1 Process Modeling for Dynamic Disperse Particle Separation …
9
The charging mechanism is based on particle size and electric field strength.
Particles charge fast if they are either in a high electric field or if their surface can
collect many electrons e (high surface area and, therefore, particle diameters d p ). A
comparison of particles in an electric field E is done by utilizing the dimensionless
charging numbers of
w =
d p
2
E
kT
e
(11)
at a normal temperature T = 21.5
◦ C, where k is the Boltzmann constant. The
dimensionless charge is calculated by
c
=
ne
2
2πε 0 d p kT
(12)
and the dimensionless time by
τ =
bρ E t
ε 0
.
(13)
Both curves are in principal agreement with simulations in [25]. In the beginning,
field charging is the dominant effect responsible for particle charging. At later times
field charging becomes less important, as surface charges of particles reduce the
electric field around the particle and electrons are more frequently transported around
the particle. For a better understanding of the mechanism, upper and lower bounds of
particle charging are shown in the diagram. The lower bound is obtained assuming
only the dominant charging takes place. The sum of charges method assumes that
diffusive and field charging as described in [25] are additive. This solution differs
only slightly from the simulative results in this work. For particle charging with
various permittivity the saturation charge 3w must be recalculated replacing it by the
quantity
1 + 2
ε r − 1
ε r + 2
.
(14)
This factor is a measure for distortion of the electric field around the particle.
2.6 Experimental ESP Setup
The electrostatic precipitator studied in experiments allows the analysis of the deposition of airborne particles. Construction and operation of the laboratory plant for
the investigation of electrostatic precipitators are shown in Fig. 3. The particles
are fed virtually pulsation-free via a twin-screw particle feeder and dispersed into
9
The charging mechanism is based on particle size and electric field strength.
Particles charge fast if they are either in a high electric field or if their surface can
collect many electrons e (high surface area and, therefore, particle diameters d p ). A
comparison of particles in an electric field E is done by utilizing the dimensionless
charging numbers of
w =
d p
2
E
kT
e
(11)
at a normal temperature T = 21.5
◦ C, where k is the Boltzmann constant. The
dimensionless charge is calculated by
c
=
ne
2
2πε 0 d p kT
(12)
and the dimensionless time by
τ =
bρ E t
ε 0
.
(13)
Both curves are in principal agreement with simulations in [25]. In the beginning,
field charging is the dominant effect responsible for particle charging. At later times
field charging becomes less important, as surface charges of particles reduce the
electric field around the particle and electrons are more frequently transported around
the particle. For a better understanding of the mechanism, upper and lower bounds of
particle charging are shown in the diagram. The lower bound is obtained assuming
only the dominant charging takes place. The sum of charges method assumes that
diffusive and field charging as described in [25] are additive. This solution differs
only slightly from the simulative results in this work. For particle charging with
various permittivity the saturation charge 3w must be recalculated replacing it by the
quantity
1 + 2
ε r − 1
ε r + 2
.
(14)
This factor is a measure for distortion of the electric field around the particle.
2.6 Experimental ESP Setup
The electrostatic precipitator studied in experiments allows the analysis of the deposition of airborne particles. Construction and operation of the laboratory plant for
the investigation of electrostatic precipitators are shown in Fig. 3. The particles
are fed virtually pulsation-free via a twin-screw particle feeder and dispersed into