Electrical Properties of Particles

1. Electrical Properties of Particles Lecturer: Nima A-Mohajer Aerosol Mechanics Spring 2012

2. Coulomb Force • A charged particle is acted upon Coulomb force due to: • Existence on other charged particles • Existence of an external electrostatic field FE: Coulomb force (N) qp: Charge of particles (C) KE: Electric constant (Nm2/C2) R: The distance between the charged particles • Unit conversion between SI and cgs units: • Statcoulomb (stC): • the charge that causes a repulsive force of 1 dyne when 2 equal charges are separated by 1 cm (3.3310-10C) • Unit charge: 4.8 10-10 stC(1.610-19 C)

3. Coulomb Force • Electric Fields • An electric field exists in the space around a charged object and causes a charged particle to be acted upon the force. • The direction of electric field vector is the same as FE • Its strength is obtained from Coulomb force equation • The location & magnitudes of all charges on a surface are difficult to know

4. Electric field & electric potential • Potential difference • Defined as the work required to move a unit charge between 2 points (∆W) • Assuming the distance between the points to be ∆x, it is written as: • Alternative equation for the magnitude of electric field: • Field strength between two oppositely charged parallel plates • Field strength inside a cylindrical tube ∆W: Voltage difference between the wire and tubeV) R: Radius of the cylinder (m) dt: Diameter of the tube (m) dw: Diameter of the wire (m) ∆W: Electric potential (V) D: Distance between the plates (m)

5. Terminal velocity • Terminal velocity in Stokes regime • The terminal velocity of a charged particle inside an electric field is obtained by equating electrostatic field and Stokes drag force. • Terminal velocity in Non-Stokes regime • Then from Figure 3.4 or using these equations, we have:

6. Millikan oil-drop experiment Robert Millikan, (1868-1953) Winner of Nobel Prize in 1923 for his work on photoelectric effect Aerosol Technology by William Hinds (1998), Edition 2nd page 321.

7. Electrical mobility • Electrical mobility expresses the ability of a particle to move in an electric field; and it is symbolized by Z. • The electrical mobility is the velocity of a particle with qp = ne in an electric field of unit strength. • For Stokes regime the electrical mobility is obtained from: • Electrical mobility is usually appears in m2/V.s [cm2/st V.s]. • The true value of electrical mobility in non-Stokes regime is greater. • Relationship between electrical and mechanical mobility • Acceleration and deceleration in electric field is expressed by relaxation time and follows relationships in section 5.2 of the textbook.

8. Charging mechanisms • Principal mechanisms are: • Flame charging • Static electrification • Diffusion charging • Field charging • Electrolytic charging, Spray electrification, Contact charging • Diffusion charging: • Due to random collisions of ions with particles following Brownian motion • No external electric field • No dependence on the particle material • Charge accumulation creates an electric field which tends to repel later ions

9. Diffusion charging • Rate of charge accumulation decreases with time • Ions have Boltzmann distribution of velocities • Approximate equation for number of diffused charge: Ci: Mean thermal speed of the ions (240 m/s @ STP) e: Unit charge of an electron (1.6 × 10-19 C) Ni: Concentration of the ions (#/m3) k: Boltzmann constant (1.38 × 10-23 J/K) KE: Electric constant (9 × 109 Nm2/C2) • In conclusion, • Even in the presence of an electrostatic field, diffusion charging is the predominant mechanism for dp < 0.2 µm.

10. Field charging • The process of charging by unipolar ions in existence of a strong E-field • Rapid motion of ions inside the e-field to be collided with particles • Distortion of E-field lines • Ions move on E-field lines and collide particles • Presence of charge reduces the converging lines • There is no converging line at q = qs Zi: Ion mobility (about 0.00015 m2/V.s) Ni: Ion number concentration (#/m3)

11. Field charging • Sensitivity analysis on ion concentration

12. Field charging • Sensitivity analysis on electrostatic field

13. Field charging • In conclusion, • Surface charge is proportional to surface area and strength of the E-field • The rate of charging only depends on ion concentration. • For Ni = 1013/m3, 95% of charging takes place in 3 s. • The charge acquired is proportional to dp 2. • Field charging is dominant for dp> 1 µm and diffusion charging is dominant for dp < 1 µm.

14. Combined Field and diffusion charging • The surface charge equation is no longer explicit. • Estimation of the surface charge required numerical computation. # of electrons vsdp for diffusion & field charging at E = 500 kV/m and Nit = 1013 s/m3 Electrical mobility vs particle size for diffusion, field and combined charging at E = 500 kV/m and Nit = 1013 s/m3

15. Combined Field and diffusion charging • Example: • Plot shows the fly ash size distribution of typical fly ash emission. ESP is applied on particle-laden flow. How does size distribution looks like at the ESP outlet? Typical size distribution of Fly Ash

16. Corona discharge • Methods of Ion generation in air: • Radioactive discharge • UV radiation • Flame • Corona discharge • Only Corona discharge can make high enough concentration of ions. • A thin layer at the surface of the wire is the only region with sufficient field strength with air conductivity (breakdown). • Required breakdown field strength inside a cylinder: dw: wire diameter (cm) dt: tube diameter (cm) ∆V: Electrical potential difference between wire and tube r: Tube radius • Field strength inside a cylinder:

17. Corona discharge • Definition • Production of dense cloud of free electrons and positive ions around wire • Types of Corona discharge: • Negative corona • Positive corona • Applied difference: • Negative corona comes with lower energy but higher electrons concentration.

18. Corona discharge - + + - Step 2 + + - + - + + Step 3 - - - + + Step 4 + - Positive Corona Negative Corona - - + + Step 1 Electrode Collection Plate Electrode Collection Plate particle electron molecule

19. Electrostatic Precipitator (ESP) • Drift velocity of particles between the ESP plates

20. Deutsch-Anderson equation • Assumptions for turbulent flow with lateral mixing in wire-and-tube geometry • Particle concentration is uniformly distributed at each section of the ESP • Negligibility of the gravitational force • No bouncing and re-entrainment • Residence time Q: Flow rate of particle –laden stream L: Length of the ESP R: Radius of the cylinder-shaped ESP

21. Deutsch-Anderson equation • Derivation in wire-and-tube ESP

22. Electrostatic Precipitator (ESP) • Types of ESPs in terms of shape • Cylindrical type • Plate type • Types of ESPs in terms of flow direction • Vertical gas-flow • Horizontal gas-flow • Types of ESPs in terms performance • One stage or two stages • Dry or wet • Plate type, horizontal gas-flow, one stage and dry ESPs are the most common ESP type in industrial application.

23. Electrostatic Precipitator (ESP) One-stage ESP Two-stage ESP Collecting electrodes Discharge electrodes The observed minimum is because of Cunningham factor in calculation of drift velocity.

24. Electrostatic Precipitator (ESP) • General advantages of ESPs • Effectively collection of fine particles • Working under wide range of temperature and pressure • Experiencing relatively a low pressure drop (typically 1 to 2 kPa) • General disadvantages of ESPs • Not suitable for explosive and flammable dusts • High investment cost • Other considerations • Electrode robustness to avoid vibration • Electrode material to avoid erosion • Separation between the discharging electrodes is usually 20 ~ 25 cm • Taking the right angle for the hoppers • Frequent mechanical rapping to clean the collecting plates

25. Electrostatic Precipitator (ESP) • Selecting the right ESP • One-stage ESP is good for avoiding re-entrainment of collected particles • One-stage ESP working conditions maintain between 102 to 108Ωm • Two-stage ESP provides more collecting area for the same size of ESP • Two-stage ESP is good for low dust concentration, adhesive dusts and mists • Two-stage ESP is good for coagulating the fine particles • Wet ESP eliminates particle re-entrainment and collects gaseous pollutants • Wet ESP has the highest collection efficiency but higher operating cost • Wet ESP is good for particles with very low or high resistivity • Wet ESP removes NO2, SO2, HCl and NH3. • Wet ESP may be used in the downstream of a dry ESP

26. Electrostatic Precipitator (ESP) • Re-entrainment • Re-entry of collected dust into inter-electrode spacing. • Due to rapping • Due to increase in stream velocity near the collecting electrodes • Due to poor charging of the collected particles • Dust resistivity less than 102Ωm Abnormal re-entrainment • Injection of adhesive agents (like Ammonia, Ammonium sulfate or oil mists may reduce the entrainment.

27. Electrostatic Precipitator (ESP) • Back corona • Establishment of an electric field, Ed, inside the dust layer on the collecting electrode due to corona current. • Happens usually at ρd > 5 × 108Ωm ρd: Dust resistivity (Ωm) Edb: Breakdown strength of the dust layer (V/m) id: Corona current density (A/m2) • Happens in negative corona • Positive streamers head to discharge electrodes, the flashover voltage reduces sparking occurs • Using scraping or brushing is effective in avoiding back corona • Varying temperature and humidity to change ρd • Generally, back corona is reduced at lower temperatures but this increases re-entrainment

28. Charge limits • Negatively charged particles • Spontaneous emission of electrons from the particle • Corona discharge of particles due to reaching charge upper limit • Charge limit is proportional to particle surface area • Positively charged particles • Spontaneous emission of positive ions from the particle • Higher EL is needed compared to negatively charged particles • Charge limit for solid and spherical particles: nL: Maximum number of electrons EL: Required surface field strength 9 × 108 (V/m) for negatively charged particles and 2.1 × 1010 V/m for positively charged particles • Rayleigh limit for liquid droplets: ϒ: Surface tension

29. Charge limits Particle charge limits (ϒ = 0.073 N/m)

30. Equilibrium charge distribution • Ions concentration in air: 103 #/cm3 • Initially neutral particles acquire charge due to impact with air ions • Initially charged particles lose charge attracting opposite air ions • This leads to Boltzmann Equilibrium charge distribution • For particles larger than 0.5 µm it is practically normal distribution:

31. Equilibrium charge distribution • Number of charges on a particle after getting exposed to bipolar ions: • Rapid discharge of a highly charged aerosol is done with mixing with a high concentration of bipolar ions. • Soft X-Ray or Radioactive sources (Kr-85, Po-210)

32. Electrical Mobility Analyzer ∆V: Potential difference between the plates (V) u: Mean flow velocity (m/s) h: Half of the inter-plate distance (m) L: Inlet to exit distance (m) Q: If monodisperse aerosols are introduced, what information can we obtain using this instrument?

33. Electrical measurement • EAA • Electrical Aerosol Analyzer • DMA • Differential Mobility Analyzer

34. Electrical measurement • Criteria for EAA • Prescribed conditions must be met (T, P and ion concentration) • Stable concentration and size distribution during measurement • Only for solid or non-volatile liquids • Below 0.02 µm, a fraction of particles is uncharged • Above 0.3 µm, mobility curves becomes flat Q: If two DMAs are connected in series/tandem (TDMA), what kind of information can be obtained?