© 2002 by CRC Press LLC Microdroplet generators usually employ mechanical actuation to generate high pressure to overcome liquid surface tension and viscous force for droplet ejection. Depending on the droplet size, the applied pressure is usually greater than several atmospheres. The operation principles, structure/process designs and materials often play key roles in the performance of droplet generators. The applications of microdroplet generators, in addition to the well-known application of inkjet printing, cover a wide spectrum of fields, including direct writing, fuel injection, solid freeform, solar cell fabrication, light emitting polymer display (LEPD) fabrication, packaging, microoptical components, particle sorting, microdosage, plasma spraying, drug screening/delivery/dosage, micropropulsion, integrated circuit cooling and chemical deposition. Many of these applications may become key technologies for integrated microsystems in the near future. This chapter provides the reader with an overview of the operation principles, physical properties, design issues, fabrication process and issues, characterization methods and applications of microdroplet generators. 30.2 Operation Principles of Microdroplet Generators Many attempts have been made to generate controllable microdroplets [Buehner et al., 1977; Twardeck, 1977; Carmichael, 1977; Ashley et al., 1977; Bugdayci et al., 1983; Darling et al., 1984; Lee et al., 1984; Myers and Tamulis, 1984; Nielsen, 1985; Bhaskar and Aden, 1985; Allen et al., 1985; Krause et al., 1995; Chen and Wise, 1995; Tseng et al., 1996; Hirata et al., 1996; Zhu et al., 1996]. Most of these methods have employed the principle of creating pressure differences, either by lowering the outer pressure or increasing the inner pressure of a nozzle, to push or pull liquid out of the nozzle to form droplets. Typical examples are pneumatic, piezoelectric, thermal bubble, thermal buckling, focused acoustic-wave and electrostatic actuations. The basic principles of those droplet generators are introduced in the following sections. An ejection method by acceleration is also included in the last section, in which inertial force is employed for droplet generation. 30.2.1 Pneumatic Actuation The spray nozzle is one of the most commonly used devices for generating droplets nowadays for airbrush or sprayer applications. Two types of spray nozzles are shown in Figure 30.1. Figure 30.1a shows that the air brush generates lower pressure at the outer edge of the capillary tube by blowing air across the tube FIGURE 30.1 Operation principle of airbrush and sprayer. (After Tseng, 1998.) (b) Sprayer Refilling cycle (a) Air brush Liquid inlet Air inlet Airflow Air flow Air flow Droplet Droplets Spraying cycle Liquid © 2002 by CRC Press LLC Microdroplet generators usually employ mechanical actuation to generate high pressure to overcome liquid surface tension and viscous force for droplet ejection. Depending on the droplet size, the applied pressure is usually greater than several atmospheres. The operation principles, structure/process designs and materials often play key roles in the performance of droplet generators. The applications of microdroplet generators, in addition to the well-known application of inkjet printing, cover a wide spectrum of fields, including direct writing, fuel injection, solid freeform, solar cell fabrication, light emitting polymer display (LEPD) fabrication, packaging, microoptical components, particle sorting, microdosage, plasma spraying, drug screening/delivery/dosage, micropropulsion, integrated circuit cooling and chemical deposition. Many of these applications may become key technologies for integrated microsystems in the near future. This chapter provides the reader with an overview of the operation principles, physical properties, design issues, fabrication process and issues, characterization methods and applications of microdroplet generators. 30.2 Operation Principles of Microdroplet Generators Many attempts have been made to generate controllable microdroplets [Buehner et al., 1977; Twardeck, 1977; Carmichael, 1977; Ashley et al., 1977; Bugdayci et al., 1983; Darling et al., 1984; Lee et al., 1984; Myers and Tamulis, 1984; Nielsen, 1985; Bhaskar and Aden, 1985; Allen et al., 1985; Krause et al., 1995; Chen and Wise, 1995; Tseng et al., 1996; Hirata et al., 1996; Zhu et al., 1996]. Most of these methods have employed the principle of creating pressure differences, either by lowering the outer pressure or increasing the inner pressure of a nozzle, to push or pull liquid out of the nozzle to form droplets. Typical examples are pneumatic, piezoelectric, thermal bubble, thermal buckling, focused acoustic-wave and electrostatic actuations. The basic principles of those droplet generators are introduced in the following sections. An ejection method by acceleration is also included in the last section, in which inertial force is employed for droplet generation. 30.2.1 Pneumatic Actuation The spray nozzle is one of the most commonly used devices for generating droplets nowadays for airbrush or sprayer applications. Two types of spray nozzles are shown in Figure 30.1. Figure 30.1a shows that the air brush generates lower pressure at the outer edge of the capillary tube by blowing air across the tube FIGURE 30.1 Operation principle of airbrush and sprayer. (After Tseng, 1998.) (b) Sprayer Refilling cycle (a) Air brush Liquid inlet Air inlet Airflow Air flow Air flow Droplet Droplets Spraying cycle Liquid © 2002 by CRC Press LLC 31 Micro Heat Pipes and Micro Heat Spreaders 31.1 Introduction Capillary Limitation • Viscous Limitation • Sonic Limitation • Entrainment Limitation • Boiling Limitation • Heat Pipe Thermal Resistance 31.2 Individual Micro Heat Pipes Modeling Micro Heat Pipe Performance • Testing of Individual Micro Heat Pipes 31.3 Arrays of Micro Heat Pipes Modeling of Heat Pipe Arrays • Testing of Arrays of Micro Heat Pipes • Fabrication of Arrays of Micro Heat Pipes 31.4 Flat-Plate Micro Heat Spreaders Modeling of Micro Heat Spreaders • Testing of Micro Heat Spreaders • Fabrication of Micro Heat Spreaders 31.5 New Designs 31.6 Summary and Conclusions 31.1 Introduction As described by Peterson (1994), a heat pipe operates on a closed two-phase cycle in which heat added to the evaporator region causes the working fluid to vaporize and move to the cooler condenser region, where the vapor condenses, giving up its latent heat of vaporization. In traditional heat pipes, the capillary forces existing in a wicking structure pump the liquid back to the evaporator. While the concept of utilizing a wicking structure as part of a device capable of transferring large quantities of heat with a minimal temperature drop was first introduced by Gaugler (1944), it was not until much more recently that the concept of combining phase-change heat transfer and microscale fabrication techniques (i.e., microelectromechanical systems, or MEMS, devices for the dissipation and removal of heat) was first proposed by Cotter (1984). This initial introduction envisioned a series of very small “micro” heat pipes incorporated as an integral part of semiconductor devices. While no experimental results or prototypes designs were presented, the term micro heat pipe was first defined as one “so small that the mean curvature of the liquid–vapor interface is necessarily comparable in magnitude to the reciprocal of the hydraulic radius of the total flow channel” [Babin et al., 1990]. Early proposed applications of these devices included the removal of heat from laser diodes (Mrácek, 1988) and other small localized heat-generating devices [Peterson, 1988a; 1988b]; thermal control of photovoltaic cells [Peterson, 1987a; 1987b]; removal or dissipation of heat from the leading edge of hypersonic aircraft [Camarda et al., 1997]; applications involving the nonsurgical treatment of cancerous tissue through either hyper- or hypothermia [Anon., 1989; Fletcher and Peterson, 1993]; and space applications in which heat pipes are embedded in silicon radiator panels to dissipate the large amounts of waste heat generated [Badran et al., 1993]. G. P. “Bud” Peterson Rensselaer Polytechnic Institute © 2002 by CRC Press LLC 32 Microchannel Heat Sinks 32.1 Introduction 32.2 Fundamentals of Convective Heat Transfer in Microducts Modes of Heat Transfer • The Continuum Hypothesis • Thermodynamic Concepts • General Laws • Particular Laws • Governing Equations • Size Effects 32.3 Single-Phase Convective Heat Transfer in Microducts Flow Structure • Entrance Length • Governing Equations • Fully Developed Gas Flow Forced Convection • Fully Developed Liquid Flow Forced Convection 32.4 Two-Phase Convective Heat Transfer in Microducts Boiling Curves • Critical Heat Flux • Flow Patterns • Bubble Dynamics • Modeling of Forced Convection Boiling 32.5 Summary Acknowledgments 32.1 Introduction The last decade has witnessed impressive progress in micromachining technology enabling the fabrication of micron-sized mechanical devices, which have become more prevalent in both commercial applications and scientific research. These micromachines have had a major impact on many disciplines, including biology, chemistry, medicine, optics, aerospace and mechanical and electrical engineering. This emerging field not only provides miniature transducers for sensing and actuation in a domain that we could not examine in the past but also allows us to venture into research areas in which the surface effects dominate most of the physical phenomena [Ho and Tai, 1998]. Fundamental heat-transfer problems posed by the development and processing of advanced integrated circuits (ICs) and microelectromechanical systems (MEMS) are becoming a major consideration in the design and application of such systems. The demands on heat-removal and temperature-control functions in modern devices that have highly transient thermal loads require an approach providing high cooling rates and uniform temperature distributions. As the field of microfluidics and micro heat transfer continues to grow, it becomes increasingly important to understand the mechanisms and fundamental differences involved with heat transfer in single- and two-phase flow in microducts. The idea of fabricating microchannel heat sinks is not new. As early as two decades ago, Tuckerman and Pease (1981) pioneered the use of microchannels for the cooling of planar integrated circuits. They demonstrated that by flowing water through small cooling channels etched in a silicon substrate, heat-transfer rates of about 10 5 W/m 2 K could be achieved. This rate is about two orders of magnitude higher than that in the state-of-the-art commercial technologies Yitshak Zohar Hong Kong University of Science and Technology . and microelectromechanical systems (MEMS) are becoming a major consideration in the design and application of such systems. The demands on heat-removal and temperature-control functions in modern. not until much more recently that the concept of combining phase-change heat transfer and microscale fabrication techniques (i.e., microelectromechanical systems, or MEMS, devices for the dissipation. which have become more prevalent in both commercial applications and scientific research. These micromachines have had a major impact on many disciplines, including biology, chemistry, medicine, optics,