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 Authorized 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,
and 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 Washington, 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. Any 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 Electrical 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. With higher density of electronic 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.
This 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 and
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 columbic 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.
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 current-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 charged 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
i
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 geometry ................. 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
ii
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 Corona current-voltage relationship. .............................................................. 11
Figure 2.3 Visual difference between positive corona and negative corona [28]............ 14
Figure 2.4 Electrostatic dehumidification technology. ..................................................... 20
Figure 2.5 Corona air pump can be used for cooling of computer chips. ......................... 24
Figure 2.6 Contrast of air movement profile difference between a traditional fan and coronadriven 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
dielectrophoretic 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
iii
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 displayed 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
distance 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 charge.................................................... 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. ................................................................................. 40
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 the 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
iv
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-potential 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
charge 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 (Vc) vs. air speed (lfm) on the outlet exhibits linear
relationship. ............................................................................................................... 58
Figure 5.10 Measured corona voltage ( VC ) vs. current through collector electrode ( I C ) exhibits
exponential dependence. ........................................................................................... 59
Figure 5.11. Measured air resistance ( RA ) as a function of corona voltage ( VC ). .......... 59
Figure 5.12. Energy efficiency as a function of input voltage V . .................................. 60
Figure 5.13. Fan efficiency in CFM/W as a function of input voltage V . ...................... 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
v
LIST OF TABLES
Table 4.1: Comparison of three designs ........................................................................... 43
vi
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 patience 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 JewellLarsen 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 young 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
vii
like to acknowledge (in reverse chronological order) Kyle Pendergrass, John Burnette, Dan
Brown, David Parker, Tram Kim 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 skills.
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.
viii
1
C
h
a
p
t
e
r
1. Introduction
1.1 Background
Heat transfer has always been an essential research subject in microelectronics 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 100oC for its
steady 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 transmission 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 environments, 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
concentrated around heat pipes [2] and micro-channels (see Figure 1.2) [1]. Advantages offered
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 have 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” (Dow Corning), and “Freons” (Du Pont) [1]. Liquids like water can not be
utilized this way due to their low dielectric strength. In 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 electronics 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 layers 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 Air-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 1971, 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
45
Desktop average
heat flux
70
40
35
60
30
50
25
40
20
30
15
20
10
10
5
0
AverageHeat
heatFlux
flux AW/cm
density [W/cm2]
Thermal design power [W]
80
0
Pentium Pro
Pentium II
Pentium III
Pentium IV
Pentium
66-133 MHz 150-233 MHz 266-600 MHz 600-1000 MHz 1.5 GHz
Pentium IV
2 GHz
Figure 1.4 Heat generation trend for Pentium microprocessors.
In addition to common digital microelectronics, 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/cm2) makes specific cooling systems absolutely
necessary for each 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 dramatic
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 largely 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 dissipated. 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 to 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 device 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 itself [6]. One of the first references to moving air sensation
near a charged tube appeared 300 years ago in a book by Francis Hauksbee [7]. Many pioneers
of electricity, including Newton, Faraday, and Maxwell, studied this phenomenon [8-10].
Studies continued to these days. Extensive work was conducted on modeling 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 cylinders [14-18]. The fundamental aspects of electron wind technology have 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, advances 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 voltages
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 empirical equation
C
(1.1)
b1/ 3
where E0 is the breakdown field at the surface of the inner electrode, b is the radius of the
E0  A 
cylinder, A and C are experimental constants. Rőntgen [22] (1878) started studies of the pointplane corona, where he found the existence of a critical voltage, corona onset voltage, below
which no current 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 function 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 structure 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 simulations
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 conclusions 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 corona 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 discussed 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 geometry. 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 device 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. Tentative procedures
for prototype testing and evaluation are proposed in the same chapter.
Chapter 7 draws the conclusions of the thesis.
9
C
h
a
p
t
e
r
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 enhancement 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
photocopiers 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 turbulence. 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.
Collector
Electrode
Corona
Electrode
Gas molecules
+ HVPS
HVPS
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 applied 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
Current
Voltage
Breakdown
Corona
Onset
Voltage
Figure 2.2 Corona current-voltage 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 balance 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 1019 neutral molecules per cm3 , is
much lower compared to solid and liquid materials. 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 processes
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 move 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. Electrons 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
electrodes 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 equation form as
dn   ndx
(2.1)
where dn is the incremental increase in the number of electrons produced by n electrons moving
a distance dx 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
n  n0 e x
(2.2)
where n0 is the number of free electrons at x  0 .
In a more general case, where the field varies with x and  is also a function of x
x
 dx
n  n e 0
0
(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, oxygen, and
sulfur, which are deficient in electrons in their outer electron shells and therefore have high
electron affinity. Gas such as Cl2, CCl4, HF, O2, SO2, and SF6 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
n  n0e  x
(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 n for uniform fields is:
n  n0e
   x
(2.5)
At low electric fields,  exceeds  , and the number of electrons declines with distance. At the
threshold value ET ,    , and n remains constant. At E  ET ,  exceeds  , and the number 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 negative 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 positive 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
molecules 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 electrode. 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 negative. 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, electrons 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 2  105 cycles per second [29].
2.4 Theoretical current-voltage relationship
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]:
2V  4
(2.6)
where  is the space charge density and V is the electric potential.
In cylindrical coordinates, assuming axial symmetry,  and  won’t affect the voltage
distribution, therefore, equation (2.6) reduces to
d 2V 1 dV
 
 4  0
(2.7)
dr 2 r dr
Here  is the space charge density, given by

i
2 rKE
where i is corona current, K is a constant, and
(2.8)
16
dV
dr
Combining the above three equations, we get
E
rE
dE
2i
 E2   0
dr
K
(2.9)
(2.10)
This equation can be integrated to
dV

dr
where C = constant of integration.
E
 2i / K    C 2 / r 2 
(2.11)
Integrating (2.11), we get
 C 2   2ia 2 / K   C 

V  C log 
(2.12)
 C 2  2ib 2 / K  C 




Integration constant C 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 point is E0 and the
corresponding radius is r0 . Then C can be expressed as
C  r0 E0  (2i / K )
2
(2.13)
With the value of C in (2.13), the current-voltage relationship can be expressed as
2 2

1  1  (2i / K )  (b 2 / E0 r0 ) 
a
2 2
V  r0 E0 log  1  1   2i / K   b 2 / E0 r0  log

b
2




(2.14)
where a is the diameter of the corona wire, b is the diameter of the outer pipe, r0 is the outer
radius of the plasma region around the wire and E0 is the corona initiation field strength at this
point.
According to Peek’s law, E0 is
E0  30 f  (1  0.30  / a )
(2.15)
where

T0 P

T P0
(2.16)
17
In equation (2.16), T0 is the absolute room temperature, 293K ; P0 is the normal atmospheric
pressure, 760 mmHg; T and P are the actual temperature and pressure of the air. In (2.15), f is
a roughness factor of the wire, which increases when the wire is rough, marred, or specked with
dust. The parameter f is usually between 0.5 and 0.7 for dirty, scratched wire. Corona initiation
field strength E0 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 calculated through (2.14) by setting i  0 and r0  a
V0  aE0 log
b
b
 30 fa (1  0.30  / a ) log
a
a
(2.17)
2.5 Electric field distribution
Ions are generated in gas when the electric field exceeds the initiation field strength E0 . The
electric field strength is determined by the geometric design and the operation of the device. Eq.
(2.18) is a simple way to characterize the electric field.
U
(2.18)
d
where U is the applied voltage on the corona electrode, and d is the distance between the
E
corona and collector electrodes. The electric field is U / s for plate-type and U / r2 for the tubetype designs, where r2 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 supposing 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 described as.
E r  
U
r
r  ln 2
r1
(2.19)
18
where U is the applied voltage, r1 is the corona wire radius, and r2 is the radius of the collecting
tube [31]. Assuming a constant space charge distribution, Robison derived the distribution as:
E r  
r2  j
r  2
r j 
 1  E0  2

 0  b   r 
 0  b   
(2.20)
where j is the current density per unit collecting area on the tube, b   is the electrical
mobility of gas ions,  0 is the dielectric permittivity of vacuum ( 8.85 1012 F/m), and E0 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 different electrode geometries. For the
dimensionless electric field distribution without charge
E '  r ' 
where r ' 
1
(2.21)
1
r ' ln
r1 '
r
r
, r1 '  1 .
r2
r2
For the dimensionless electric field distribution with charge
E '  r ' 
j '
1 1
 r1 '

r '  r1 'U '2

j '

(2.22)
where the dimensionless voltage is
U'
U
E0  r1
(2.23)
and the dimensionless current density is
j'
j
 0  b  
r2
3
(2.24)
U
2
19
2.6 Enhancement of heat exchange through water
evaporation
In addition to cooling for electronics and MEMS through forced 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 dehumidification 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 systems 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 maintenance 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 fulfill 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. Water 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 an 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
application 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 water 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 uniform electric field E0 with an initially uniform unipolar ion density n0,
the potential distribution V is given by Poisson’s equation:
 2V  
qni
(2.25)
0
where  0 is the permittivity, q is the charge per ion (q=-e for an electron), and ni is the distributed
ion density. The boundary conditions are E  V  E0 at infinity and E   Ze / 4 0 a 2 for Z
charges ( Z >0 for positive charges and Z <0 for negative charges) on the surface at any given
time. It is readily shown that at any point on the sphere,
Ea  3E0 cos 
Ze
(2.26)
4  0 a 2
where  is the azimuthal angle in the spherical coordinate.
The total electric flux  entering the molecular sphere is given by



0


Ze
4  0 Ea 2 a sin  d  12  0 a E0 1 
2 
 12  0 E0 a 
2
2
2
(2.27)
At saturation, the flux   0 , the saturation charges on the dielectric water sphere is

 1 
4 0 E0 a 2 1  2 r
 r  2 

Zs 
q
(2.28)
where  r   /  0 ,  is the relative dielectric permittivity of water.
The rate of charging is given by the charging current i ,
ni qK d ( Ze)

4 0
dt
where K is the ion mobility. Integration gives
i
Z
n qKt
Zs
 i

4 0 1  Z
Zs
(2.29)
(2.30)
22
This shows the relationship between the increase of charges on a water molecule with
time when it is just been placed into a corona electric field. White [26] showed that for nz=5 x
1014m-3, K= -2.2(cm/sec)/(V/cm); and q= - e, the time to reach Z/Zs =1/2 is two milliseconds.
Average time the water droplets are under the influence of a strong electric field is much greater
than 2 ms while average ion density nz usually exceeds 1015m-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 highly 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 f q is given by the following
approximation to their numerical result [34]:
fq
f Di
f  f Di

f Di
1/ 2
1



 e 0  
 e 0   2 0 e 0   


 1  exp  2.4  
 
2 2 
 E 
 E   ni a e   



(2.31)
Here f is the total drag, f Di is the drag force of an uncharged sphere due to number density ni
of ions or electrons; E is the ion kinetic energy relative to the sphere, E 
1
mi v 2 , where mi is
2
the mass of ion, v is its velocity; and  0 is the surface potential.
The efficiency 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:
f mc =
ò
d*
r ×Edz Þ r =
f mx
=
f my
ò r ×E
ò r ×E
lx
ly
x
dx
y
dy
(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 the previous equation, a more comprehensive figure of merit should include
dielectrophoretic forces (connected to electric field gradient), and with certain design, BiotSavart forces (connected to magnetic field interaction with moving charges).
23
2.6.3 Stability of 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 immiscible 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 ratio of the forces of electrostatic repulsion over surface tension is usually denoted
as the electrosurface number Nes ,
N es  2(q 2 / 2 0 a) / 4 a 2 s
(2.33)
where  s is the surface tension.
Rayleigh [35] found that a conducting spherical droplet is stable for Nes < 4. Aliam and
Gallily [36] extended this stability criterion to cases of ellipsoids of revolution. Denote the semiprincipal axis along the axis of 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 G1* in the oblate ellipsoid and G2*
in the prolate ellipsoid. For each Nes , there exists a minimum energy G1*min when x < 1 and
G2*min when x > 1. Further conclusion drawn by Soo [2] is that there might be a non-linear
oscillation of a droplet from a prolate to a spherical to an oblate form and back. Also, normally
G1*min > G2*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 through 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, Nes of each droplet is
equal to the original Nes divided by the number of similar droplets 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 presence 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 understand 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 inside 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.)
High density electronic
device with heat sink
CPU heat sink fin
Collector electrode
Corona
electrode
Air/Ion flow
trajectory
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
fins, 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 solidfluid 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.
y
0
y
v
0
v
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 tips, 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 mechanical 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 the 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
0V
1 kV
-1 kV
0V
0V
0V
10 kV
10 kV
0V
10 kV
-1 kV
1 kV
Figure 2.7 Dynamic airflow pattern can be controlled through varying voltage
distribution.
27
C
h
a
p
t
e
r
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 discussed 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 electrostatic
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 proportional 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 gradient values.
3.2 Columbic force
The columbic force fC acting on an unpaired charge q in electric field E is equal to
fC = q ×E
(3.1)
28
Typically, electric field is strongest near corona electrodes; 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 critical 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 understanding of fluid dynamics in this
device.
L
t
VS
Figure 3.1 Columbic force distribution of an air pump.
3.3 Dielectrophoretic (polarization) forces
In general, a total dielectrophoretic force fd acting on an electric dipole with a dipole
moment vector p is:
fd = (p ×Ñ )E
(3.2)
where E is the electric field at the dipole location point. Dipole moment of the water molecule is
p w = 6.2´ 10- 30 C·m
(3.3)
4
A typical value of the electric field gradient in the vicinity of the corona wire is 10 V/m2 to 105
V/m2 [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 Er of concentric cylinder electrodes with space charge accounted for is
described by [30]:
 2i   E r 
Er      0 0 
K  r 
2
(3.4)
where i is corona current, K is the ion mobility, E0 is the critical corona field for ionization, r0 is
the corresponding value of r approximately 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
p  pr r  p   pz z

1 

r
 z
r
r 
z
 p 

p    pr  
 pz
r r 
z
2
2 2
pr E0 r0
  2i  E0 r0  

f d  (p ) Er  pr 




2
r  k  r  
 E0 r0 
3 2i


r


k  r 
For the dimensionless force distribution without charge

fd '  
pr
1
r ' ln
r 'SE
2
(3.5)
(3.6)
(3.7)
(3.8)
(3.9)
30
where r ' 
r
r
, r 'SE  SE , in which rNE is the cylinder tube’s radius and rSE is the discharge
rNE
rNE
wire radius [31].
For the dimensionless force distribution with charge
fd '  
2r '
2
 1

pr 
 r 'SE j 'NE 
2
 r 'SE U '


1 1
j 'NE  

r
'
j
'
SE
NE

r '  r 'SE U '2

(3.10)
where the dimensionless voltage is [31]
U
E0  rSE
and the dimensionless current density is [31]
U'
(3.11)
jNE
(3.12)
0  K 2
U
r 3 NE
in which U is the voltage applied on the corona wire, jNE is the current density per unit
j 'NE 
collecting area on the tube, K is the gas ion mobility, and  0 is the dielectric permittivity of
vacuum 8.85 1012 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 H2O molecule with 1e- net charge is shown in Figure 3.3.
31
Force in newtons
1E-18
1E-20
1E-22
1E-24
1E-26
1E-28
1E-30
0
0.2
0.4
0.6
0.8
Dimensionless Radial Position r'
Dielectrophoretic force
Columbic force
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.
-
H
O
-
H
+
-
+
A single water molecule
-
-
-
+
-
+
+
-
+
+
+
-
-
+
-
-
+
+
+
-
+
+
+
+
Water conglomerates
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. These
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 reversal 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 first-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 columbic 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 midregion for the space-charge case, the absolute change is larger; 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 columbic 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 distance 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, normally 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 moving charged particles in the corona region has not been studied before. Eq. (3.13) is the
expression of Biot-Savart force.
fb = q ×v´ m0 H
(3.13)
where v is the velocity of moving charged particles, m0 is the magnetic constant, H is the
magnetic field strength.
36
Chapter 4. Device design and simulation
The
purpose
of
numerical
modeling
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 ionic 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.
Chamber well
Low
Direction of E-field
Outgoing air
molecules
200 m
Figure 4.1 Basic design concept of a corona air pump pair.
4.1.1 Methodology
200 m
Incoming air
molecules
High
37
ANSOFT Maxwell 2D simulator has 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
f m generated by the electric field to move air molecules can be approximated with the columbic
force in charge-free field distribution [13].
r
f m     Edz
(4.1)


(4.2)
f mx

f my
lx
ly
  Ex dx
  E y dy
Equation (4.2) represents the force ratio in x and y directions,  is charge density and E is the
magnitude of the electric field. Numerical and qualitative comparison of the design variations
can be made based on the metrics of force distribution and the force ratio (
Fx
). These metrics
Fy
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:

Electrode Material – W (Corona = 0V, Collecting = 100V)

Insulating Wall
o Material: Glass
o Dimension: 50 m  800 m

Background – Charged Air (Density =-0.001C/m 2 )Design I
Two un-powered parallel plates aligning the two electrodes (one 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
L
t
VS
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 electric 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 distribution 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 the inner edge of the aligning
plates. Electrical field and force distribution are shown respectively in Figure 4.9 and Figure
4.10.
42
Figure 4.8. Design III of ionic pump.
Figure 4.9. Electric field and equipotential line plot of Design III.
43
Figure 4.10. Force distribution between two electrodes in Design III.
Table 4.1: Comparison of three designs
Parameter
Voltage on
Top and
Bottom
Plates
Geometry
Force
Distribution
Force Ratio
Design I
Design II
Design III
None
50V
Insulated (unpowered) top &
bottom plates
Powered top &
bottom plates
Gradient
(10V ~ 90V)
top & bottom
array
(non-corona
voltage)
Slight bias
toward xdirection
1.517
Equally
distributed in
both direction
0.987
Predominant in xdirection
5.063
The third model with gradient voltages applied along the inner parallel plates is the best
design to maximize the integral ratio of two orthogonal forces according to the numerical
simulations. In all the designs analyzed, materials selection does not appear to have much affect
44
on the force ratio. The voltage difference across the two electrodes, the geometry of the device,
and the charge distribution in the volume all affect the ratio to a varying degree.
4.2 Simulation on optimum air movement vs. collection
efficiency
It was mentioned in Section 3.2 that the desired orientation of electric field is different for
purposes of energy-efficient air movement and for energy-efficient dehumidification. For air
movement, maximum alignment along the line connecting the corona electrode and the collector
electrode is desired. In the second case, sedimentation of water molecules on collector electrodes
is far more critical than direction of airflow. Below is the numerical modeling for these two
cases.
Figure 4.11 shows a two-dimensional schematic view of a simple electrode arrangement.
The small circle indicates the corona electrode (not to scale), and the large circle indicates the
collector electrode. The strips of electrodes above and below are used to alter electric field
distribution. For maximum pressure of air movement, electric field should be directed to the
right. On the other hand, for maximum collection efficiency, it should be directed up and down.
The compromise between these two arrangements is expected for the optimally performing set of
electrodes.
Figure 4.12 and Figure 4.13 show examples of both field distributions, simulated with
Ansoft Maxwell software. These figures show equipotential lines and electric field arrows whose
size is logarithmically proportional to the electric field magnitude. The first condition (Figure
4.12) can be achieved either by active drive of individual strips shown in Figure 4.11 or by using
semi-conductive coating with voltage distribution controlled by the strength of corona current
and surface conductivity of the coating. In this simulation, the electric field lines are nearly
parallel to the side electrodes. In the second case (Figure 4.13), electric field lines are
perpendicular to the side electrodes, which is a boundary condition for perfect conductors. This
example illustrates general direction of optimization for electric field distribution. Both cases are
suitable in different applications. For example, the stage shown in Figure 4.12 can be used for
extensive media charging and air propulsion in cooling, and the stage shown in Figure 4.13 can
be used for sedimentation of droplets in dehumidification. They can also be combined together
for use in the same device to acquire a desired effect.
45
Figure 4.11. Geometry of a single pair of electrodes with possible non-linear
voltage distribution at sidewalls.
Figure 4.12. Field strength and voltage distribution of the electrode geometry for
optimum air movement.
46
Figure 4.13. Field strength and voltage distribution of the electrode geometry for
optimum collecting efficiency.
4.3 Design and simulation of the air pump with channel
geometry
4.3.1 Design of the air pump with channel geometry
4.3.1.1 Size of corona electrodes
This new design for the air pump is believed to be a more efficient way to move air. The
initial intention is to shrink the size of electrodes. As discussed before, the generation of corona
is due to the non-uniform electric field on the curved tip of the corona electrode when high
voltage is applied. If the size of the electrodes is reduced, the same electric field intensity can be
achieved with smaller voltage. Consequently, more electrode pairs can be put into the same
space, which results in a greater airflow. The equation describing the number of electrodes
accommodating within a 2-D space is:
1
(4.3)
d2
where d is the size of the electrode. With smaller electrodes, more electrodes can be introduced
N
into this region.
47
The number of corona electrodes in the space increase when the size of the electrode is reduced,
which results in greater airflow.
4.3.1.2 Electrodes are shielded with walls
When smaller devices are built, new problems are introduced.
1. When the distance between electrodes decreases, there is more interaction between
corona electrodes, which affects the electric field.
2. Due to a higher density of wire electrodes, air resistance becomes bigger.
One possible solution is to put shields between electrode pairs. Interaction would be greatly
diminished and the distance between electrode pairs can be reduced even more as shown in
Figure 4.14.
Figure 4.14 Corona electrodes are shielded with walls separating them.
4.3.1.3 Using razors as corona electrodes
The scaling-down of electrode pairs has other effects that need to be addressed. If the
diameter the wire is 1/2 the original, its cross sectional area is 1/4 of original. The thinner wire is
more prone to damage caused by electrical discharges. Besides, a thinner wire increases
packaging and shipping costs. Razor electrodes are used here to replace thin corona wires to
generate plasma. Two-dimensional electrodes are much more robust, easier to implement, and
cheaper. Moreover, the erosion of razor corona electrodes after long time usage has much less
effect on plasma generation, compared to wire electrodes.
48
4.3.1.4 Film attached on channel walls acting as collector electrodes
As seen from Figure 4.14, the disadvantage of using thick wire collector electrodes is that
the electrode itself inhibits the airflow since it stands in the middle of air movement. To solve
this problem, these thick wire electrodes need to be removed and replaced with something else.
One way is to attach a material on the sidewalls of channels acting as collector electrodes (see
Figure 4.15).
Figure 4.15 Channel geometry with film collector electrodes attached on
sidewalls.
4.3.2 Maxwell simulation of an air pump with single channel geometry
In order to study the multi-channel air pump’s behavior, it is important to model a single
channel performance under different situations. Moreover, a single channel has more variables to
manipulate and is more flexible to simulate. In Figure 4.15, we could see that the distances
between the corona tip and different regions on a collecting electrode are not the same. The
regions directly on top of the corona electrode and under it are much closer to the corona
electrode, compared to the other end of collecting electrodes. This feature increases the chance of
spark-over in these regions. Another design of a single channel with a tilted end increases the
distance between the corona electrode and collector electrodes. As shown in Design III of
Section 4.1.2, voltage gradient applied on the inner walls of the channel could optimize the
desired air movement along the channel. Moreover, since generated space charge affects the
electric field intensity as discussed in Section 2.5, its effect needs to be included in the single
channel simulations.
49
In the channel geometry, Teflon sheets on both sides spread from each other, facing
down. The 10 kV voltage is applied to the corona electrode. Eighteen pairs of copper foil strips
are lined up along the Teflon sheet on both sides. A voltage gradient from 0 V to 3400 V is
applied from the top pair to the bottom pair, with a step increase of 200V on each pair. As
mentioned before, the space charge generated from corona electrodes has an effect on the electric
field. Therefore, three cases of space charge conditions are discussed here: no space charge, a
constant space charge density, and a radially decreasing space charge distribution from the
corona electrode. Normally, the space charge density is on the scale of 10-5 C/m3. An
approximate space charge density 1.6110 5 C/m3 is calculated with the measured current and
geometric size of the current device. Figure 4.16 shows the electric field and equipotential
distribution of this geometry without space charge. Arrows start from the corona electrode, and
point upward to Teflon sidewall, showing orientation of columbic force acting on charged air
molecules. The length of arrows is proportional to the intensity of electric field. In Figure 4.17,
dielectrophoretic force in the region is shown as arrows. It can be seen that dielectrophoretic
force points along the voltage gradient. The regions with no arrows have very little voltage
changes and thus, almost no dielectrophoretic force. Next, we assume a constant space charge
distribution of 0.0858 C/m3. The electric field and dielectrophoretic force distribution are shown
in Figure 4.18 and Figure 4.19. In this case, the region with the highest voltage is not around the
corona electrode, but in the region above the corona electrode, due to the high density of space
charge. The case for radially decreasing space charge distribution of Geometry I is seen in Figure
4.20 and Figure 4.21. From Figure 4.20, it can be seen the region with the highest voltage shifts
downward compared to the case of constant space charge distribution, although still above the
corona electrode.
50
Figure 4.16 Electric field and equipotential line distribution of Geometry I
without space charge.
Figure 4.17 Dielectrophoretic force distribution of Geometry I without space
charge.
51
Figure 4.18 Electric field and equipotential line distribution of Geometry I with
constant space charge distribution.
Figure 4.19 Dielectrophoretic force distribution of Geometry I with constant
space charge distribution.
52
Figure 4.20 Electric field and equip-potential line distribution of Geometry I with
radially decreasing space charge distribution.
Figure 4.21 Dielectrophoretic force distribution of Geometry I with radially
decreasing space charge distribution.
53
Chapter 5. Experimental setup,
measurements, and results
5.1 Experimental setup
The experimental setup of a single channel air pump is shown in Figure 5.1. On the left of
this figure is a high voltage DC power supply, HIPOTRONICS–R30B. On the right is the setup
of the single channel air pump: the aluminum platform on the top is to support side channel
collector electrodes; the x-y-z translation stage (Figure 5.2, from Newport Corporation) is used
to position the corona razor electrode; the whole stage is screwed to the aluminum base.
Figure 5.1 Experimental setup of a single channel air pump.
54
Figure 5.2 The x-y-z translation stage to position the corona electrode.
Figure 5.3 shows a closer view of the single channel air pump. A stainless steel razor
corona electrode is positioned between two collector electrodes. Insulating Kapton films attached
around the razor are used to prevent breakdown of the high intensity corona field. Two pieces of
white Teflon sheets are used as the channel sidewalls. Thin films made from different materials
are attached on the sidewalls as collector electrodes. Semi-conductive Kapton films are used as
collector electrodes in Figure 5.4.
In Figure 5.5, the collector electrode is made of copper foil paralleled on top of an
insulating Kapton film. We call it the “Zebra” electrode. Each copper foil is wired to a specific
node along a circuit, which generates a voltage gradient to optimize air movement. The setup of
it is shown in Figure 5.6. The wires stretching out of “Zebra” are connected to different nodes on
a series circuit on a breadboard; the probe in front of DC voltage supply is a high voltage probe
to measure the voltage applied on the corona electrode; the metal pole on the top of Teflon
sidewalls is connected to an airflow sensor (VELOCICALC PLUS 8386, a multi-parameter
ventilation meter) to measure outcoming air speed.
55
Figure 5.3 The corona electrode standing between collector electrodes.
Figure 5.4 Semiconductive Kapton film attached to Teflon sheet forms the
collector electrode.
56
Figure 5.5 Zebra electrode: voltage gradient applied on insulating Kapton film
through copper foil.
.
Figure 5.6 Experimental setup with Zebra collector electrode.
5.2 Air speed profile on the outlet of the air pump
Due to the symmetrical channel geometry of the corona air pump and the higher air
movement resistance along the channel, the air speed has a non-uniform profile at the outlet
along and across the channel sidewall. The air speed along the channel sidewall can be seen in
57
Figure 5.7. From the figure, it can be seen that two peaks of air speed are present along the
outlet. This is not surprising since the airflow has the longest accelerating pass along those two
directions. The air speed across the channel sidewall of the outlet is shown in Figure 5.8. The
peak is reached at the middle across the channel outlet. The highest airflow speed of the air
pump reached is 1115 lfm. The unit of air speed here is lfm (linear feet per minute). It is much
faster compared to conventional computer fan’s air speed of several hundred lfm.
900
Air speed va, (lfm)
800
700
600
500
400
300
200
100
0
0
10
20
30
40
50
60
70
Measuring position along the channel sidewall on the outlet, X (mm)
Figure 5.7 Air speed profile along the sidewall from the outlet.
58
900
Air speed va, (lfm)
800
700
600
500
400
300
200
100
0
0
2
4
6
10
8
Measuring position across the channel sidewall on the outlet, Y (mm)
Figure 5.8 Air speed profile across the sidewall from the outlet.
5.3 Voltage-air speed relationship
Measurement of air speed (at the spot with the highest air speed) when increasing the
corona electrode voltage shows a linear relationship as seen in Figure 5.9. The noticeable airflow
is detected after 6 kV. After that, the air speed increases almost linearly with the voltage. When
the applied voltage exceeds 11 kV, sparks occur between the corona electrode and collector
electrodes with the current device.
800.0
Air speed, va (lfm)
700.0
600.0
500.0
400.0
300.0
200.0
6
7
8
9
10
11
12
Corona electrode voltage, VC (kV)
Figure 5.9 Measured corona voltage (Vc) vs. air speed (lfm) on the outlet exhibits
linear relationship.
59
5.4 Current-voltage relationship and air resistance
Current grows exponentially as applied voltage is higher than corona onset voltage in the
measurement shown in Figure 5.10, which is in good agreement with classic theory. It can be
seen that the corona onset voltage is 5.2 kV. Figure 5.11 shows the dramatic decrease of air
resistance in log scale as the voltage on the corona electrode increases.
120
90
60
30
0
5
5.5
6
6.5
7
7.5
Figure 5.10 Measured corona voltage ( VC ) vs. current through collector electrode
( I C ) exhibits exponential dependence.
Figure 5.11. Measured air resistance ( RA ) as a function of corona voltage ( VC ).
5.5 Energy efficiency
60
The prototype is tested for its energy efficiency. One traditional definition of energy
efficiency is the percentage of the kinetic energy of generated airflow over the input electric
power. For the air pump prototype, the kinetic energy is calculated from the air speed measured
at the outlet; the input electric power is multiplication of the voltage applied on the corona
electrode and the current flowing through the collector electrode. As it is shown from Figure
5.12, the efficiency of air pump according this definition is very low, below 0.5%. When the
input voltage increases, the energy efficiency decreases further.
0.50
Efficiency (%)
0.40
0.30
0.20
0.10
0.00
6
7
8
9
10
11
12
Input voltage V, ( kV)
Figure 5.12. Energy efficiency as a function of input voltage V .
Another common measure of fan efficiency in industry is to divide the airflow rating in
cfm (cubit feet per minute) by the power consumption in watts. Its physical meaning is very selfexplanatory: for a given amount of input power, the more and faster airflow is generated, the
more efficient the fan is. The efficiency of the air pump according this definition is shown in
Figure 5.13. It can be seen that at lower input voltage, the fan efficiency is much higher.
61
Fan efficiency, (CFM/W)
9
8
7
6
5
4
3
2
1
0
6
7
8
9
10
11
12
Input voltage V, (kV)
Figure 5.13. Fan efficiency in CFM/W as a function of input voltage V .
For traditional rotational fan, the fan efficiency in CFM/W is normally provided in the
manufacturer’s literature that accompanies the fan. Traditional computer cooling fan’s efficiency
in this unit normally ranges from 1 to 15 cfm per watt. Also, a rotational fan with a small
diameter has lower efficiency than a fan with a bigger diameter [38]. Basically, the corona air
pump we built has the efficiency in the same magnitude with conventional rotational computer
fans, with even smaller size. However, as mentioned before, the airflow profile of corona air
pump along the channel makes it much more efficient for cooling than parabolic airflow profile
of conventional fans. Also, corona air pumps for cooling purpose have several other advantages:
no moving parts, low noise, customizable airflow profiles and compatibility with chip structure.
Therefore, from the perspective of energy efficiency and other advantages, it is worthwhile to
minimize the corona air pump, and eventually build a micro air pump to test for computer chip
cooling.
62
Chapter 6. Future research
6.1 Current problem
In this thesis, a macro single channel air pump with different geometric parameter, and
materials has been simulated, built, and studied in detail. However, translation of the research
results to micro-scale, needs extensive research efforts. Such efforts include numerous system
integration issues; the choice of materials for corona and collector electrodes; a method to apply
the ionization voltage between the fins of computer chips. Eliminating the generation of ozone or
removal of ozone production needs to be addressed. Ozone generation should be less than
required by Occupational Safety & Health Administration (OSHA).
Moreover, in the current macro-scale design, the working voltage is in the range of
kilovolts, which does not fall in the common electronics voltage working range. Of course, as the
size of the air pump shrinks, the voltage should be able to decrease to an acceptable range, as
discussed in Section 4.3.1.1.
Another problem in this technology is the lifetime of corona electrodes. They erode due
to the bombardment or attachment of charged dust particles in the air. Figure 6.1 shows the
contrast between the surface region without erosion on a corona wire and the region with
erosion. The black spots in the second picture correspond to defects on the surface after erosion.
Therefore, corona electrodes need to be cleaned or replaced after working for a period of time.
The current component of stainless steel razors as corona electrodes are more robust. However,
an unevenly eroded razor tip generates unevenly distributed airflow or even sparks in the current
device. This problem needs to be investigated further.
63
Surface without erosion
Surface with erosion
Figure 6.1 Contrast between the surface region without erosion and the region
with erosion on a corona wire using SEM (Scanning Electron Microscopy).
6.2 Future plans
The next step in this project is to continue optimizing macro air pump cooling efficiency
with different geometries, materials, and working conditions to reach higher energy efficiency.
One of the most significant aspects in choosing fabrication materials is the desire to reduce
electrode erosion and eliminate ozone generation. The relatively low voltage used in the device
would still result in high electric field intensity near the electrode tip while ozone concentration
is expected to be lower. Currently, stainless steel is used as the corona electrode material.
Alternative materials that might perform better include silicon, tungsten, lanthanum hexaboride,
and alumina. Another possible technique to eliminate ozone generation and reduce electrode
erosion is to use liquid electrodes.
The main focus of future research is to shrink the size of the corona pump and eventually
build a prototype on the scale of a computer chip for integration. The technological and physical
limitations of electrostatic air pump technology at micron distances will be investigated. System
integration issues mentioned above should be addressed. MEMS modeling software can be
utilized to simulate a micro air pump and its performance with different design parameters. After
all these, the design should be mature enough to be used to build the first prototype.
Prototype testing and evaluation require special procedures that will be developed separately
and require additional manufacturing steps. The direct gas flow measurement at micron scale is
64
difficult and, therefore, requires indirect methods. Several test procedures should be developed
during the time of prototype design and manufacturing, including measurement of ozone and
evaluation of cooling efficiency.
65
Chapter 7. Conclusions
This thesis explores the possibility of building an electrostatic air pump for enhancement of
heat withdrawal from microelectronics and MEMS at chip level. Corona-driven air pumps may
serve as a catalyst for the next generation of high-density microelectronics. Its main advantages
include elimination of moving parts, low noise, dynamic airflow profiles, versatile shape and
sizes, and compatibility with chip structure. In the device modeling conducted in this thesis,
different geometry variations of the air pump are simulated with finite-element software. The
channel geometry with the razor corona electrode is found to be one of the most promising
designs for heat removal. A prototype of air pump of this kind has been built on macro-scale for
investigation. The air speed measurement at the outlet confirmed laminar nature of airflow and
uniform speed distribution in the cross-section of the air pump. It has also been found that the
measured air speed increases linearly as the applied voltage increases. Measured current flowing
through the device grows exponentially with increasing voltage after the corona onset voltage as
expected. The airflow speed of this air pump is about 1115 lfm (linear feet per minute), which is
much higher than the speed of a conventional fan (several hundred lfm). Future research
directions include optimization of geometry and driving electronics; system integration;
numerical simulation of the electrodynamics of moving media in micro-scale; and a micro-scale
fabrication.
66
REFERENCES
[1] A. E. Bergles, Heat Transfer in Electronic and Microelectronic Equipment, Troy, New
York, USA, Hemisphere Publishing Corporation, 1990.
[2] Xie, J., Ali, A., and Bhatia, R., The Use of Heat Pipes in Personal Computers, The Sixth
Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic
Systems, 1998, pp. 442-448.
[3] Gromoll, B., Advanced Micro Air-Cooling Systems for High Density Packaging,
Proceedings of 10th Semiconductor Thermal Measurement and Management
Symposium, 1994, pp. 53-58.
[4] M. Favreau, "GB-185, Hot Markets: Thermal Management Technology for Electronics,"
. 1996. Business Communications Company Inc.
[5] Cross, J. A., Electrostatically Assisted Heat Transfer, International Electrostatics
Conference, 1975, pp. 191-199.
[6] M. Robinson, "Movement of Air in the Electronic Wind of Corona Discharge," AIEE
Transactions, vol. 80, pp. 143-150, May 1961.
[7] F. Hauksbee, Physico-Mechanical Experiments on Various Subjects, London, England,
1709, pp. 46-47.
[8] Isaac Newton, Opticks, London, England, 1718, pp. 315-316.
[9] Michael Faraday, Experimental Researches in Electricity, London, England, 1839, pp.
665, 1443, 1444, 1535, 1592, 1595.
[10] James Clerk Maxwell, Treatise on Electricity and Magnetism, London, England, 1873,
pp. 52-54.
[11] O. M. Stuetzer, "Ion Drag Pressure Generation," Journal of Applied Physics, vol. 30, no.
7, pp. 984-994, July 1959.
[12] W. F. Pickard, "Ion Drag Pumping. I. Theory," Journal of Applied Physics, vol. 34, no. 2,
pp. 246-250, Feb. 1963.
[13] P. Atten, "On the Use of an Ionic Pump in a Convector Heater," IEEE Transactions on
Industry Applications, vol. 32, no. 1, pp. 80-89, Jan. 1996.
[14] K. Adamiak, "Adaptive Approach to Finite Element Modelling of Corona Fields," IEEE
Transactions on Industry Applications, vol. 30, no. 2, pp. 387-393, Mar. 1994.
67
[15] J. E. Bryan and J. Seyed-Yagoobi, "Analysis of 2-Dimensional Flow Field Generated by
a 1-Electrode-Pair Ion-Drag Pump," IEEE Transactions on Dielectrics and Electrical
Insulation, vol. 1, no. 3, pp. 459-466, June 1994.
[16] G. M. Colver and S. El-Khabiry, "Modeling of DC Corona Discharge Along an
Electrically Conductive Flat Plate With Gas Flow," IEEE Transactions on Industry
Applications, vol. 35, no. 2, pp. 387-394, Mar. 1999.
[17] K. Sakai, S. Tsuru, D. L. Abella, and M. Hara, "Conducting Particle Motion and ParticleInitiated Breakdown in Dc Electric Field Between Diverging Conducting Plates in
Atmospheric Air," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 6, no.
1, pp. 122-130, Feb. 1999.
[18] E. J. Shaughnessy and G. S. Solomon, "Electrohydrodynamic Pressure of the Point-ToPlane Corona Discharge," Aerosol Science and Technology, vol. 14, no. 2, pp. 193-200,
1991.
[19] Z. Y. Gu and R. A. Schill, "Novel Quasi-Electrostatic Air Filter: A Single-Particle
Study," Journal of Electrostatics, vol. 39, no. 3, pp. 203-230, July 1997.
[20] Z. Gu and R. A. Schill, "The Two-Dimensional Electrostatic Field Configuration for
Parallel Plate Dust Particle Guide Including End Effects," Journal of Electrostatics, vol.
38, no. 4, pp. 317-336, Dec. 1996.
[21] J. M. Gaugain, "On the Disruptive Discharge," Annales de Chimie et de Physique, vol.
64, pp. 175, 1862.
[22] V. Rontgen, Gottinger Nach., pp. 390, 1878.
[23] F. W. Peek, Dielectric Phenomena in High Voltage Engineering, New York:McGrawHill, 1929.
[24] L. B. Loeb, Basic Processes of Gaseous Electronics, Berkeley, Univ. of Calif. Press,
1955.
[25] L. B. Loeb, Fundamental Processes of Electrical Discharge in Gases, New York, Wiley
& Sons Inc., 1939.
[26] H. J. White, Industrial Electrostatic Precipitation, Addison-Wesley, 1963.
[27] J. S. Townsend, Philosophical Magazine, vol. 6, pp. 358, 1903.
[28] J. Zeleny, Phys.Rev., vol. 24, pp. 255, 1924.
[29] G. W. Trichel, "The Mechanism of the Negative Point-to-Plane Corona Near Onset,"
Physical Review, vol. 54, pp. 1078, 1938.
68
[30] J. H. Jeans, Electricity and Magnetism, 5th ed. New York, Cambridge University Press,
1927.
[31] K. R. Parker, Applied Electrostatic Precipitation, London, Blackie Academic &
Professional, 1997.
[32] S. L. Soo, Multiphase Fluid Dynamics, Science Press and Gower Technical, 1990.
[33] J. D. Cobine, Gaseous Conductors, Dover Publications, 1958.
[34] Jastrow, R. and Pearse, C. A., 62, 1957, pp. 413.
[35] J. W. Strutt, (Lord Rayleigh) Theory of Sound, Dover Publications, 1929.
[36] Aliam, G. and Gallily, I., 5, 1962, pp. 575.
[37] K. Adamiak, "Simulation of Corona in Wire-Duct Electrostatic Precipitator by Means of
the Boundary Element Method," IEEE Transactions on Industry Applications, vol. 30,
no. 2, pp. 381-386, Mar. 1994.
[38] R. Jarnagin, "Selecting a Ceiling Fan," Florida Energy Extension Service, pp. Fact Sheet
EES-31. 2002. University of Florida, Institute of Food and Agricultural
Sciences,(UF/IFAS).