ANALYSIS OF INFLUENCES OF DIELECTRIC AND ELECTRICAL

PROPERTIES ON PARTICLE CHARGING

Yihan Liu, Igor V. Timoshkin, Scott J. MacGregor, Mark P. Wilson, Martin J. Given and

Tao Wang Department of Electronic and Electrical Engineering, University of Strathclyde,

204 George Street Glasgow, United Kingdom, G1 1XW, UK

Abstract

Particles with dimensions less than 2.5μm (PM2.5) pose

a notable health risk. Potentially, airborne PM2.5 particles

can penetrate deep into the human respiratory system.

Electrostatic precipitation of fine and ultra-fine particulate

matter, including an impulsive micro-electrostatic

precipitation technology [1], is proven to be an efficient

method for air cleaning. An important factor which

influences the efficiency of precipitation is the electric

charge accumulated by particles in non-thermal corona

plasma discharges. Recent study [2] shows that the rate of

charging depends on the dielectric and electrical

properties of particles to be removed and the external

medium. The present paper is focused on an investigation

of the influence of the dielectric and electrical properties

(permittivity and conductivity) on the particle charging

process in the space charge developed by non-thermal

plasma. Dynamics of air-borne particles charged in a

coaxial corona reactor is discussed in this paper.

I. INTRODUCTION

Airborne particles with dimension less than 2.5μm

(PM2.5) pose a noticeable health risk to human beings.

Potentially, airborne PM2.5 airborne particles can

penetrate deep into the human respiratory system.

Electrostatic precipitation has been proved to be an

effective way to remove particles from air flow. In this

process, particles are charged by ions which are generated

by non-thermal plasma (corona discharges) and removed

from the air flow by the externally applied electric field.

Although electrostatic precipitators can provide relatively

high removal efficiency for larger airborne particles with

dimensions m or 10’s m (99.5% and above), the

efficiency for fine airborne particles drops to 90%.

Figure 1 shows a particle concentration in flue gas and

penetration of particles (percentage of particles which are

released into atmosphere) of Tarong South coal power

station in Australia [3].

Figure 1. Particle concentration and penetration flue gas

of Tarong South coal power station in Australia, adapted

from [3].

Figure 1 shows that penetration of particles with

diameter smaller than 1μm is relatively high, especially

when particle diameter is 0.8μm, the penetration is over

10%.

Two important factors which affect the efficiency of

precipitation are migration velocity of particles and size

distribution of particles. The migration velocity depends

on the charge accumulated by particles in non-thermal

plasma discharges. The rate of charging is dictated by

dielectric and electrical properties of particles (their

conductivity and permittivity).

In previous analytical studies in which a conventional

charging approach was used, the conductivity of airborne

particles is not directly included into analysis. A model

which simulates the movement of particles inside the

cylindrical precipitator is designed to evaluate the

difference between conventional and advanced charging

mechanisms [2].

Let’s consider a particle in the electrostatic precipitator

of vertical coaxial topology. Electrical force, Fe and drag

force, Fv act on the particle into opposite directions

horizontally, which gives the total force as:

))()(( tQtQECo

FF

Co

FF pc

ve

vtotal (1)

where Fv, according to the Stoke’s law, is given by

0.1 1 100

2

4

6

8

10

12

0

2

4

6

8

10

12

Co

nce

ntr

atio

n, g

/m3

Particle concentration

Penetration

Pen

etra

tio

n,

%Aerodynamic diameter, m

978-1-4673-5168-3/13/$31.00 ©2013 European Union

VRF pv 6 (2)

where η is the gas viscosity (1.8x10-5

Ns/m3), Rp is the

radius of particle (m), V is the migration velocity of

particle (m/s). The Cunningham correction factor is:

)/87.0exp(

/42.0/246.11

p

pp

R

RRCo

(3)

where η is mean free path of gas molecules (6.67 x 10

-8 m

for air).

In the conventional approach developed in [6], the

Laplacian electric field is used:

)/ln(

0

AB

AB

RRr

VE (4)

where r is the displacement of particle (m), VAB is the

voltage of the cylinder (5x106 V), RB is the outer radius of

the cylinder (0.25 m) and RA is the inner radius of the

cylinder (0.025 m).

The final form of the equation which governs the

movement of particle is:

2

2

)/ln(

))()((216)(

tRR

tQtQV

dt

dV

CoVR

dt

dVm

AB

pcAB

p

(5)

where m is mass of particle (kg).

Two charging approaches for calculation of the

dynamic charge, Q(t), are used in this simulation model.

In the conventional charging approach [7], the only

electrical parameter which is considered is the relative

permittivity of the particle (εp). In the advanced charging

approach, the relative permittivities and the conductivities

of both the particle and the medium are considered (εp, εm,

σm and σp). In the conventional charging approach, the

charge on particle as a function of time (Q(t)) is given by

[8]:

Net

tREtQ

p

p

p

c0

2

00 4)

2(

212)(

(6)

where μ is ion mobility (1.8x10

-4 m2/Vs for positive ions)

and N is ion number density (1x1016

/m3) for simulation

in Section I). In the advanced charging approach, the field charge on

particle is a function of time, Q(t), and is a combination of

conduction charge, Qc(t), and polarization charge, Qp(t).

Conduction charge is given by [2]:

)1(2

6)(/

00

2MWt

pm

pmpm

pc eERtQ

(7)

and polarisation charge is given by [2]

MWt

mp

mp

ppp eERtQ

216)( 00

2 (8)

where the Maxwell-Wagner relaxation time τMW:

02

2

pm

pm

MW

(9)

The particle migration velocity as a function of time has

been calculated using Equation (5) and is shown in

Figure 3.

(a)

(b)

(c)

Figure 3. Particle migration velocity as a function of time.

Relative permittivity of medium is 1. Conductivity of

medium and particle is 10-10

S/m. (a): Diameter of particle

is 10-6

m. Relative permittivity of particle is 2. (b):

Diameter of particle is 10-6

m. Relative permittivity of

particle is 6. (c): Diameter of particle is 10-5

m. Relative

permittivity of particle is 6.

Figure 3 shows that the migration velocity increases as

particle relative permittivity increases for the same

particle size. The migration velocity also increases as

particle size increases for the same particle relative

permittivity. Therefore, the increase of particle relative

permittivity or particle size result in the increase of the

particle velocity. It also shows that the migration velocity

obtained using the advanced charging approach is higher

than the migration velocity obtained using the

conventional approach. The difference is much more

obvious with an increase in particle relative permittivity

and particle size.

II. ANALYSIS OF PARTICLE DYNAMICS

IN ELECTROSTATIC

PRECIPITATORS

This section discusses the dynamics of particles in

coaxial electrostatic precipitators. Particles are charged by

the field charging and diffusion charging mechanisms

which will be discussed below.

A. Electric Field with the Influence of the Space

Charge

In this study the influence of space charge is considered. In the ccylindrical topology which is simulated in this model, the electric field with space charge is given by:

AE

r

RArE r

p 2

2

2

2 (10)

where Er is the electric field which is close to the critical

ionization field in atmospheric air (2.9x106 V/m), and A is:

m

IA

02 (11)

where I is corona current (2x10-6

A) and ℓ is length of

precipitator (ℓ =0.1 m).

B. Diffusion Charging

In the case of diffusion charging, diffusing ions collide

with particles due to random Brownian motion resulting

in the charge transfer. Diffusion charging is significant for

100’s nm and smaller particles. Diffusion charging is

given by [5]:

kTm

Ntde

e

kTdtQdiffusion

221ln

2)(

0

2

0 (12)

where k is Boltzmann constant, T is temperature (300 K),

d is diameter of particle (m), N is ion number density (1 x

106 /m

3 for simulation in Section II).

C. Field Charging

In the case of field charging, ions move in the electric

field, and ionic flux charges airborne particles. The ions

continue to bombard the particle until the charge on that

particle is saturated. The field charging is significant for

1 m and larger particles. As shown in Equation (8) and

Equation (9) in Section I, total field charge is the

combination of conduction charge, Qc(t), and polarization

charge, Qp(t). Figure 4 shows the field and diffusion

charging for different particle dimensions.

Figure 4. Field and diffusion charging for different

particle dimensions.

Figure 4 shows that diffusion charging makes a greater

contribution to the total induced charge for particles with

radiuses 1 m and below, while the field charging makes

a greater contribution for particles with radiuses above

1 m.

D. Dynamics of Charged Particles

Therefore, the total charge on the particle is a

combination of conduction charge, Qc(t), polarization

charge, Qp(t), and diffusion charge, Qdiffusion(t). Therefore

Equation (1) becomes

))()()(( tQtQtQECo

FF diffusionpc

v

total (13)

E. Equation of Motion

Combination of the equation of motion and equation for

the total force provides the final equation which governs

the dynamics of charged particles:

0.01 0.1 1 10 1001

10

100

1000

10000

100000

1000000

Diffusion

charge

Ch

arg

e,

e

Radius, m

Total field induced

charge

dt

drD

rER

Q

e

e

rECdt

rd

diffusion

t

mp

mp

p

t

pm

pmpm

MW

MW

2

0

0

2

2

2

6

21

12

1

(14)

where coefficients C and D are given by

26 pR

mC

(15)

CoRD

p

(16)

F. Simulation Results

The equation of motion (14) was solved for particles

with low conductivity and relative permittivity, for

particles with intermediate conductivity and relative

permittivity and for particles with high conductivity and

relative permittivity. Particle velocity, particle saturation

velocity and particle displacement have been obtained.

Simulation parameters are selected as follows:

Particle with low conductivity and relative

permittivity:

εp = 2; εm =1; σm = 1x10-11

S/m; σp = 1 x 10-10

S/m.

Particle with intermediate conductivity and relative

permittivity:

εp = 100; εm =1; σm = 1x10-9

S/m; σp = 1 x 10-8

S/m.

Particle with high conductivity and relative

permittivity:

εp = 103; εm =1; σm = 1x10

-5 S/m; σp = 1 x 10

-4 S/m.

Figure 5 shows particle velocity as a function of time

with different particle radiuses for low, intermediate and

high particle conductivity and relative permittivity.

(a)

(b)

(c)

Figure 5. Particle velocity as a function of time for

different particle radiuses. (a): low particle conductivity

and relative permittivity. (b): intermediate particle

conductivity and relative permittivity. (c): high particle

conductivity and relative permittivity.

The velocity-time curves for smaller particles in

Figure 5 follow the same tendency, which shows the

dynamics of smaller particles inside the precipitator:

particle velocity goes up to its peak and then drops down,

the velocity saturates when particle charge is saturated.

The curves for larger particles are different: when the

particle velocity reaches its peak value, it saturates instead

of dropping down. The peak velocity is the saturation

velocity for larger particles. Figure 5 also shows that

particle saturation velocity increases with an increase in

particle conductivity and relative permittivity for different

sizes of particles.

Using data from Figure 5, particle saturation velocities

as a function of particle radius have been obtained and

shown in Figure 6.

(a)

(b)

(c)

Figure 6. Particle saturation velocity as a function of

particle radius. (a): low particle conductivity and relative

permittivity. (b): intermediate particle conductivity and

relative permittivity. (c): high particle conductivity and

relative permittivity.

Figure 6 shows particle saturation velocity has a

minimum value for a certain dimension of particles. The

minimum saturation velocity for low particle conductivity

and relative permittivity occurs when particle radius is

about 10-7

m. The minimum saturation velocity for

intermediate particle conductivity and relative permittivity

occurs when particle radius is between 10-8

m and 10-7

m.

The minimum saturation velocity for high particle

conductivity and relative permittivity occurs when

particle radius is about 10-8

m.

Particle displacement as a function of time with

different particle radiuses is obtained and shown in

Figure 7.

(a)

(b)

(c)

Figure 7. Particle displacement as a function of time with

different particle radiuses. (a): low particle conductivity

and relative permittivity. (b): intermediate particle

conductivity and relative permittivity. (c): high particle

conductivity and relative permittivity.

Figure 7 shows that the displacement of larger particles

is more significant than the displacement of smaller

particles. Particle displacement increases with an increase

in particle conductivity and relative permittivity for

different sizes of particles.

III. CONCLUSION

In this paper a model has been developed and used for

comparison of the conventional charging approach and

the advanced charging approach in electrostatic

precipitation. The difference between these two charging

approaches shows that the conventional approach

provides a lower particle velocity as compared with the

advanced approach. This is a confirmation that dielectric

and electrical properties of particles and medium have a

significant influence on the dynamics of particles in

electrostatic precipitators. A more detailed simulation

model with space charge influenced electric field has been

developed, in which conduction charging, polarization

charging and diffusion charging are considered. The

results show that both particle saturation velocity and

particle displacement increase as particle conductivity and

relative permittivity increase for different sizes of

particles. The results also show that the particle saturation

velocity has a minimum value which depends on

particle’s size and its conductivity and permittivity.

IV. REFERENCES

[1] A. Mermigkas, I. Timoshkin, S. MacGregor, M.

Given, M. Wilson, T. Wang, “Superposition of DC voltage

and sub-μs impulses for energisation of electrostatic

precipitators”, IEEE Trans. on Plasma Science, v.40,

no.10, pp. 2388 – 2394, 2012.

[2] A. Mermigkas, I. Timoshkin, S. MacGregor,

M. Wilson, M. Given, T. Wang, “Removal of Fine and

Ultra-Fine Particles from Air by Micro-Electrostatic

Precipitation”, IEEE Trans. Plasma Science, n.99, 2013.

[3] B. Halliburton, J. Carras, P. Nelson,”Fine particle

emissions from power stations”, CSIRO Energy

Technology, Report 55, 2006.

[4] H. Yi, J. Hao, L. Duan et al, “Fine particle and trace

element emissions from an anthracite coal-fired power

plant equipped with a bag-house in China”,Fuel, 2008,

pp.2050-2057.

[5] K. Parker, Electrical operation of electrostatic

precipitators, Inst. Eng. Technol., UK, 2003.

[6] H. J. White, “Particle Charging in Electrostatic

Precipitation,” American Institute of Electrical Engineers,

Transactions of the, vol. 70, no. 2, pp. 1186-1191, 1951.

[7] J. S. Clements et al,’’Development of an electrostatic

precipitator to remove Martian atmospheric dust from

ISRU gas intakes during planetary exploration missions”

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2011 IEEE, pp. 1-8.