The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M Gad el Hak Part 7 pdf
The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 7 pdf
... 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 1.0 2.0 ... channel, the tangential velocity component to the wall is retained, while the velocitycomponent normal to the wall is neglected at wall boundaries in the region 0 Յ x Յ 1 m. The first-order 8-2 8 ... Wall-Boundary Conditions The no-slip-/no-temperature-jump boundary conditions are employed at the wall when solving the contin-uum Navier–Stokes equations for Kn Ͻ 0.001. In the continuum–transition...
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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. 1 17, 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 ... cantilever microbeammade of piezoelectric material. The emphasis may be on modeling the electronic circuit and the motion,and thus a simple model for the motion-induced hydrodynamic damping may be ... 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....
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 5 ppsx
... formicrofluidic problems.Molecular-Based Microfluidic Simulation Models 6-1 9© 2006 by Taylor & Francis Group, LLC 7- 1 7 Hydrodynamics ofSmall-Scale InternalGaseous Flows 7. 1 Introduction 7- 1 Overview ... 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...
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The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 6 potx
... (2002) “Molecular-Based Microfluidic Simulation Models,” in Handbook of MEMS, 1st ed., M. Gad- el- Hak, ed., CRC press, Boca Raton.Bird, G.A. (1994) Molecular Gas Dynamics and the Direct Simulation ... 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 ... characteris-tic of small scale devices (Pe Ͻ 1), the Nusselt number defined byNuTϭ (7. 20)q2Hᎏᎏκ(TwϪ Tb) 7- 1 4 MEMS: Introduction and Fundamentals 5 The dependence on the flow field comes from...
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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 ... 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 ... meets the simple electroosmotic flow conditionssummarized above. As shown in the figure, the electroosmotic flow field streamlines are very well approx-imated by electric field lines.For the...
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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 ... 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
... 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 ... 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 ... compact form must be tract-able and, at the same time, complex enough to retain the main features of the problem at hand. The most appropriate analytical method of dealing with the above complexities...
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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 ... Layers in the Diffuse-Interface Model Coupled to Hydrodynamics,” Phys. Rev. E 62, pp. 2480–92.1 2-4 6 MEMS: Introduction and Fundamentals © 2006 by Taylor & Francis Group, LLCMomentum fluxes...
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