Part I: Background and Fundamentals Introduction, Mohamed Gad-el-Hak, University of Notre Dame Scaling of Micromechanical Devices, William Trimmer, Standard MEMS, Inc., and Robert H. Stroud, Aerospace Corporation Mechanical Properties of MEMS Materials, William N. Sharpe, Jr., Johns Hopkins University Flow Physics, Mohamed Gad-el-Hak, University of Notre Dame Integrated Simulation for MEMS: Coupling Flow-Structure-Thermal-Electrical Domains, Robert M. Kirby and George Em Karniadakis, Brown University, and Oleg Mikulchenko and Kartikeya Mayaram, Oregon State University Liquid Flows in Microchannels, Kendra V. Sharp and Ronald J. Adrian, University of Illinois at Urbana-Champaign, Juan G. Santiago and Joshua I. Molho, Stanford University Burnett Simulations of Flows in Microdevices, Ramesh K. Agarwal and Keon-Young Yun, Wichita State University Molecular-Based Microfluidic Simulation Models, Ali Beskok, Texas A&M University Lubrication in MEMS, Kenneth S. Breuer, Brown University Physics of Thin Liquid Films, Alexander Oron, Technion, Israel Bubble/Drop Transport in Microchannels, Hsueh-Chia Chang, University of Notre Dame Fundamentals of Control Theory, Bill Goodwine, University of Notre Dame Model-Based Flow Control for Distributed Architectures, Thomas R. Bewley, University of California, San Diego Soft Computing in Control, Mihir Sen and Bill Goodwine, University of Notre Dame Part II: Design and Fabrication Materials for Microelectromechanical Systems Christian A. Zorman and Mehran Mehregany, Case Western Reserve University MEMS Fabrication, Marc J. Madou, Nanogen, Inc. LIGA and Other Replication Techniques, Marc J. Madou, Nanogen, Inc. X-Ray-Based Fabrication, Todd Christenson, Sandia National Laboratories Electrochemical Fabrication (EFAB), Adam L. Cohen, MEMGen Corporation Fabrication and Characterization of Single-Crystal Silicon Carbide MEMS, Robert S. Okojie, NASA Glenn Research Center Deep Reactive Ion Etching for Bulk Micromachining of Silicon Carbide, Glenn M. Beheim, NASA Glenn Research Center Microfabricated Chemical Sensors for Aerospace Applications, Gary W. Hunter, NASA Glenn Research Center, Chung-Chiun Liu, Case Western Reserve University, and Darby B. Makel, Makel Engineering, Inc. Packaging of Harsh-Environment MEMS Devices, Liang-Yu Chen and Jih-Fen Lei, NASA Glenn Research Center Part III: Applications of MEMS Inertial Sensors, Paul L. Bergstrom, Michigan Technological University, and Gary G. Li, OMM, Inc. Micromachined Pressure Sensors, Jae-Sung Park, Chester Wilson, and Yogesh B. Gianchandani, University of Wisconsin-Madison Sensors and Actuators for Turbulent Flows. Lennart Loefdahl, Chalmers University of Technology, and Mohamed Gad-el-Hak, University of Notre Dame Surface-Micromachined Mechanisms, Andrew D. Oliver and David W. Plummer, Sandia National Laboratories Microrobotics Thorbjoern Ebefors and Goeran Stemme, Royal Institute of Technology, Sweden Microscale Vacuum Pumps, E. Phillip Muntz, University of Southern California, and Stephen E. Vargo, SiWave, Inc. Microdroplet Generators. Fan-Gang Tseng, National Tsing Hua University, Taiwan Micro Heat Pipes and Micro Heat Spreaders, G. P. "Bud" Peterson, Rensselaer Polytechnic Institute Microchannel Heat Sinks, Yitshak Zohar, Hong Kong University of Science and Technology Flow Control, Mohamed Gad-el-Hak, University of Notre Dame) Part IV: The Future Reactive Control for Skin-Friction Reduction, Haecheon Choi, Seoul National University Towards MEMS Autonomous Control of Free-Shear Flows, Ahmed Naguib, Michigan State University Fabrication Technologies for Nanoelectromechanical Systems, Gary H. Bernstein, Holly V. Goodson, and Gregory L. Snider, University of Notre Dame Index

The MEMS Handbook

A revision of Newton's law of viscosity appearing in the role of the deviatoric stress tensor in the Navier–Stokes equation is proposed for the case of compressible fluids, both gaseous and liquid. Explicitly, it is hypothesized that the velocity v appearing in the velocity gradient term ∇ v in Newton's rheological law be changed from the fluid's mass-based velocity v m , the latter being the velocity appearing in the continuity equation, to the fluid's volume velocity v v , the latter being a stand-in for the fluid's volume current (volume flux density n v ). A similar v m → v v alteration is proposed for the velocity v appearing in the no-slip tangential velocity boundary condition at solid surfaces. These proposed revisions are based upon both experiment and theory, including re-interpretation of the following three items: (i) experimental “near-continuum” thermophoretic and other low Reynolds number phoretic data for the movement of suspended particles in fluids under the influence of mass density gradients ∇ ρ , caused either by temperature gradients in single-component fluids undergoing heat transfer or by species concentration gradients in inhomogeneous two-component mixtures undergoing mass transfer; (ii) the hierarchical re-ordering of the Burnett terms appearing in the Chapman–Enskog gas-kinetic theory perturbation expansion of the viscous stress tensor from one of being based upon small Knudsen numbers to one of being based upon small Mach numbers; (iii) Maxwell's (1879) ubiquitous v m -based “thermal creep” or “thermal stress” slip boundary condition used in nonisothermal gas-kinetic theory models, recast in the form of a v v -based no-slip condition. The v v vs. v m dichotomy in the case of compressible fluids is shown to lead to a fundamental distinction between the fluid's tracer velocity as recorded by monitoring the spatio-temporal trajectory of a small non-Brownian particle deliberately introduced into the fluid, and the fluid's “optical” or “colorimetric” velocity as monitored, for example, by the introduction of a dye into the fluid or by some photochromic- or fluorescence-based scheme in circumstances where the individual fluid molecules are themselves responsive to being probed by light. Explicitly, it is argued that the fluid's tracer velocity, representing a strictly continuum nonmolecular notion, is v v , whereas its colorimetric velocity, which measures the mean velocity of the molecules of which the fluid is composed, is v m .

Navier–Stokes revisited

The main theoretical and experimental results from the literature about steady pressure-driven gas microflows are summarized. Among the different gas flow regimes in microchannels, the slip flow regime is the most frequently encountered. For this reason, the slip flow regime is particularly detailed and the question of appropriate choice of boundary conditions is discussed. It is shown that using second-order boundary conditions allows us to extend the applicability of the slip flow regime to higher Knudsen numbers that are usually relevant to the transition regime. The review of pulsed flows is also presented, as this kind of flow is frequently encountered in micropumps. The influence of slip on the frequency behavior (pressure gain and phase) of microchannels is illustrated. When subjected to sinusoidal pressure fluctuations, microdiffusers reveal a diode effect which depends on the frequency. This diode effect may be reversed when the depth is shrunk from a few hundred to a few μm. Thermally driven flows in microchannels are also described. They are particularly interesting for vacuum generation using microsystems without moving parts.

Rarefaction and compressibility effects on steady and transient gas flows in microchannels

This paper describes the design, fabrication, and testing of a single-chip micromachined implementation of a Knudsen pump, which uses the principle of thermal transpiration, and has no moving parts. A six-mask microfabrication process was used to fabricate the pump using a glass substrate and silicon wafer. The Knudsen pump and two integrated pressure sensors occupy an area of 1.5 mm /spl times/ 2 mm. Measurements show that while operating in standard laboratory conditions this device can evacuate a cavity to 0.46 atm using 80 mW input power. The pumpdown time of an on-chip chamber and pressure sensor cavity with a total volume of 80 000 cubic micrometers is only 2s, with a peak pump speed of 1/spl times/10/sup -6/ cc/min. High thermal isolation is obtained between the polysilicon heater and the rest of the device.

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On-chip vacuum generated by a micromachined Knudsen pump

Due to the rapid advances in micro-electro-mechanical systems (MEMS), the study of microflows becomes increasingly important. Currently, the molecular-based simulation techniques are the most reliable methods for rarefied flow computation, even though these methods face statistical scattering problem in the low speed limit. With discretized particle velocity space, a unified gas-kinetic scheme (UGKS) for entire Knudsen number flow has been constructed recently for flow computation. Contrary to the particle-based direct simulation Monte Carlo (DSMC) method, the unified scheme is a partial differential equation-based modeling method, where the statistical noise is totally removed. But, the common point between the DSMC and UGKS is that both methods are constructed through direct modeling in the discretized space. Due to the multiscale modeling in the unified method, i.e., the update of both macroscopic flow variables and microscopic gas distribution function, the conventional constraint of time step being less than the particle collision time in many direct Boltzmann solvers is released here. The numerical tests show that the unified scheme is more efficient than the particle-based methods in the low speed rarefied flow computation. The main purpose of the current study is to validate the accuracy of the unified scheme in the capturing of non-equilibrium flow phenomena. In the continuum and free molecular limits, the gas distribution function used in the unified scheme for the flux evaluation at a cell interface goes to the corresponding Navier-Stokes and free molecular solutions. In the transition regime, the DSMC solution will be used for the validation of UGKS results. This study shows that the unified scheme is indeed a reliable and accurate flow solver for low speed non-equilibrium flows. It not only recovers the DSMC results whenever available, but also provides high resolution results in cases where the DSMC can hardly afford the computational cost. In thermal creep flow simulation, surprising solution, such as the gas flowing from hot to cold regions along the wall surface, is observed for the first time by the unified scheme, which is confirmed later through intensive DSMC computation.

A Unified Gas-Kinetic Scheme for Continuum and Rarefied Flows III: Microflow Simulations

Applications of Knudsen compressors as both microscale and macroscale vacuum pumps have been investigated. The study is based on a cascade analysis incorporating available transitional thermal transpiration and Poiseuille flow results for slender channels. It was found that the Knudsen compressor is an attractive possibility for microscale pumps down to a pressure of about 1 mTorr and for macroscale pumps to about 0.1 mTorr. A microscale pump for a micromass spectrometer providing a molecule flow rate of 5×1014 molecules/s results in the following pump characteristics: energy use of 2.4 W, pump volume of 13.9 ml at an inlet pressure of 1 mTorr and an energy use of 28.5 mW, and pump volume of 0.16 ml at an inlet pressure of 10 mTorr. A macroscale pump providing a pumping speed of 103 l/s results in a pump with an energy use of 1786 W, and pump volume of 1695 l at an inlet pressure of 0.1 mTorr. Several Knudsen compressor characteristics such as pressure rise, pumping speed, volume, energy use and mass flow...

G. R. Shiflett

Papers

Knudsen compressor as a micro- and macroscale vacuum pump without moving parts or fluids