Corona-driven air propulsion for cooling of microelectronics

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Corona
-
driven air propulsion for cooling of microelectronics




By

Fumin Yang



A thesis submitted in partial fulfillment of the

requirements for the degree of



Master of Science in Electrical Engineering



University of Washington

2002



Program Aut
horized to Offer Degree: Electrical Engineering



University of Washington

Graduate School







This is to certify that I have examined this copy of a master’s thesis by



Fumin Yang


and have found that it is complete and satisfactory in all respects,

a
nd that any and all revisions required by the final

examining committee have been made.







Committee Members:



___________________________________________________

Alexander Mamishev


____________________________________________
_______

Jiri Homola


___________________________________________________

Ann Mescher




Date: ______________________





In presenting this thesis in partial fulfillment of the requirements for a Master’s degree at the
University of Wa
shington, I agree that the Library shall make its copies freely available for
inspection. I further agree that extensive copying of this thesis is allowable only for scholarly
purposes, consistent with "fair use" as prescribed in the U.S. Copyright Law. An
y other
reproduction for any purposes or by any means shall not be allowed without my written
permission.





Signature
______________________




Date
__________________________





University of Washington

Abstract

Corona
-
driven air propulsion for cooling of microelectronics

by Fumin Yang

Chair of the Supervisory Committee

Assistant Professor Alexander Mamishev

Department of Elect
rical Engineering


Rapid development of microelectronics has led to high component density

that has
doubled every 12 months in the last decade. Each semiconductor component emits heat
associated with its electrical resistance.
W
ith higher density of electr
onic components on a chip,
heat sinks get denser and channels between them get narrower.
Existing cooling devices are not
efficient because gases become viscous in narrow channels
, which greatly hinders the air
movement
.
The problem of heat dissipation is
one of the most profound obstacles in the
electronics industry today.

The object of this thesis is to develop an electrostatic air pump that
could be later incorporated into a chip structure for heat withdrawal from microelectronics and
MEMS devices.

Th
is thesis explores the possibility of building an electrostatic air pump used for cooling
at chip level. Numerical simulations are conducted for different device geometries and materials
to achieve the optimal performance of air pumps. Based on the results

of simulations, several
prototypes of the electrostatic air pump were built. Measurements conducted to characterize this
device included air velocity profile at the outlet, voltage
-
air speed relationship, current
-
voltage
relationship, and air resistance.
Working efficiency of the device is calculated. It is found that the
efficiency of current air pump with single channel geometry has the same magnitude as that of
traditional computer cooling fans. At the same time, it has more efficient airflow profile an
d
several other advantages compared to rotational computer fan.




A possibility of enhanced heat exchange through evaporation is explored. Analytical
model of forces involved in the dehumidification process of air pumps is being developed.
Comparison of co
lumbic and dielectrophoretic forces is provided. The latter is rarely discussed
in framework of electrostatic devices, but may become a significant force component under
certain conditions. Future direction of this research project towards miniaturization
of existing
devices is proposed.




i


TABLE OF CONTENTS


List of Figures

iii

List of Tables

vi

Acknowledgements

vii

Chapter

1.

Introduction

................................
................................
................................
.....

1

1.1

Background

................................
................................
................................
.......

1

1.2

Motivation

................................
................................
................................
..........

4

1.3

State of the art

................................
................................
................................
...

6

1.3.1

Corona driven pump for air movement

................................
.......................

6

1.3.2

Corona discharge

................................
................................
........................

6

1.4

Thesis Outline

................................
................................
................................
....

7

Chapter

2.

Basic principles of electrostatic air pump operation

................................
......

9

2.1

Operation of the electrostatic air pump

................................
..........................

9

2.2

Ion generation in gases

................................
................................
...................

10

2.2.1

Properties of gas in corona discharge

................................
.......................

11

2.2.2

Ionization processes

................................
................................
..................

11

2.2.3

Mathematical description of corona discharge

................................
.........

12

2.3

Positive and negative corona discharges

................................
.......................

13

2.3.1

Positive corona

................................
................................
..........................

14

2.3.2

Negative corona

................................
................................
........................

15

2.4

Theoretical cu
rrent
-
voltage relationship

................................
......................

15

2.5

Electric field distribution

................................
................................
...............

17

2.6

Enhancement of heat exchange through water evaporation
.......................

19

2.6.1

Charging process

................................
................................
.......................

20

2.6.2

Electric drag

................................
................................
..............................

22

2.6.3

Stability of a charg
ed liquid droplet
................................
..........................

23

2.7

Advantages of corona technology in micro
-
cooling

................................
.....

24

Chapter

3. Theoretical background

................................
................................
................

27

3.1

Comparison of forces acting on water droplets and particles in the air

....

27

3.2

Columbic force

................................
................................
................................

27

3.3

Dielectrophoretic (polarization) forces

................................
.........................

28

3.4

Biot
-
Savart force

................................
................................
.............................

35



ii

Chapter

4. Device design and simulation
................................
................................
........

36

4.1

Simulation of a single pair electrodes air pump

................................
...........

36

4.1.1

Methodology

................................
................................
.............................

36

4.1.2

Results

................................
................................
................................
.......

37

4.2

Simulation on optimum air movement vs. collection efficiency

.................

44

4.3

Design and simulation of the air pump with channel geometr
y

.................

46

4.3.1

Design of the air pump with channel geometry

................................
........

46

4.3.2

Maxwell simulation of an air pump with single channel geometry

..........

48

Chapter

5.

Experimental setup, measurements, and results

................................
..........

53

5.1

Experimental setup

................................
................................
.........................

53

5.2

Air speed profile on the outlet of the air pump

................................
............

56

5.3

Voltage
-
air speed relationship

................................
................................
.......

58

5.4

Current
-
voltage relationship

and air resistance

................................
..........

59

5.5

Energy efficiency

................................
................................
.............................

59

Chapter

6.

Future research

................................
................................
.............................

62

6.1

Current problem

................................
................................
.............................

62

6.2

Future plans

................................
................................
................................
.....

63

Chapter

7. Conclusions

................................
................................
................................
....

65

References


66



iii


LIST OF FIGURES


Figure 1.1 Structural levels of a computer [1].

................................
................................
...

2

Figure 1.2 Microchannels on silicon chip [1].

................................
................................
....

3

Figure 1.3 Air
-
cooled multi
-
chip module used in IBM 4381 Processor [1].

......................

4

Figure 1.4 Heat generation trend for Pentium microprocessors.

................................
........

5

Figure 2.1 Principle

of operation of corona air pump. High voltage power supply (HVPS)
provides required potential difference.

................................
................................
.....

10

Figure 2.2 Coron
a current
-
voltage relationship.

................................
..............................

11

Figure 2.3 Visual difference between positive corona and negative corona
[28]
.

...........

14

Figure 2.4 Ele
ctrostatic dehumidification technology.

................................
.....................

20

Figure 2.5 Corona air pump can be used for cooling of computer chips.

.........................

24

Figure 2.6 Contr
ast of air movement profile difference between a traditional fan and corona
-
driven pump.

................................
................................
................................
.............

25

Figure 2.7 Dynamic airflow pattern can be controlled through varying voltage distribution.

................................
................................
................................
................................
...

26

Figure 3.1 Columbic force distribution of an air pump.

................................
...................

28

Figure 3.2 Dielectrophoretic force in an electric field of corona air pump

......................

29

Figure 3.3 Columbic force and dielectrophoretic force along the radial position for a single water
molecule with the 1e
-

net charge.

................................
................................
..............

31

Figure 3.4 Large water conglomerates in a strong electric field became polarized and elongated.

................................
................................
................................
................................
...

31

Figure 3.5 Relationship between electric field gradient, dipole value, and the corresponding
di
electrophoretic force produced.

................................
................................
.............

32

Figure 3.6 Calculated electric field intensity displayed as a function of dimensionless radial
distance from corona electrode without space charge.

................................
.............

33

Figure 3.7 Calculated electric field intensity displayed as a function of dimensionless radial
distance from corona electrode with space charge.
................................
...................

33



iv

Figure 3.8 Calculated columbic force displayed as a function of dimensionless radial distance
from corona electrode without space charge.
................................
............................

33

Figure 3.9 Calculated columbic force displa
yed as a function of dimensionless radial distance
from corona electrode with space charge.

................................
................................
.

34

Figure 3.10 Calculated dielectrophoretic force displayed as a function of dimensionless radial
dist
ance from corona electrode without space charge.

................................
.............

34

Figure 3.11 Calculated dielectrophoretic force displayed as a function of dimensionless radial
distance from corona electrode with space charg
e.
................................
...................

34

Figure 4.1 Basic design concept of a corona air pump pair.

................................
.............

36

Figure 4.2 Design I of ionic pump.

................................
................................
...................

38

Figure 4.3 Electric field and equipotential line plot of Design I.

................................
....

38

Figure 4.4 Force distribution between two electrodes in Design I.

................................
.

39

Figure 4.5. Design II of ionic pump.

................................
................................
.................

4
0

Figure 4.6. Electric field and equipotential line plot of Design II.

................................
...

40

Figure 4.7. Force distribution between two electrodes in Design II.

................................

41

Figure 4.8. Design III of ionic pump.

................................
................................
...............

42

Figure 4.9. Electric field and equipotential line plot of Design III.

................................
..

42

Figure 4.10. Force distribution between two electrodes in Design III.

.............................

43

Figure 4.11. Geometry of a single pair of electrodes with possible non
-
linear voltage distribution
at sidewalls.

................................
................................
................................
...............

45

Figure 4.12. Field strength and voltage distribution of th
e electrode geometry for optimum air
movement.

................................
................................
................................
.................

45

Figure 4.13. Field strength and voltage distribution of the electrode geometry for optimum
collecting efficiency.

................................
................................
................................
.

46

Figure 4.14 Corona electrodes are shielded with walls separating them.

.........................

47

Figure 4.15 Channel geometry with film collector electrodes attached on sidewalls.

.....

48

Figure 4.16 Electric field and equipotential line distribution of Geometry I without space charge.

................................
................................
................................
................................
...

50

Figure 4.17 Dielectrophoretic

force distribution of Geometry I without space charge.

...

50



v

Figure 4.18 Electric field and equipotential line distribution of Geometry I with constant space
charge distribution.

................................
................................
................................
...

51

Figure 4.19 Dielectrophoretic force distribution of Geometry I with constant space charge
distribution.

................................
................................
................................
...............

51

Figure 4.20 Electric field and equip
-
po
tential line distribution of Geometry I with radially
decreasing space charge distribution.
................................
................................
........

52

Figure 4.21 Dielectrophoretic force distribution of Geometry I with radially decreasing space
charg
e distribution.

................................
................................
................................
...

52

Figure 5.1 Experimental setup of a single channel air pump.

................................
...........

53

Figure 5.2 The x
-
y
-
z translation stage to position

the corona electrode.

..........................

54

Figure 5.3 The corona electrode standing between collector electrodes.

.........................

55

Figure 5.4 Semiconductive Kapton

film attached to Teflon sheet forms the collector electrode.

................................
................................
................................
................................
...

55

Figure 5.5 Zebra electrode: voltage gradient applied on insulating Kapton film through copper
foil.

................................
................................
................................
............................

56

Figure 5.6 Experimental setup with Zebra collector electrode.

................................
........

56

Figure 5.7 Air speed profile along the sidewall from the outlet.

................................
......

57

Figure 5.8 Air speed profile across the sidewall from the outlet.

................................
....

58

Figure 5.9 Measured corona voltage (
V
c
) vs. air speed (lfm) on the outlet exhibits line
ar
relationship.

................................
................................
................................
...............

58

Figure 5.10 Measured corona voltage (
) vs. current through collector electrode (

) exhibits
exponential dependence.

................................
................................
...........................

59

Figure 5.11. Measured air resistance (
) as a function of corona voltage (
).

..........

59

Figure 5.12. Energy efficiency as a function of input voltage

.

................................
..

60

Figure 5.13. Fan efficiency in CFM/W as a function of input voltage
.

......................

61

Figure 6.1 Contrast between the surface region without erosion and the region with erosion on a
corona wire using SEM (Scanning Electron Microscopy).
................................
.......

63



vi


LIS
T OF TABLES


Table 4.1: Comparison of three designs

................................
................................
...........

43





vii



ACKNOWLEDGEMENTS



I want to express gratitude to my research advisor, Prof. Alexander Mamishev, for giving
me the
opportunity to work on this research project. I am especially grateful for his deep insights,
consistent guidance, and availability in each step of research process. I am very fortunate to have
an advisor who has genuine caring, support, and patienc
e for his students in different situations.
His humor, optimistic attitude, and great leadership make the entire SEAL lab’s working
environment much more relaxed and cooperative. Last two years of working with him as his
graduate student are invaluable to
my professional development and future career.

I would like to thank my thesis committee members Prof. Jiri Homola and Prof. Ann
Mescher for taking their time to read my thesis and giving me instructive feedback. A significant
portion of my research time
was spent in the company of our industrial collaboration partner,
Kronos Air

Technologies
, Inc. I am very grateful to Dr.
Igor Krichtafovitch, Chief Scientific
Officer of the company, for providing resources and ideas for the research. I greatly appreciate

his genuine advice and availability.

This project is supported by the Royalty Research Fund of the University of Washington
and the United Engineering Foundation.

I would like to express my sincere appreciation to an undergraduate student Nels Jewell
-
Larsen for his enthusiastic participation from the beginning of this research project until now. He
made contributions in almost all aspects and phases of this project: introducing other talented
undergraduate students to this project, setting up research
plans for each quarter, working on
theoretical calculations, computer simulations, building the device, making posters, and giving
thesis feedback. His industriousness, integrity, grace, communication skills, and leadership
served me as a role model of a y
oung leader and good researcher. I would like to express my
great thanks to the funding resources that support his work: Mary Gates Scholarship, Washington
State Space Grant and
Electric Energy Industrial Consortium
.

Numerous experiments and simulations

in this thesis were done by several talented
undergraduates under my supervision, as part of their undergraduate research at UW. I would


viii

like to acknowledge (in reverse chronological order)
Kyle Pendergrass, John Burnette, Dan
Brown, David Parker, Tram Ki
m Thai and Michelle Raymond, for their diligence and creativity.

I also want to thank graduate students in SEAL lab: Min Wang, Bing Jiang, Shane

Cantrell, and Xiaobei Li, for their genuine support, meaningful discussions, and sharing of
knowledge and skil
ls.

I want to thank my friends Lily Sun, Bryan and Shing Chen, Dorcas Wang, Xiaolin Sun,
Ouyang Gong, Xiaoguang Zheng, Xiaohong Chen and Christine Qiu, who cheered me up when I
needed it (usually) and helped me when I was in trouble (often).

Finally, I
would like to thank my parents in China for their sacrificial love and
encouragement. I also want to thank my brother for his support all along.




1




1.

Introduction


1.1

Background


Heat transfer has always been an essential research subject in microelectronic
s industry. With
increasing density of transistors and other electronic components on silicon chips, the problem of
high heat generation has been a significant bottleneck to further advancements in the
microelectronic revolution. Micro chips are operating
in all kinds of electronics and computers:
refrigerators, electric rice cookers, CD players, digital cameras, cell phones, robotics control
boards, medical instruments, and a myriad of other devices. They not only work under room
temperature environment of

homes, schools, and offices, but also under stressful thermal
environment like cars, ships, submarines, and satellites. As we know, the most abundant material
in semiconductor chips is silicon, which requires a working environment below 100
o
C for its
stea
dy functioning
[1]
. Therefore, it is essential to remove heat efficiently from electronics to
reduce thermal stresses on silicon

chips and other supporting components.

Generally, 3D electronics packaging systems can be divided into three levels: the chip,
the module, and the printed circuit board (PCB)
[1]
, as shown in
Figure
1
.
1
. Chips are the
smallest components in the system; a module isolates the chip from the ambient atmosphere and
at the same time provides the leads for transmiss
ion of signals and the supply of power. Printed
circuit boards (PCB) integrate modules into a working network. To dissipate heat from the
electronics system, cooling systems must be integrated on a chip level and efficiently interact
with board and system
level thermal management devices.




2



Figure
1
.
1

Structural levels of a computer
[1]
.


Different modes of cooling include natural convection, forced convection, conduction,
radiation, and phase
-
change heat transfer
[1]
. Forced convection cooling has been the most
commonly used mode for heat removal purposes. Natural convection cooling reduces acoustic
noise inherent in forced air
-
cooling of equipment. It also operates at remote locations and
extreme thermal e
nvironments, where normal air
-
moving mechanical devices can’t operate very
long. Conduction transfers heat from the unit through direct contact with outside components.

Liquid cooling is a major alternative cooling technology, with main research efforts
c
oncentrated around heat pipes
[2]

and micro
-
channels (see
Figure
1
.
2
)
[1]
. Advantages off
ered
by liquid coolants are related to their relative high specific heat, enabling large thermal transfers
out of a system with corresponding small increase in coolant temperatures. However, because of
the need for electrical insulation, the liquid must ha
ve high enough dielectric strength to have
direct contact with the chips. Since the 1950s, major efforts have been waged to develop coolants
of high dielectric strength and good chemical stability, which include “FCs” (3M), “Coolanols”
(Monsanto), “DCs” (D
ow Corning), and “Freons” (Du Pont)
[1]
. Liquids like water can not be
utilized this way due to their low dielectric strength. I
n order to utilize low dielectric strength
liquids for cooling, insulation structures need to be built to shield the liquids. Although liquid


3

cooling generally gives higher cooling performance than air cooling, air is still a preferred
coolant in electroni
cs because it is cheap, stable, and easy to access.


Figure
1
.
2

Microchannels on silicon chip
[1]
.



Blowing air toward heat generation units has been the most popular method of cooling.
The mechanism is removing heat through blowing air with fan toward fin heat sinks, which
connect to the heat generation unit and extend its surface.

With large surface area of heat
dissipation, the heat is removed much easier with the impinging air.
Figure
1
.
3

[1]

shows the
impingement air
-
cooled fin structure used in IBM 4381 Processor. However, air cooling is
reaching its technological limits because it requires large surfaces, high air speeds, and, most
significantly, heat conduction across several laye
rs of interconnects before the heat flow reaches
the heat exchanger
[3]
. Furthermore, with higher density of electronics components on a chip,
heat sinks get denser and channels get narrower. According to the laws of fluid mechanics,
gases
become viscous in narrow channels, which greatly hinders the

air movement, and as a result,
decreases the cooling efficiency.

To retain air as a coolant, micro
-
cooling systems that achieve
high heat transfer coefficient and are close to the heat source should be developed.




4



Figure
1
.
3

A
ir
-
cooled multi
-
chip module used in IBM 4381 Processor
[1]
.

The purpose of this thesis is to enhance heat

withdrawal from microelectronic and
MEMS devices through developing an electrostatic air pump that could be incorporated into chip
structure, which possesses better cooling ability and greater efficiency than existing devices
while operating below audible

level. This technology has the potential to enable truly
revolutionary advances in the microelectronics industry.


1.2

Motivation


Rapid development of microelectronics led to immense component density that has doubled
every 12 months in the last decade. In 1
971, the first computer microprocessor 4004 is made in
at Intel. There are about 2300 transistors on it. In 2000, Pentium IV made by Intel accommodates
42 millions transistors. By the year 2005 microelectronics technology will begin bumping up
against the
point one barrier, i.e. decreasing the size of a single component to 0.1 micron. Each
semiconductor component emits heat associated with the electrical resistance. The heat problem
is one of the most profound obstacles in the electronics industry today. It

can be seen from the
heat generation trend of Pentium microprocessors in
Figure
1
.
4
.



5


Figure
1
.
4

Heat generation trend for Pentium microprocessors.

In addition to common digital mi
croelectronics, cooling has become a critical issue for
power electronics devices, such as IGBT and power diodes, where a very high power density
under normal operation conditions (up to 400 W/cm
2
) makes specific cooling systems absolutely
necessary for ea
ch device. For high
-
speed MEMS applications, new issues are the introduction
of combustion processes in micro
-
devices and mechanical heat generation due to friction. In
power electronics, high current applications require high operating temperatures and dr
amatic
improvements in heat dissipation. Cooling of microelectronics is becoming one of the most
significant elements in a continuing progress towards faster computers.


The PC market drives the thermal management marketplace at this time but the need for

dissipation of heat from electronic devices is not limited to PCs. All related products on the
market today require some form of cooling technology. The global market for micro
-
cooling
technology is expanding year by year. While this industry has been lar
gely inhabited by
traditional fans and heat sinks, the fastest growing segment is alternative cooling, showing an
average growth rate of over 26
%

per year
[4]
.

Why is this such a hot market? The prime mover in these markets is the problem faced by
integrated circuit manufacturers as they try to put more transistors in smaller spaces. This results
in more heat per unit volume to be diss
ipated. AMD's top processor Anthlon contains 22 million
transistors, nearly 20 times the 1.2 million found in the 486, introduced in 1989, and with much
denser interconnects. According to the Semiconductor Industry Association (SIA), in a report


6

designed t
o map projections through the year 2005, the expected increase in need for thermal
dissipation is the factor of four.

Electrostatically assisted heat transfer on macro scale has been envisioned before
[5]
, but
until now it was not positioned to compete with traditional cooling. Recent advances in
microfabrication and dramatically increased need for better cooling solutions on de
vice level are
two main reasons for this technology to come to existence.


1.3

State of the art

1.3.1

Corona driven pump for air movement


The principle of ionic air propulsion with corona
-
generated charged particles has been
known almost as long as electricity itse
lf
[6]
. One of the first references to moving air se
nsation
near a charged tube appeared 300 years ago in a book by Francis Hauksbee
[7]
. Many pioneers
of electricity, including Newton, Faraday, and Maxwell, st
udied this phenomenon
[8
-
10]
.
Studies continued to these days. Extensive work was conducted on mod
eling of charge and fluid
dynamics
[6;11;12]

and heat transfer
[13]

in ionic pumps. Notably, most studies have been
conducted with classic shapes of high
-
voltage electrodes, such as needle
-
ring, needle
-
plane, and
coaxial cyl
inders
[14
-
18]
. The fundamental aspects of electron wind technology h
ave been
compiled in several authoritative references
[11
-
13;18]
. Since the 1960s, numerous studies
addressed different aspects of corona
-
driven wind, including effects of this phenomenon on air
pollution
[19;20]
, ozone generation, heat transfer, air propulsion, and bacteria sterilization.
Practical implementations of this approach appeared only in the last two decades, driven by
increased environmental awareness, adv
ances in material science, microprocessor control, and
market need.

1.3.2

Corona discharge


Corona discharge is the phenomenon of discharge happening at the surface of a conductor,
which is often accompanied by ionization of the surrounding atmosphere and often

by a power
loss. Gaugain
[21]

(1862) conducted one of the earliest research on spark
-
breakdown volt
ages
and fields for concentric
-
cylinder electrodes in air. It was found that the breakdown field


7

depends mostly on the diameter of the inner corona electrode wire and slightly on the diameter of
the outer cylinder. The result is represented by the empirica
l equation




(
1
.
1
)

where

is the breakdown field at the surface of the inner electrode,
is the radius of the

cylinder,

and

are experimental constants. Rőntgen
[22]

(1878) started studies of the point
-
plane corona, where he found the existence of a critical voltage, corona onset voltage, below
which no curren
t is detected.

The work of Peek
[23]

acted as the classic study of this subject, among the early
investigations of high
-
voltage corona. He determined the corona onset voltage as a f
unction of
the wire diameter, air temperature and pressure, coating of the corona wires with oil, water, and
dirt films, and the material of wire
-
conductor. Loeb
[24;25]

conducted outstanding research on
the basic processes and properties of the corona discharge, which covers the role of the first and
second Townsend ionization coefficients, the essential part played by electron attachment in the
negative
corona, and the intermittent effects which are characteristic of the corona
[26]
.


1.4

Thesis Outline


The thesis is focused on
developing an electrostatic air pump that could be later incorporated into
a chip struct
ure for heat withdrawal from microelectronics and MEMS devices.

The thesis starts with the basic principles of electrostatic air pump operation, followed by
the theory of different forces in the discharge process. After that, results of numerical simulatio
ns
represent different device designs with the purpose of optimizing device’s performance. Based
on the simulations, the prototype of electrostatic air pump is built and analyzed. Finally, future
development of this research project is discussed, with conc
lusions and summary at the
end
.

In Chapter 2, first, the basic components and operation of corona air pump are
introduced. The ionization process and physics of corona discharge are described, followed by
the review of two important
characteristics

of cor
ona discharge: current
-
voltage relationship and
the distribution of electric field. The advantage of this technology and its another major
application in dehumidification are discussed in the end of the chapter.



8

Chapter 3 introduces
three types of forces
present in corona electric field to produce
motion of water droplets and other particles in air: columbic force, dielectrophoretic
(polarization) force, and Biot
-
Savart force. Dielectrophoretic force is the focus of this chapter,
since it is rarely discuss
ed in framework of electrostatic devices, but it may be useful for further
technology development.

Based on the theory in the previous two chapters, Chapter 4 presents the numerical
simulations of electrostatic air pumps to find the optimal working geometr
y
. It starts with the
geometry of a pairs of cylindrical corona electrode and collector electrode. Then it explores the
channel geometry for
collector

electrode, which appears more suitable for our device.

Chapter 5 describes the experimental setup of the

air pump prototype, with further
measurements of several important characteristics of air pump: voltage
-
air speed relationship,
current
-
voltage relationship, and air resistance variation in this process. This chapter also
includes by calculations of the d
evice efficiency and its comparison with traditional computer
cooling fan on the market.

Chapter 6 discusses problems in the current design. Future research direction of this
research project towards miniaturization of existing devices is proposed. Tenta
tive procedures
for prototype testing and evaluation are proposed in the same chapter.

Chapter 7 draws the conclusions of the thesis.



9




2.

Basic principles of
electrostatic air pump operation


2.1

Operation of the electrostatic air pump



Figure
2
.
1

shows the conceptual representation of the electrostatic air pump technology.
Electric potential difference applied between the corona electrode and the collector electrode is
sufficiently high to generate corona discharge in the field enha
ncement region (near the corona
electrode), but below electric breakdown voltage. Ionized air particles are then accelerated by
columbic force, which varies throughout the volume of the device, but is directed mostly to the
right, as shown in the diagram.
Accelerated ions entrain air molecules in their movement and
produce the same wind effect as a conventional fan.

In addition to air movement, ions and electrons distributed in the volume of the device
attach themselves to previously neutral molecules and
particles. Columbic forces acting on these
molecules and particles lead to their sedimentation on the electrodes of opposite to their charge
polarity. Sometimes, this process is also accompanied by particle agglomeration.

With appropriate electrode design

and space charge control, it is possible to attract all
generated ions on the electrodes with the opposite to the corona electrode polarity. Space charge
leakage does not present problems at other devices with corona
-
induced ionization, such as
photocopie
rs and printers.

In terms of air movement, energy efficiency of electrostatic pumps is potentially higher
than that of conventional fans. Main sources of energy losses in rotating fans are induction motor
core and copper losses as well as undesired air tu
rbulence. Since electrostatic air movement of is
based on electrostatic rather than magnetic field, energy losses could be much lower.



10

The required voltage difference is proportional to the distance between the electrodes, on
the order of 1 volt per micron
. Therefore, miniaturization of electrostatic pump technology can
lead to important reduction of required voltage difference, which is currently on the order of
thousands of volts.




Figure
2
.
1

Principle

of

operation of corona air pump. High voltage power supply
(HVPS) provides required potential difference.

2.2

Ion generation in gases



Ions are generated due to partial discharge activity present in the air near the electrode. This
happens when the voltage appl
ied between two electrodes exceeds the critical voltage (called
corona onset voltage). Below this voltage, no current between two electrodes can be detected.
After the voltage exceeds the critical value, current is present in the air, as illustrated in
Figure
2
.
2
. A further increase in voltage leads to a dramatically increasing current until spark
-
over
occurs, which marks the electrical breakdown of the gas.



11


Figure
2
.
2


Corona current
-
v
oltage relationship.


2.2.1

Properties of gas in corona discharge


Gas differs fundamentally from solid and liquid in the way of conducting electricity. In
solid and liquid conductors, electrons are moving in a certain range of space: either vibrate
around its b
alance position or move through the conductor freely. Plus, solids and liquids have a
much more compact and connected structure, which allows charged particles travel easily across
the material. When an electric field is applied on solid and liquid, it is
much easier for charged
particles to move through the medium, creating electric current, compared to gas. For example,
in metals like copper and silver, electrons are the free charge carriers moving through the crystal
lattice with little resistance.


Gas
, on the other hand, is composed of neutral molecules without free electrons and ions
under normal conditions. Its density, normally on the order of 10
19

neutral molecules per
, is
much lower compared to solid and liquid material
s. Gases are good electrical insulators.
However, when the potential between two electrodes is increased substantially, a point is reached
where ionization and the conductivity of the gas increase dramatically. Electric current is
conducted through the gas

in this situation. Because of different nature of ionization processes,
there are different forms and characteristics of corona discharge such as sparks, arcs, coronas,
and glow discharges
[26]
.


2.2.2

Ionization proc
esses




12

Once the voltage between two electrodes exceeds the corona onset voltage, molecules
around corona electrode begin to ionize. Electrons of these neutral molecules gain enough energy
from high electric field intensity and are peeled off from them to m
ove freely. These electrons
move fast toward one direction under the influence of the electric field and the positive ions
move in the opposite direction. While moving, they collide with other neutral molecules and may
knock the electrons off them, too. El
ectrons moving with lower speed also could attach to certain
gas molecules. With high enough voltage, ionization is propagating dramatically, with the net
result of a large amount of electrons and ions in the air. Current flowing through these two
electrod
es can be measured and related to the density of moving charge carriers.

2.2.3

Mathematical description of corona discharge


Townsend
[27]

investigated the ionization process and expressed the electron ionization in a
differential equati
on form as




(
2
.
1
)


where

is the incremental increase in the number of electrons produced by
electrons mo
ving
a distance

in the electric field. The coefficient
varies with the gas and is a function of the
electric field strength and gas density. For a uniform electric field and discharge conditions,
is
also constant and (
2
.
1
) can be integrated to




(
2
.
2
)

where

is the number of free electrons at
.

In a more general case, where the field varies with

and

is also a function of





(
2
.
3
)





In addition to ionization, electrons can also attach to many neutral molecules to form
negative gas ions. This happens more for electronegative elements such as halogens, o
xygen, and
sulfur, which are deficient in electrons in their outer electron shells and therefore have high
electron affinity. Gas such as Cl
2
, CCl
4
, HF, O
2
, SO
2
, and SF
6

are strongly electronegative and
act as effective electron traps in gas discharges
[26]
. Electron attachment greatly reduces and
counteracts electron ionization. Electron attachment can be expressed as




(
2
.
4
)



13


where

is the coefficient of attachment, which depends on the gas and on the electric field.
Combining (
2
.
2
) and (
2
.
4
), the value of
for uniform fields is:




(
2
.
5
)


At low electric fields,

exceeds
, and the number of electrons dec
lines with distance. At the
threshold value
,
, and
remains constant. At
,
exceeds
, and the n
umber of
electrons increases with distance
[26]
.

2.3

Positive and negative corona discharges



There are two types of corona discharge: positive corona and negative corona. Polarity of
corona discharge is determined
by the sign of the voltage applied to the corona electrode. Zeleny
[28]

described the striking difference in visual appearance between the positive and negative
corona. The positive corona appears as a motionless, diffuse glow over the end of the point
,
while the negative corona appears as a localized brush originating from a tiny spot on the end of
the point and spreading out into the gap in fountain
-
shape form. Fine wires exhibit the same
general visual characteristics between the positive and negativ
e coronas. For a given geometry,
the corona onset voltage and the electrical breakdown of the gas occur at higher voltages for
negative corona than for positive.



14


Figure
2
.
3


Visual difference between

posit
ive corona and negative corona
[28]
.

2.3.1

Positive corona


Positive corona has a very high positive voltage applied on the corona electrode, which generates
a strong electric field in its ambient atmosphere. This field with high intensity ionizes the air
mo
lecules into positive ion
-

electron pairs. Electrons are drawn to the corona electrode. While
moving, they bombard other neutral molecules and break them into more positive ions and


15

electrons. All the positive ions are propelled toward the collector elect
rode. Positive corona is
characterized by a smooth glow around the corona electrode.

2.3.2

Negative corona


In the negative corona case, high intensity of electric field is also present around the corona
electrode, and the voltage applied to the electrode is ne
gative. Positive ion and electron pairs are
generated in the ambient atmosphere of corona wire, but this time positive ions are attracted to
the corona electrode and negative electrons are propelled to the collector electrode. Having much
smaller mass, ele
ctrons move faster than ions. Some electrons attach to neutral air molecules and
thus produce negative ions. Negative corona shows as rapid dancing brushes. It is characterized
by intermittent Trichel pulses which can reach the frequency of

cycles per second
[29]
.

2.4

Theoretical current
-
voltage relation
ship


Current
-
voltage characteristics for the corona are functions of many variables which include gas
composition, gas temperature and pressure, electrode geometry, voltage polarity, particles on the
electrodes, and particle suspensions in the gas
[26]
. Equations can be derived for concentric
cylinder electrodes, but for most other cases, the relationship can only be determined
experimentally.


The Poisson’s equation which governs all electrostatic phenomena is
[30]
:




(
2
.
6
)


where

is the space charge density and

is the elect
ric potential.

In cylindrical coordinates, assuming axial symmetry,

and

won’t affect the voltage
distribution, therefore, equation (
2
.
6
) reduces to




(
2
.
7
)


Here

is the space charge density, given by




(
2
.
8
)


where

is corona current,

is a constant, and



16




(
2
.
9
)

Combining the above three equations, we get




(
2
.
10
)

This equation can be integrated to




(
2
.
11
)

where

= co
nstant of integration.

Integrating (
2
.
11
), we get




(
2
.
12
)

Integration constan
t

may be calculated from (
2
.
11
) by using the boundary condition at the
outer radius of the plasma region near the wire. Electric field at this poin
t is

and the
corresponding radius is
. Then

can be expressed as




(
2
.
13
)

With
the value of

in (
2
.
13
), the current
-
voltage relationship can be expressed as





(
2
.
14
)


where

is the diameter of the corona wire,

is the diameter of the outer pipe,

is the outer
radius of the plasma region around the wire and

is the corona initiation field strength at this
point.

According to Peek’s law,

is




(
2
.
15
)


where




(
2
.
16
)



17

In equation (
2
.
16
),

is the absolute room temperature,
;

is the normal atmospheric
pressure,

760 mmHg;

and

are the actual temperature and pressure of the air. In (
2
.
15
),
is
a roughness factor of the wire, which increa
ses when the wire is rough, marred, or specked with
dust. The parameter

is usually between 0.5 and 0.7 for dirty, scratched wire. Corona initiation
field strength

is also a function of gas density
[26]
.

Corona initiation field strength is determined solely by the geometry of the corona
electrode. Corona onset voltage, on the other hand, is set by the design of both corona and
collector electrodes. It can be c
alculated through (
2
.
14
) by setting

and





(
2
.
17
)


2.5

Electric field distribution


Ions are generated in gas when the electric field exceeds the initiation field strength
. The
electric field strength is determined by the geometric design and the opera
tion of the device. Eq.
(
2
.
18
) is a simple way to characterize the electric field.




(
2
.
18
)

where

is the applied voltage on the corona electrode, and

is the distance between the
corona and collector electrodes. The electric field is

for plate
-
typ
e and

for the tube
-
type designs, where

is the radius of the collecting tube. This is an approximation since this
equation only applies to electrodes with parallel plate geometry. The electric field is

also affected
by space charge distribution. Therefore, a complicated iterative procedure to solve Poisson’s
equation and the equation of space charge continuity is necessary. To make the calculation
easier, simpler approaches ignoring space charges or sup
posing a constant space charge
distribution are utilized
[31]
.

For tube
-
type electric field, the electric field strength for the coaxial geometry without
considering space charge can be desc
ribed as.




(
2
.
19
)



18

where

is the applied voltage,

is the corona wire radius, and

is the radius of the collecting
tube
[31]
. Assuming a constant space charge distribution, Robison derived the distribution as:





(
2
.
20
)


where

is the current density per unit collecting area on the tube,

is the electrical
mobility of gas ions,

is the dielectric permittivity of
vacuum (

F/m), and

is the
corona initiation strength.

The electric field distribution can also be expressed in dimensionless form, which is very
helpful in comparing electric field strength with differ
ent electrode geometries. For the
dimensionless electric field distribution without charge




(
2
.
21
)

where
,
.

For the dim
ensionless electric field distribution with charge




(
2
.
22
)


where the dimensionless voltage is




(
2
.
23
)


and the dimensionless current density is




(
2
.
24
)




19

2.6

Enhancement of heat exchange through water
evaporation


In addition to cooling for electronics and MEMS through forc
ed convection, it is also
possible to enhance heat exchange through the step of condensation in refrigerant circulating
system using electrostatic air pumps. Evaporation of water droplets in the ambient atmosphere of
devices can enhance heat removal. Like
the compressor in the refrigerator, corona air pump can
be used in the condensation process of the cooling cycle to be used for cooling purpose.
Actually,
dehumidification is also one major application of corona air pumps.

Currently available dehumidifica
tion equipment includes condensation
-
based or
desiccant based systems. A condensation
-
based system
chills the air below its dew point, causing
moisture to form as condensation on the cold surface of the cooling coil and thus removes water
from the air. The

desiccant
-
based dehumidification system uses a chemical to directly absorb
moisture from the air while it is a vapor.

Both systems require multiple steps and significant
additions to traditional HVAC systems. Conventional solid and liquid desiccant system
s generate
heat when operating. Besides, they require an additional heat source to complete the collection
and regeneration processes, which results in high energy consumption. Moreover, current HVAC
system in air conditioners requires significant maintena
nce to prevent mechanical failure during
operation. A humidity control, air
-
cooling, air purification, and air movement all in one device
would save money, space, and energy. The corona air pump is the alternative technology that
has the potential to fulf
ill all the above requirements.



20



Figure
2
.
4

Electrostatic dehumidification technology.

The mechanism of corona air pump is shown in
Figure
2
.
4
. Water vapor droplets in

the
air are ionized as they pass through the high voltage plasma fan array, which is composed of
corona electrodes and collector electrodes. Then, ionized water vapor is deflected by an electric
field and forms larger droplets which fall out of the air. W
ater droplets are then removed into a
water collector. Theoretical discussion on several processes involved in this technology is given
in the next few sections.

2.6.1

Charging process


Analytical studies of the forces and the movement of water molecules in a
n electrostatic
field that exceeds the corona onset voltage have been conducted for many years and entered
classical treatises
[32]
. Several processes deserve attention because they are critical for
applicatio
n of electrostatic air pump in dehumidification. These processes include field distortion
due to space charge, dynamic force variation due to globalization of aerosol particles, and
interaction of ionic drag of non
-
polar gas molecules and highly polar wate
r molecules and
droplets.

The fundamental physics of the charging process of water droplets in corona field has
been studied extensively
[26;33]
. Suppose that a water droplet is a sphere of radius
a
. When the


21

droplet is placed in a u
niform electric field
E
0

with an initially uniform unipolar ion density
n
0
,
the potential distribution
V

is given by Poisson’s equation:




(
2
.
25
)


where

is the permittivity,
q

is the charge per ion (
q=
-
e

for an electron), and
n
i

is the distributed
ion density. The boundary conditions are

at infinity and

for

charges (
>0 for positive charges and
<0 for negative charges) on the surface at any given
time. It is readily shown that at any point on the sphere,






(
2
.
26
)




where

is the azimuthal angle in the spherical coordinate.



The total electric flux

entering the molecular sphere is given by




(
2
.
27
)


At saturation, the flux
, the saturation charges on the dielectric water sphere is




(
2
.
28
)


where
,

is the relative dielectric permittivity of water.

The rate of charging is given by the charging current
,




(
2
.
29
)

where
K

is the ion mobility. Integration gives




(
2
.
30
)




22

This shows the relationship between the increase of charges on a water molecule with
time when it is j
ust been placed into a corona electric field. White
[26]

showed that for
n
z
=5 x
10
14
m
-
3
,
K
=
-
2.2(cm/sec)/(V/cm); and
q
=
-

e
, the time to reach
Z/Z
s

=1/2 is two milliseconds.
Average time the water droplets are un
der the influence of a strong electric field is much greater
than 2 ms while average ion density
n
z

usually exceeds 10
15
m
-
3
.

2.6.2

Electric drag


After the water sphere has been electrically charged, it is dragged by the electrostatic
forces. Jastrow and Pearse

[34]

analyzed high velocity motion of a sphere in a high
ly ionized
gas. They recognized that a sphere of radius
a

is negatively charged due to greater mobility of
electrons in comparison to ion mobility. The electric drag force

is given by the following
approximation to their numeric
al result
[34]
:




(
2
.
31
)


Here

is the total drag,

is the drag force of an uncharged sphere due to number density

of ions or electrons;

is the ion kinetic energy relative to the sphere,
, where

is
the mass of ion,

is its velocity; and

is the surface potential.

The ef
ficiency of the electrostatic pump in large part depends on the direction of the
forces acting on charged particles. A figure of merit
r

proposed here is the integral ratio of two
orthogonal forces, with x
-
directed airflow:




(
2
.
32
)


This figure of merit can be estimated analytically only for the most primitive electrode
arrangements, and is a strong function of space charge density. In addition to columbic forces
addressed in th
e previous equation, a more comprehensive figure of merit should include
dielectrophoretic forces (connected to electric field gradient), and with certain design, Biot
-
Savart forces (connected to magnetic field interaction with moving charges).



23

2.6.3

Stability o
f a charged liquid droplet


Liquid droplets follow similar relations to those of a solid sphere except that deformation
of a spherical droplet should be expected. This phenomenon is particularly well visualized in
classic experiments with two transparent i
mmiscible liquids, for example, corn oil and water.
The surface tension of the water droplet acts against the force of electrostatic repulsion of
electric charges distributed over the surface of a conducting spheroid in an insulating fluid
medium. The rati
o of the forces of electrostatic repulsion over surface tension is usually denoted
as the electrosurface number
,




(
2
.
33
)

where

is the surface tension.

Rayleigh
[35]

found that a conducting spherical droplet is stable for

< 4. Aliam and
Gallily
[36]

extended this stability criterion to cases of ellipsoids of revolution. Denote the semi
-
principal axis along the axis o
f symmetry as
c

and the semi
-
principal axis normal to the axis of
symmetry as
b
. If
b
>
c
, the droplet is an oblate ellipsoid, and when
b
< c, it is a prolate ellipsoid.
Suppose
x = c/b
, in which case the total energy can be called
G
1
* in the oblate ellips
oid and
G
2
*
in the prolate ellipsoid. For each
, there exists a minimum energy
G
1
*
min

when
x
< 1 and
G
2
*
min

when
x
> 1. Further conclusion drawn by Soo [2] is that there might be a non
-
linear
oscillation of a droplet from a prola
te to a spherical to an oblate form and back. Also, normally
G
1
*
min

>
G
2
*
min
, which shows that prolate ellipsoid is more energy favorable as the steady
droplet shape. Further, when the oscillation occurs, the charged droplet tends to shatter more
often th
rough stretching to prolate ellipsoid or rod shape, than to thin out to an oblate or disk
shape. The form is very similar to a liquid filament. As the droplet shatters,
N
es

of each droplet is
equal to the original
N
es

divided by the number of similar dropl
ets produced by it.

While these models form a good starting point, they do not address the issue of field
distortion by space charge, and influence of airflow dynamics on droplet stability. It is likely that
a parametric continuum model will perform more
successfully than an analytical model drawn
on fundamental physics of individual droplets and particles. The challenge of the theoretical part
of the application on dehumidification is to provide practical parametric models of space
-
charge
dynamics in pres
ence of forced airflow.



24

2.7

Advantages of corona technology in micro
-
cooling


Although air velocity produced by the electrostatic air pump is incomparable to that of
conventional fans, the characteristics of generated airflow in the new device are advantageous

for
heat sink cooling. Two most significant positive aspects of this technology are (a) the ability to
generate aerodynamic forces inside the narrow channels and (b) the ability to remove the
boundary layer at the interface of the heat sink and air.

To un
derstand the first property, visualize a conventional fan positioned above a dense
array of heat sink fins. The pressure difference is generated at the fan blades, and the flow stream
tends to go around the closely positioned fins instead of penetrating in
side and thus taking
advantage of the increased total area of the heat sink. On the other hand, the forces that generate
air movement are borne between the fins by corona electrodes. The airflow in the narrow
channels is much stronger and does not require
high air speeds at the outer region of the heat
sink, as it is shown in
Figure
2
.
5
. (The channel geometry for computer chip cooling is discussed
in Chapter 4.)


Figure
2
.
5

Corona air pump can be used for cooling of computer chips.



25


The distribution of electric potential around the shielding electrodes determines the exact
pattern of air movement at the boundary layer. When the corona electrode is inserted between the
fin
s, with the collector electrode attached to the sidewall, the space charge is accelerated near the
electrode surface. The local columbic forces create local air movement otherwise unobtainable
with external to the channel air. This can be seen in
Figure
2
.
6
. In traditional fan, a parabolic air
velocity profile is formed due to viscous effects, resulting in

inefficient heat removal at the solid
-
fluid boundary. Ionized air propulsion counters much of the frictional losses

because the local
columbic forces to move charged air molecules are applied inside the channel. Thus, the corona
driven pump has much flatter flow profile, which greatly enhance the heat removal efficiency.



Figure
2
.
6

Contrast of air movement profile difference between a traditional fan
and corona
-
driven pump.


A very important advantage of the air pump is that it can be made into different
geometry, shapes and sizes. Corona electrodes can be made into tip
s, wires, edges of razors;
collector electrodes can be made from films of different materials. They can be built in linear
arrays to increase the airflow. Also, corona driven pumps don’t have moving parts. This greatly
reduces the noise that normal mechani
cal fan makes during computer operation and thus
provides a more quiet and relaxed working environment.


A special feature of the corona air pump is that it can have very dynamic airflow profile.
One way to change the airflow pattern is through changing t
he voltage distribution applied on the
device, which changes the ion moving trajectory and eventually the airflow pattern. This can be
seen from
Figure
2
.
7
.



26


Figure
2
.
7

Dynamic airflow pattern can be controlled through varying voltage
distribution.





27




3.

Theoretical background


3.1

Comparison of forces acting on water droplets and
particles in the air


Three types of forces of electromagnetic origin may conceivably be

used to produce
motion of water droplets and other particles in air: columbic force, dielectrophoretic
(polarization) force, and Biot
-
Savart force. Here our focus is forces on water droplets since it is
relevant to the application of electrostatic pump in

dehumidification. columbic force is the most
commonly used, analyzed, and discussed in electrostatic precipitator applications. It is a
dominant force in traditional designs. Dielectrophoretic force is of potential interest in this study,
and is rarely di
scussed in framework of electrostatic devices. It is negligible in comparison with
the columbic force, but may be useful with further technology development. The Biot
-
Savart
force is not likely to be used in the current device, but may resurface if electro
static
dehumidification is combined with heating/cooling cycles and magnetic field becomes available
from heating coils.

One of the promising approaches still subject to future exploration is agglomeration of
water vapor into mist, in which case the propo
rtional share of dielectrophoretic forces grows. For
larger droplets, dielectrophoretic forces are more effective and may play a significant role in the
dehumidification process. The forces should be computed for typical electric field and electric
field g
radient values.

3.2

Columbic force

The columbic force
f
C

acting on an unpaired charge
q

in electric field
E

is equal to




(
3
.
1
)




28

Typically, electric field is strongest near corona electr
odes; it weakens in the mid
-
volume of the
device, and, again, becomes stronger near the collector electrodes. The desired orientation of
electric field is different for purposes of energy
-
efficient air movement and for energy
-
efficient
dehumidification. In

the first case, maximum alignment along the line connecting the corona
electrode and the collector electrode is desired in order to produce maximum air pressure in the
general direction of airflow. In the second case, direction of airflow is far less crit
ical than
sedimentation of water molecules on collector electrodes. Numerical modeling on these two
cases is presented in Chapter 4. The purpose of analytical modeling is to compare relative
contributions of different types of forces and gain better unders
tanding of fluid dynamics in this
device.


Figure
3
.
1

Columbic force distribution of an air pump.

3.3

Dielectrophoretic (polarization) forces


In general, a total dielectrophoretic force
f
d

acting on an electric

dipole with a dipole
moment vector
p

is:




(
3
.
2
)


where

is the electric field at the dipole location point. Dipole moment of the water molecule is



C∙m


(
3
.
3
)

A typical value of the electric field gradient in the vicinity of the corona wire is 10
4

V/m
2

to 10
5

V/m
2

[37]
.



29

Compared to columbic force, dielectrophoretic force is acting on an electric dipole,
instead of a net charge. (
Figure
3
.
2
)



Figure
3
.
2

Dielectrophoretic force in an electric field of corona air pump


Electric field
E
r

of concentric cylinder electrodes with space charge accounted for is
described by
[30]
:




(
3
.
4
)


where
i

is corona current,
K

is the ion mobility,
E
0

is the critical corona field for ionization,
r
0

is
the corresponding value of
r

a
pproximately equal to the radius of the corona
-
glow sheath.
Consequently, the dielectrophoretic force distribution is obtained by applying (
3
.
2
) to (
3
.
4
).
Compared to

columbic force, the dielectrophoretic force




(
3
.
5
)




(
3
.
6
)




(
3
.
7
)




(
3
.
8
)

For the dimensionless force distribution without charge





(
3
.
9
)



30

where
,
, in which

is the cylinder tube’s radius and

is the discharge
wire radius
[31]
.

For the dimensionless force distribution with charge




(
3
.
10
)


where the dimensionless voltage is
[31]




(
3
.
11
)

and the dimensionless current density is
[31]




(
3
.
12
)

in which

is the voltage applied on the corona wire,

is the current density per unit
collecting area on the tube,

is the

gas ion mobility, and

is the dielectric permittivity of
vacuum

F/m
[31]
.

As we could see from the definition, dielectrophoretic force
is proportional to the dipole
moment and the gradient of the electric field. For a small molecule in a comparatively uniform
field, dielectrophoretic force is very small compared to columbic force. The columbic force vs.
dielectrophoretic force on a single

H
2
O molecule with 1e
-

net charge is shown in
Figure
3
.
3
.



31



Figure
3
.
3

Columbic force and dielectrophoretic force along the radial position
for a single water molecule with the 1e
-

net charge.

The larger the size of the water droplet, the higher the amount of dipole charges on it. As
a result, larger dielectrophoretic force acts on it. Also, large water conglomerates under strong
electric field are elongated as seen from
Figure
3
.
4
.


Figure
3
.
4

Large water conglomerates in a strong electric field became polarized
and elongated.

In order to achieve high value of the dielectrophoretic force, large dipole values

at very
high electric field gradients need to be present.
Figure
3
.
5

quantifies this argument by showing
the relative change of the dielectrophoretic force as the function of dipole value and gradient of
the electric field.




32



Figure
3
.
5

Relationship between electric field gradient, dipole value, and the
corresponding dielectrophoretic force produced.

Figure
3
.
6

through
Figure
3
.
11

show distribution of field quantities for different cases.
Even
-
numbered figures present calculations without space charge, and the odd numbered ones
assume an evenly distributed space charge due to ionic current density of 0.68 mA/m
2
. Th
ese
models serve as the base calculation for the discussion of forces acting on droplets (as opposed to
individual molecules). Ideally, a non
-
even distribution of space charge should be used for a more
accurate modeling of electric field and especially rev
ersal of direction of dielectrophoretic forces
due to sign change in the spatial derivative of electric field magnitude. The latter occurs due to
shielding effects of ion cloud in the corona region. Nevertheless, a uniform space charge is a
reasonable firs
t
-
level approximation for the purpose of trend analysis. By comparing
Figure
3
.
6

and
Figure
3
.
7
, one can see that the electric field distribution is more uniform for the space
charge case. Consequently, the columbi
c force distribution is more uniform as well, as seen in
Figure
3
.
8

and
Figure
3
.
9
. Although relative change of the electric field is smaller in the mid
-
region for the space
-
charge case, the absolute change is larg
er; hence the dielectrophoretic force
is also larger in that region. Next stages of this research project will use this analysis as the basis
for more accurate modeling of electric field distributions.



33


Figure
3
.
6

Calculated electric field intensity displayed as a function of
dimensionless radial distance from corona electrode without space charge.




Figure
3
.
7

Calculated electric field intensity displayed as a function of
dimensionless radial distance from corona electrode with space charge.


Figure
3
.
8

Calculated col
umbic force displayed as a function of dimensionless
radial distance from corona electrode without space charge.




34


Figure
3
.
9

Calculated columbic force displayed as a function

of dimensionless
radial distance from corona electrode with space charge.



Figure
3
.
10

Calculated dielectrophoretic force displayed as a function of
dimensionless radial dist
ance from corona electrode without space charge.



Figure
3
.
11

Calculated dielectrophoretic force displayed as a function of
dimensionless radial distance from corona electrode

with space charge.





35

3.4

Biot
-
Savart force


It is not likely that Biot
-
Savart force would be used in common applications like
dehumidification or cooling; however, it deserves consideration until proven inefficient. This
force requires magnetic field, normall
y produced by electric current. The heat losses would
normally be prohibitive. However, there may be a need to run currents through the wires of the
second
-
generation prototype, for example, to prevent corrosion. The interaction of magnetic field
and movin
g charged particles in the corona region has not been studied before. Eq. (
3
.
13
) is the
expression of Biot
-
Savart force.




(
3
.
13
)


where

is the velocity of moving charged particles,

is the magnetic constant,

is the
magnetic field strength.




36




4.

Device design and simulation


The purpose of numerical m
odeling is to optimize distribution of

voltages and electrode geometry for control of fluid dynamics, space charge dynamics, and
energy transfer. It is an essential step before building prototypes.

4.1

Simulation of a single pair electrodes air pump


An ion
ic micro
-
pump has been modeled using ANSOFT Maxwell 2D Field Simulator.
Figure
4
.
1

shows the basic design of the air pump. This design simulated the negative corona, in which
the corona electrode has a lower voltage. It

consists of two electrodes (5
m

diameter corona
electrode and 20
m
diameter collector electrode). They are separated by 200 microns and have
a potential difference of 100 volts. The electrons emitted by
negative corona discharge propel the
air molecules and chemicals in it, and move in the same direction.


Figure
4
.
1

Basic design concept of a corona air pump pair.

4.1.1

Methodology




37

ANSOFT Maxwell 2D simulator h
as been used for numerical analysis. The first simulation runs
were limited to qualitative testing of different geometries. A more specific parametric sweep of
the final selection was done through varying voltages, material properties, and device geometry.

In a corona
-
generated plasma environment, a certain amount of ions (charges) is generated.
Under high electric field, these ions move in a certain direction. As they move, they propel air
molecules and this creates wind. When there is a charge density in
the background air, the force

generated by the electric field to move air molecules can be approximated with the columbic
force in charge
-
free field distribution
[13]
.



(
4
.
1
)



(
4
.
2
)


Equation
(
4
.
2
)
rep
resents the force ratio in x and y directions,

is charge density and

is the
magnitude of the electric field. Numerical and qualitative comparison of the design variations
can be made based on the metr
ics of force distribution and the force ratio (
).
These metrics
were calculated using a macro (Appendix A).

4.1.2

Results


For all designs, the common parameters for materials selection and boundary conditions are
listed below:



Electr
ode Material


W (Corona = 0V, Collecting = 100V)



Insulating Wall

o

Material: Glass

o

Dimension:



Background


Charged Air (Density
)
Design I


Two un
-
powered parallel plates aligning the two electrodes (o
ne corona and one target).

The electric field and equipotential line are plotted in
Figure
4
.
3
.
Figure
4
.
4

shows the force
distribution in the space between two electrodes.



38



Figure

4
.
2

Design I of ionic pump.






Figure
4
.
3

Electric field and equipotential line plot of Design I.



39





Figure
4
.
4

Force distribution between two electrodes in Design I.


Design II


The second design is very similar to Design I except 50 V is applied on the parallel plates as
shown in
Figure
4
.
5
. The electr
ic field of Design II is shown in
Figure
4
.
6

and the force
distribution of Design II is plotted in
Figure
4
.
7
.



40



Figure
4
.
5
.

Design II of ionic pump.





Figure
4
.
6
.

Electric field and equipotential line plot of Design II.




41



Figure
4
.
7
.
Force distributio
n between two electrodes in Design II.


Design III


In design III, two grounded parallel plates align with the two electrodes (
Figure
4
.
8
). A voltage
gradient from 10 V to 90 V are applied on smaller electrodes along th