The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M Gad el Hak Part 3 pptx
The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 3 pptx
... process. The present section discusses molecular-based models and their relation to the continuum models previously considered. The most fundamental of the molecular models is deterministic. The motion ... IsotropicFluid,” J. Fluids Eng. 117, pp. 3 5. Gad- el- Hak, M. (1999) The Fluid Mechanics of Microdevices: The Freeman Scholar Lecture,” J. FluidsEng. 121, pp. 5 33 . Gad- el- Hak, M. (2000) Flow Control: Passive, ... the wall. The tangential-momentum-accommodation coefficient σvand the thermal-accommodation coeffi-cientσTare given by respectivelyσvϭ (4.42)σTϭ (4. 43) where the subscripts i, r, and...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 13 pptx
... UncertainDynamical Systems,” SIAM J. Control Optimization 21, pp. 246 35 5.1 4 -3 0 MEMS: Introduction and Fundamentals © 2006 by Taylor & Francis Group, LLC14 .3. 3 Basic Robust Control The main idea motivating ... in the clockwise direction the samenumber of times that there are zeros of G(s)within the contour minus the number of times that there are1ᎏK1ᎏ1 ϩ K1 4-1 4 MEMS: Introduction and Fundamentals Frequency ... because there are no sign changes in the elements in the first column of the array.One aspect of performance concerns the steady-state error exhibited by the system. For example, from the time-domain...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 2 doc
... polysilicon, electroplated nickel, and A- 533 B steel. These arefrom microspecimens tested in the author’s laboratory.20 m (a)(b)FIGURE 3. 12 Microstructure of two common MEMS materials. Note the ... films fabricated in the shapes of beams and plates by comparing the measured curvatures. These were two-layer compositeMechanical Properties of MEMS Materials 3- 9 1 mmFIGURE 3. 5 A cantilever microbeam ... of Thin Films inMicromachining: Beam Pull-In Voltage (VPI) Method and Long Beam Deflection (LBD) Method,”Sensor. Actuator. A (Phys.) 48, pp. 137 – 43. 3- 3 2 MEMS: Introduction and Fundamentals ©...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 4 pps
... andσTare the tangential momentum and thermal accommodation coef-ficients respectively. The accommodation coefficients model the momentum and energy exchange of gas mol-ecules impinging on the walls. ... of the membrane. We see that a two-to three-orders of magnitude speed-up can be obtained using the graph-based algorithm.5 .3. 3 The Structural Simulator The membrane of the micropump is modeled ... simple elements are implemented as lumped elements or compact models. These elements areelectromechanical transducers (piezoelectric actuator) and thermoresistors. Flow sensors are much morecomplicated...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 5 ppsx
... of the Navier–Stokes equations, as well as the molecular interaction models of the MD and the DSMC methods. Although it may seem that the molecular simulation methods are more fundamental, theyrequire ... particularly important for simulation of gas flows in MEMS components.If we consider a micromotor or a micro-comb-drive mechanism, gas flow in most of the device can besimulated using the slip-based ... Microfluidic Simulation Models 6-2 3 © 2006 by Taylor & Francis Group, LLC6 .3. 3 Molecular Dynamics Method The molecular dynamics method requires simulation of motion and interactions of all molecules...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 6 potx
... and Ducts at Micro and NanoScales,” Microscale Thermophys. Eng. 3, p. 43. Beskok, A. (2002) “Molecular-Based Microfluidic Simulation Models,” in Handbook of MEMS, 1st ed., M. Gad- el- Hak, ed., CRC ... above Mach numbers of approximately two. Furthermore, the application of the 1 3- or 35 -moment systems to three-dimensional problems remains computationally prohibitive at present.Because of the ... 2kbTp /m and Tpis the particle temperature. More complex accommodation models can alsobe treated; in [Gallis et al., 2001] an extended Maxwell accommodation model is presented.In the DSMC implementation,...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 7 pdf
... dynamics models beyondNavier–Stokes are needed. These models are known as extended, or generalized, hydrodynamics modelsin the literature. Some of these models are the Burnett equations; 1 3- moment ... m. The first-order 8-2 8 MEMS: Introduction and Fundamentals y/ymax0.00.51.00.0 1.0 2.0 3. 0 4.0 5.0x/ymaxFIGURE 8.29Microchannel geometry and grid.y/ymax1.00.50.00.01.02.0 3. 0 ... with the DSMC 8 -3 0 MEMS: Introduction and Fundamentals 0.0 1.0 2.0 3. 0 4.0 5.00.0 1.0 2.0 3. 0 4.0 5.00.0 1.0 2.0 3. 0 4.0 5.00Navier−StokesAugmented Burnett15001000500Mach number Temperature...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 9 ppsx
... Taylor & Francis Group, LLC1 1-2 MEMS: Introduction and Fundamentals attention of MEMS researchers since the early days of MEMS development, and there have been severaldemonstrations of micromotors ... field). Sample ions migrate from the high-field–high-drift-velocity of the sample region to the low-field–low-drift-velocity region andaccumulate, or stack, at the interface between the low and ... gradients in the microchannel. Probably the most common cause of this is a mis-match in the height of the fluid level at the reservoirs. Although there may not be a mismatch of fluid levelat the start...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 10 pps
... Because the MEMS constraint is the minimum gap dimension, the wave bearingin a MEMS machine can be implemented only by selectively enlarging the bearing gap. Piekos (2000) ana-lyzed the performance ... along with the theoretical predictions based on the assumed geometry. The right-hand frame shows the same measurements comparedwith the same model but using slightly modified geometric parameters. ... LLC1 1-2 0 MEMS: Introduction and Fundamentals them undesirable in a practical MEMS rotor system. The primary difficulty is that, in order to satisfy the requirements of sub-synchronous stability, the...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 11 ppsx
... BH)21ᎏ21 2 -3 2 MEMS: Introduction and Fundamentals © 2006 by Taylor & Francis Group, LLC1 2-6 MEMS: Introduction and Fundamentals FIGURE 12.4 Infrared images of various states as seen in the experiments. ... parameters.∂φᎏ∂hσa2ᎏd2∂φᎏ∂h1ᎏ 3 1ᎏ 3 1ᎏ 3 1 2-2 2 MEMS: Introduction and Fundamentals © 2006 by Taylor & Francis Group, LLCspatial variation ofφand directed from the less to the more wettable domains on the solid. ... offilm surface deformations is well-correlated with the wavelength of the most amplified linear mode pro-portional to d2. Similar conclusions about the dominance of the nucleation mechanism were...
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