQ

TE

2exp11

22

QAVE cTEexp1area)colletion (total 2 Define RLAc

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Comparison of Diffusion & Field Charging

Q: How does n vary wrt dp? Which mechanism is more important?

Q: Does collection efficiency increase as particle size increase (because of a higher number of charges)?

dp (um) ndiff nfield ntotal Zdiff ZField Z (stC•s/g)0.01 0.10 0.02 0.12 0.66 0.10 0.760.02 0.30 0.06 0.36 0.49 0.11 0.600.05 1.1 0.40 1.50 0.31 0.12 0.430.1 2.8 1.6 4.38 0.23 0.13 0.360.2 7 6.5 13.2 0.18 0.17 0.350.5 21 40 61.2 0.15 0.30 0.451 48 161 209 0.16 0.52 0.682 108 646 754 0.16 0.98 1.145 311 4035 4346 0.18 2.34 2.5210 683 16140 16824 0.20 4.61 4.8020 1490 64562 66052 0.21 9.16 9.3750 4134 403510 407644 0.23 22.78 23.0

Number of Charges vs dp

dp (um)0.01 0.1 1 10

n

10-2

10-1

100

101

102

103

104

105

106

Diffusion chargingField Charging

Nit = 107 s/cm3

= 5.1E = 5 KV/cmT = 298 K

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ELectrical Mobility vs dp

dp (um)0.01 0.1 1 10

Z (s

tC.s

/g)

0.1

1

10 Diffusion chargingField ChargingCombined Charging

Typical fly ash size distribution

Q: If the ESP is used to collect the fly ash, how will the particle size distribution at ESP outlet look like?

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Equilibrium (Boltzmann) Charge Distribution

kTden

kTdef

ppn

22

exp

dp Average % of particles carrying the indicated number of charges(m) Charges < -3 -3 - 2 -1 0 +1 + 2 + 3 > +30.01 0.007 0.3 99.3 0.30.02 0.104 5.2 89.6 5.20.05 0.411 0.6 19.3 60.2 19.3 0.60.1 0.672 0.3 4.4 24.1 42.6 24.1 4.4 0.30.2 1.00 0.3 2.3 9.6 22.6 30.1 22.6 9.6 2.3 0.30.5 1.64 4.6 6.8 12.1 17.0 19.0 17.0 12.1 6.8 4.61.0 2.34 11.8 8.1 10.7 12.7 13.5 12.7 10.7 8.1 11.82.0 3.33 20.1 7.4 8.5 9.3 9.5 9.3 8.5 7.4 20.15.0 5.28 29.8 5.4 5.8 6.0 6.0 6.0 5.8 5.4 29.810.0 7.47 35.4 4.0 4.2 4.2 4.3 4.2 4.2 4.0 35.4

tNeZntn ii4exp)( 0

Number of charges on a particle after it has been exposed to a bipolar ion concentration

(dp > 0.05 m)

pdn 37.2Average equilibrium charge

(dp in µm)

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Bipolar Charging

Q: How to produce bipolar charges?Soft X-ray (< 9.5 keV)

• Radioactive source: Kr-85, PO-210• Alternating corona

http://en.wikipedia.org/wiki/File:Krypton_discharge_tube.jpg

Kr discharge tube

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Electrical Measurement: Electrical Mobility Analyzer

VLUhZ pL

22 V: potential difference between plates

U: mean flow velocityh: half the inter-plate distanceL: inlet to exit distance

Q: If monodisperse aerosols are introduced, what information can we obtain using this instrument?

hVE2

U

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Electrical MeasurementEAA (Electrical Aerosol Analyzer) DMA (Differential Mobility Analyzer)

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Smoke Detector – Ionization type

Ionization Chamber

http://en.wikipedia.org/wiki/Smoke_detector

• 241Am emitting particles as the radiation source. • particles permit a small, constant current between two

electrodes• If particles are absorbed by smoke aerosol absorbs, the

current is interrupted which sets off the alarm

http://www.cna.ca/curriculum/cna_nuc_tech/images/smoke1.gif

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Reflections