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Corona-driven air propulsion for cooling of microelectronics By Fumin Yang A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering University of Washington 2002 Program 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 66-133 MHz Pentium Pro Pentium II Pentium III Pentium IV 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 cm 3 , 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 n0 e 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 1012 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 0e 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 1012 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). 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