The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M Gad el Hak Part 11 ppsx
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. ... 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 ... τRis the time of rupture and b is the constant which should be determined from the matching with the far-from-rupture solution. The minimal thickness of the film close to the rupture point is thereforebξᎏ2b2ᎏ2dᎏhЈ048π2d5σᎏAЈσa2ᎏ3dAЈᎏ2πσ1ᎏdPhysics...
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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 ... “Numerical Modeling of Micromechanical Devices Using the DirectSimulation Monte Carlo Method,” J. Fluids Eng. 118 , pp. 464–69. 6-2 6 MEMS: Introduction and Fundamentals © 2006 by Taylor & ... 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...
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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 ... Reduced-Order Models for Complex Geometries 11. 6 Lubrication in Rotating Devices 1 1-9 11. 7 Constraints on MEMS Bearing Geometries 1 1-1 1Device Aspect Ratio • Minimum Etchable Clearance 11. 8 Thrust ... 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 2 doc
... indeterminate set of equations. The continuum model is easier to handle mathematically (andis also more familiar to most fluid dynamicists) than the alternative molecular models. Continuum mod-els ... listed in the comments columns of the tables. The question of the effect of size on the strength of MEMS materials often arises. This is because MEMS structural components can be on the same size ... polysilicon, electroplated nickel, and A-533B 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...
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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: ... illustrateother ramifications of the large surface-to-volume ratio unique to MEMS and provide a molecular view-point to surface forces.Uᎏh ϩ 2Los 4-2 8 MEMS: Introduction and Fundamentals 1.94.58.216.80.360.140.100.06Ls/o␥c5432100.01...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 4 pps
... LLC5Integrated Simulationfor MEMS: CouplingFlow-Structure-Thermal-ElectricalDomains5.1 Introduction 5-1 Full-System Simulation • Computational Complexity of MEMS Flows • Coupled-Domain Problems • A ... 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. ... actuators, thermoresistors, and flow sensors are described as lumped elementsand/or compact models.● The pump is modeled at the detailed physical level.●All lumped elements and models are implemented...
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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 ... on the molecular distribution function of the surrounding gas, the ther-mophoretic force can be calculated by integrating the momentum flux imparted by the molecules strik-ing the particle. The ... 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...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 7 pdf
... 1997]. The profiles generally agree well with the DSMCresults. The temperature and Mach number profiles especially show very close agreement with the DSMC 8-3 0 MEMS: Introduction and Fundamentals 0.0 ... region 0 Յ x Յ 1 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/ymax1.00.50.00.01.02.03.0 ... beyondNavier–Stokes are needed. These models are known as extended, or generalized, hydrodynamics modelsin the literature. Some of these models are the Burnett equations; 13-moment Grad’s equations;...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 10 pps
... used for MEMS. This alleviates many of the reservations and costs that mightinhibit their adoption. Because the MEMS constraint is the minimum gap dimension, the wave bearingin a MEMS machine ... shows the measurements (from a 26:1 scaled-up experimental rig) along with the theoretical predictions based on the assumed geometry. The right-hand frame shows the same measurements comparedwith ... Group, 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...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 12 doc
... various examples of their dynamics relevantfor MEMS are presented, some of them with reference to the corresponding experimental results. The examples discussed examine isothermal, non-isothermal with ... interfacial jump in the momentum flux, the combination of the fourth and the fifth terms represents the jump in the conductive heat flux at both sides of the interface,while the combination of the last ... unchanged.j2ᎏρυj2ᎏρυ21ᎏ22πRυᎏ M wϑs3/2ᎏˆαρυL1 2-3 6 MEMS: Introduction and Fundamentals © 2006 by Taylor & Francis Group, LLCThis must match with the front spherical cap of radius R that makes the quadratic tangent with the cap-illary....
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