Particle Charging
There are several mechanisms for particle charging. These include:
1) Contact or friction electrification
The separation of dry non-metallic particles from solid surfaces can result in
the transfer of charges between surfaces to equalize their Fermi levels. This
charging mechanism is important for solid particles and can result in
significant, but uncontrolled, number of charges on the particles.
2) Charging by gaseous ions:
The collisions of gaseous ions, generated by unipolar or bipolar chargers, with
aerosol particles results in particle charging.
• Diffusion charging – Collisions driven by random ion motion
• Field charging – Particle-ion collisions influenced by an applied
external field.
3) Spray charging:
During processes such as atomization/nebulization, charged droplets are
produced for liquids with surface charges.
4) Induction charging
5) Thermionic emission
Thermionic emission (also known as the Edison effect) is the flow of electrons
from a metal or metal oxide surface, caused by thermal vibrational energy
overcoming the electrostatic forces holding electrons to the surface. The effect
is important as temperatures increase beyond 1000-3000 K.
6) Electrokinetic streaming (Streaming potential)
The generation of an electric field due to relative motion between a solid and a
fluid. Separation of charges occurs in fluids as they are passed through
capillaries or through a nozzle. e.g., The pumping of jet fuel through pipe
results in the fuel being charged. The current fuel formulations overcome this
problem by the use of additives that make the fuel conductive.
7) Electrolytic charging:
When dielectric liquids are separated from solid surfaces. During atomization
these liquids strip off charge from the surfaces of the atomizers and produce
charged droplets.
For charge-based aerosol characterization, the processes must be controlled and result in
a known, and preferably, narrow distribution of charges. From this perspective, the
popular charging mechanisms for aerosol particles are diffusion and field charging.
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Diffusion charging:
Diffusion charging refers to the mechanism where particles are charged due to
random collisions with ions. No external field is applied. The ions could be of the same
polarity (Unipolar) or both polarities (Bipolar). As charge accumulates on a particle, its
charging rate reduces.
Diffusion charging (bipolar chargers):
Typically bipolar charging accomplished using radioactive sources. The radiation
from these sources ionizes the air/carrier gas molecules and the ions collide with the
particles to form charged particles. Common radionucleides include:
Source
90
Sr
90
Y
85
Kr
τ1/2
27.7 yr
2.7 days
10.76 yr
241
Am
458.6 yr
210
Po
138.4 days
Radiation type
β
β
β
γ
α
α
Energy
0.546 (max)
2.18 (max)
0.67 (max)
0.514 (0.41%)
5.49 (85%)
5.44 (13%)
5.30 (100%)
1 Curie results in 3.7E10 disintegrations/s
α particle
β particle
γ particle
He Nucleus
electron
Energy Photon
1 ion pair/35.5 ev
1 ion pair/34 ev
inefficient ion generator
The gas ions have a Boltzmann distribution of velocities and hence their collisions with
particles are expected to result in a Boltzmann distribution of charges. The number of
charges acquired by diffusion charging during a time t is:
⎡ πK E d p ci e 2 N i t ⎤
n(t ) =
ln ⎢1 +
⎥
2 K E e 2 ⎢⎣
2kT
⎥⎦
d p kT
where n(t) is the number of charges acquired by a particle of diameter dp in time t, is the
mean thermal speed of the ions (240 m/s at STP), k is the Boltzmann constant, KE is a
constant of proportionality (=1 for cgs units; =9.0E9 Nm2C-2 for SI) and Ni is the ion
concentration. For typical diffusion chargers, Nit> 1012 s m-3
For nanoparticles, the Boltzmann distribution is an underprediction. Fuchs charging
theory is better for particle sizes < ~ 50 nm.
The particle Boltzmann charge distribution is computed by:
⎛ p 2e 2 ⎞
2e
⎟
exp⎜ −
f ( p, d p ) =
⎜
⎟
πd p kT
⎝ d p kT ⎠
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where e is the elementary electrical charge, dp the particle diameter, k Boltzmann’s
constant, T the temperature, and p the number of elementary units of charge. The above
equation gives the fraction of particles with charge p for a diameter dp.
Table 1: Aerosol charge distribution at Boltzmann equilibrium (Hinds, 1999):
Dp
(μm)
Average
No. Of
Charges
Percentage of particles carrying the indicated number of
charges
< -3
-3
-2
-1
0
+1
+2
+3
>+3
0.01
0.007
0.3
99.3
0.3
0.02
0.104
5.2
89.6
5.2
0.05
0.411
0.6
19.3
60.2
19.3
0.6
0.1
0.672
0.3
4.4
24.1
42.6
24.1
4.4
0.3
0.2
1.00
0.3
2.3
9.6
22.6
30.1
22.6
9.6
2.3
0.3
0.5
1.64
4.6
6.8
12.1
17.0
19.0
17.0
12.1
6.8
4.6
1.0
2.34
11.8
8.1
10.7
12.7
13.5
12.7
10.7
8.1
11.8
2.0
3.33
20.1
7.4
8.5
9.3
9.5
9.3
8.5
7.4
20.1
5.0
5.28
29.8
5.4
5.8
6.0
6.0
6.0
5.8
5.4
29.8
10.0
7.47
35.4
4.0
4.2
4.2
4.3
4.2
4.2
4.0
35.4
The particle charging efficiency drops dramatically below 20 nm.
Figure 1: Fraction of particle with p charges as a function of particle size.
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Field charging:
Charging by unipolar ions in the presence of a strong electric field. The interaction of the
electric field generated by the particle with the external electric field results in a
maximum charge that can be attained by a particle. This is referred to as saturation
charge (ns).
Figure 2: Electric field lines in the vicinity of a conducting particle with n charges
The charge on a particle as a function of time is:
2
⎛ 3ε ⎞⎛⎜ Ed p ⎞⎟ ⎡ πK E eZ i N i t ⎤
n(t ) = ⎜
⎟
⎢
⎥
⎝ ε + 2 ⎠⎜⎝ 4 K E e ⎟⎠ ⎣1 + πK E eZ i N i t ⎦
Where E is the applied electric field, Zi is the mobility of the ions (~ 0.00015 m2/V.s; 450
cm2/StV.s), ε depends on the particle material and ranges from 1.0 for vaccum to ∞ for
conducting particle.
After a sufficient time t, saturation is reached:
2
⎛ 3ε ⎞⎛⎜ Ed p ⎞⎟
ns = ⎜
⎟
⎝ ε + 2 ⎠⎜⎝ 4 K E e ⎟⎠
Typical saturation time ~ 3 s for Ni > 1013 /m3. Particle charge acquired due to field
charging is particle surface area dependent, while diffusion charging is largely
proportional to particle diameter. Field charging results in significant particle charge for
dp >1.0 μm, while diffusion charging is dominant for particles with dp < 100nm.
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Field charging
Figure 3: Number of charges on a particle as a function of particle size and electric field
strengths.
Corona discharge:
A common technique for generation of unipolar ions for particle charging is using
Corona discharge. A corona discharge unit typically has a thin wire in an outer cylinder
or a sharp pointed needle separated from a collection plate. For an applied potential
difference between the wire (needle) and the cylinder (plate), an electric field is
generated, with high values near the wire. For electric fields above a critical value (Es),
the gas near the wire is ionized, resulting in the generation of plasma. The electric field
and space charge effects result in repulsion of ions of polarity opposite to that of the wire.
The interaction of the ions with the particles in the channel results in effective particle
charging.
The saturation electric field for corona discharge is:
⎛
δ ⎞⎟
E s = 30 fδ ⎜⎜1 + 0.30
,
r ⎟⎠
⎝
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Where Es (kV/cm) is the saturation electric field, f is the roughness factor (=1 for smooth
T P
surfaces), δ = 0
, and r is the radius of the wire electrode (cm).
T P0
There is an optimal potential region to operate a corona discharge. Higher voltages might
results in the current (resulting from the flow of ions) from the corona discharge reaching
levels that results in a spark jumping over – this is referred to as spark over.
Typical electric fields:
1) 30,000 V/cm, breakdown field strength @ NTP
a. Above 30,000 V/cm, the air “breaks down”.
2) 3000 V/cm: Typical field inside an ESP
3) 1 V/cm: Fair weather electric field
4) 30-100 V/cm: Electric field prior to lightning
Particle Charge limits:
Electron limit:
Max electric field (Es) beyond which the particle will spontaneously emit
electrons.
Es = 2 x 108 V/cm
Ion limit:
Max electric field (Es) beyond which the particle will spontaneously emit ions.
Es = 107 V/cm
Based on the above electric fields, the limiting charge densities can be calculated as:
σ=
np
A
=
Es
4πe
; σ = 5.5E4 μm-2 for electron limit and 1.1E6μm-2 for ion limit
Rayleigh limit:
The balance of the surface tension of a liquid droplet by the repulsive force due to
the pressure induced by charges collected its surface determines the Rayleigh limit of
charges on a liquid droplet.
np =
4 πτ a
e
3
2
; where τ is surface tension and a is particle radius.
The different charge limits are shown as a function of particle size in Figure 4.
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Figure 4: Charge limits as a function of particle size (Liu and Pui, 1974)
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