Electrical Techniques
Electrical Techniques
September 23, 2010
Most aerosols carry some electric charge, and some may be highly charged. For these highly
charged particles, the force exerted on them in an electric field can be 3 orders of magnitude
higher than the force of gravity.
Charging enhances deposition, can cause contamination, used to design control equipment,
sampling instruments, particle sizing instruments.
Coulomb’s Law…
…is the fundamental equation of electrostatics giving the electrostatic repulsive force FE
between 2 point charges q and q’ of like sign separated by a distance R:
FE  KE
qq 
(1)
R2
Electric Fields
The strength of the field, E (a vector), that exists around a charged object and causes a charged
particle in the field to be acted upon by a force FE is
F
E E
ne
(2)
where n is the number of elementary charges and e is the elementary charge of an electron, 1.6 x
10-19 C = 4.8 x 10-10 statcoulomb (cgs unit). Note that in practice it is difficult to utilize equation
(1) and (2) to determine the field strength since we usually do not know the location and
magnitude of all the charges on a surface.
Alternatively we can use potential difference (voltage), which is easier to measure:
E
W
x
= potential gradient
(3)
where W is the potential difference between 2 points separated by x.
Electrical Mobility
When a charged particle is in an electric field, it will come to a terminal drift velocity, similar to
gravitational settling velocity, when forces on it are balanced. For Stokesian particles,
VTE 
neEC c
3d p
(4)

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Electrical Techniques
The Reynolds number Re always needs to be checked to make sure it is < 1 for Stokesian
behavior. Since neE can be much greater than the drag force, the Re condition can be violated
with a lot smaller particles compared to when just drag forces are present. For non-Stokesian
particles, need to follow an iterative procedure similar to that used for finding gravitational
settling velocities.
The ability of a particle to move in an electric field is typically expressed as electrical mobility,
Z, which is the velocity of a particle with a charge “ne” in an electric field of unit strength:
V
Z  TE
E
(5)
Remember, this is for the Stokes region and Re < 1.
Charging Mechanisms
Particle charging can occur by (1) attachment of small ions, (2) static electrification, (3)
thermionic charging caused by heating to the point where particles emit ions or electrons, and (4)
self-charging due to radioactive decay of particle components. The most common way is ion
attachment, which depends on the ionic atmosphere, the electric field and the particle size. In
gas cleaning by electrostatic precipitation and in certain electrical mobility analyzers, the
particles are charged by exposure to ions generated in a corona discharge. Charging by exposure
to ions of one sign is unipolar charging; exposure to mixed ions produces bipolar charging such
as what happens in the atmosphere.
Field charging – dominant mechanism for particles >> 1 micron, proportional to dp2. For
sufficiently long times, the charge on the particle approaches:

Ed2p
 1 


i  1 2


  2 
 4e
(6)
where  is the particle dielectric constant, E is field strength, e is elementary unit of charge.
Under normal conditions, time to approach conditions for equation (6) are small compared with
the time of gas treatment in a precipitator.
Diffusion charging – dominant mechanism for particles << 1 micron, proportional to dp. For the
free molecular regime,
 

1/ 2
  2 

2

i
ln
1
d
e
n
t




p
i
m kT
2e2 

  i 

d p kT
(7)
where mi is the ionic mass, ni is the concentration of ions far from the particle. For the
continuum regime, i is given as an implicit function of t.
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Electrical Techniques
Corona Discharge
How to create high concentrations of unipolar ions? Corona discharge can produce high enough
concentrations to be useful for aerosol charging. A nonuniform electrostatic field such as a
concentric wire and tube establishes it. Highest field strength nearest wire surface – this is the
corona discharge region. In this region, electrons are accelerated to a velocity sufficient to knock
an electron from an air molecule, and this creates a positive ion and a free electron. A dense
cloud of free electrons and positive ions is produced around the wire – this is what’s called the
corona discharge. For a positive corona (wire positive with respect to tube), the entire region
around the wire glows bluish green and not as much ozone is produced as with a negative
corona. Aerosols introduced into the space between wire and tube attain same polarity as the
wire.
Equilibrium Charge Distribution
Aerosol particles collide with omnipresent air ions and particles that are initially neutral will
acquire charge by collision with ions due to their random thermal motion. Aerosol particles will
also lose their charge when collide with oppositely charged ions. These competing processes
lead to an equilibrium charge state called the Boltzmann equilibrium charge distribution. It takes
around 30 minutes to reach this equilibrium.
Particle Neutralization
In a differential mobility analyzer, a polydispersed aerosol passes through a krypton-85 bipolar
charger. The purpose of this device is to convert the incoming aerosol in which the particles
have an arbitrary distribution of electrical charge, to a condition with an equilibrium charge
distribution (the krypton charger is also used to neutralize aerosols generated for testing
purposes). The charger works by the following mechanism: Kr-85 is a radioactive substance that
emits  particles (highly energetic electrons). The activity level of 2 mCi in the charger implies
that the source contains enough Kr-85 to emit 74 x 106  particles/s. These electrons may
interact with the gas flowing through the charger, producing ion pairs. A steady state is
established by the balance between ion pair production and small ion recombination at ~ 2.3 x
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Electrical Techniques
106 ions per cm3 (for a 2-mCi source) (reference: J.Aerosol Sci. 5, 465, 1974). The presence of
such a high concentration of ions means that the particles will fairly rapidly (~ 1 s) achieve an
equilibrium bipolar charge distribution described by Boltzmann’s law.
Electrical Measurement Methods
ionization-type smoke detector – simplest form of electrical aerosol instrument. A small
radioactive source generates a measurable flow of air ions. Aerosol particles capture the ions,
causing a decrease in the measured ion flow. Sensitive for small aerosol particles, thus effective
for detecting a fire in its early stages.
Electrical mobility analyzer – utilizes drift velocity of particles, which depends on size and
charge, in an electric field. Charged particles are passed through a cylindrical condenser in
which particle penetration is controlled by the voltage between the electrodes of the condenser.
Aerosol flow is introduced in the outer annulus of the analyzer tuber after passing through a
bipolar charger and clean air is introduced in the central core of the tube (for generating ions).
The electric field is generated between an outer and inner electrode – an adjustable voltage is
applied to the inner electrode (DC negative voltage up to 10 kV) with the outer cylinder
grounded. The field deflects positively charged particles towards the inner electrode.
One configuration is to operate as a low-pass filter in which high mobility particles are
precipitated out and larger particles with low mobility pass through. The following equation
gives the mean electrical mobility Zp of the particles precipitated near the lower end of the
collector rod (Willeke and Baron 1993 p. 417):
Zp 
(QT  0.5Qa )ln( a 2 / a1 )
2VL
(8)
where QT and Qa are total flow rate and aerosol flow rate in the mobility analyzer, a1 and a2 are
the inner and outer electrode radii, L is the length of the inner electrode, and V is the voltage on
the collector rod. Any particle with mobility less than Zp will penetrate the analyzer. Also, the
charge distribution of an aerosol can be obtained for a monodisperse aerosol by varying the
voltage V and measuring the corresponding particle penetration.
Another configuration is a band-pass filter in which particles within a narrow range of electrical
mobility pass through the device (also termed differential mobility analyzer (DMA) or
classifier). An extraction slit has been cut in the center rod. The particles of higher electrical
mobility will be collected on the upper portion of the rod and those with lower mobility will be
carried along with the major outlet flow. Only those with lower mobility will be carried along
with the major outlet flow. Those particles with a narrow range of electrical mobility will pass
through the narrow slit at the end of the cylinder to be detected. The mean electrical mobility of
the particles extracted through the slit is:
Zp 
QT  (Qs  Qa ) ln( a 2 / a 1 )
2VL
(9)
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Electrical Techniques
with the width of the mobility spread characterized by
Z p 
(Qs  Qa )ln( a 2 / a1 )
2VL
(10)
where Qs is sample flow and other variables are as before.
A DMA coupled to a condensation nucleus counter is used to achieve size distribution
measurements of an ultrafine aerosol. First the DMA separates a narrow size range from an
aerosol, then the CNC is used to count the particles that penetrate the DMA.
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Electrical Techniques
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