The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 10 pps

The MEMS Handbook (1st Ed) - M. Gad el Hak Part 1 ppsx

... 10 .Typical Man-MadeDevices 10 20 10 18 10 16 10 14 10 12 10 10 10 8 10 6 10 4 10 2 10 2 10 0 10 -2 10 -4 10 -6 10 -8 10 -1 0 10 -1 2 10 -1 4 10 -1 6Diameter of Protonâ 2002 by CRC Press LLC ... we review the status of our understanding of ﬂuid ﬂow physics particular to microde-vices. The chapter is an update of an earlier publication by the same author [Gad- el- Hak, 19 99]. The coverage ... FIGURE 1. 1 Scale of things, in meters. Lower scale continues in the upper bar from left to right. One meter is 10 6 à m, 10 9 nm or 10 10 .Typical Man-MadeDevices 10 20 10 18 10 16 10 14 10 12 10 10 10 8 10 6 10 4 10 2 10 2 10 0 10 -2 10 -4 10 -6 10 -8 10 -1 0 10 -1 2 10 -1 4 10 -1 6Diameter...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 2 doc

... (1997)155 — 2. 26 Tension Electroplated Greek and Ericson (1998)— 1.83 2. 20 2. 26 2. 49 Tension HI -MEMS films Sharpe and McAleavey (1998)â 20 06 by Taylor & Francis Group, LLC onto the structure. ... Microstructures:Experiments and Theory,” Proc. SPIE 322 5, pp. 12 22 . El Khakani, M.A., Chaker, M., Jean, A., Boily, S., and Kieffer, J.C. (1993) “Hardness and Young’s Modulusof Amorphous a-SiC Thin Films Determined ... — 0.30Nickel 180 — 0.30 0.50Nickel–iron 120 — 0.70 1.60Diamond-like carbon 800 0 .22 — 8.0Polysilicon 160 0 .22 — 1 .2 3.0Silicon crystal 125 –180 — — Ͼ1.0Silicon carbide 400 0 .25 — —Silicon...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 3 pptx

... molecular-based models and their relation to the continuum models previously considered. The most fundamental of the molecular models is deterministic. The motion of the molecules is gov-erned by the ... of state relating the different thermodynamic properties are needed. The stress–rate-of-strainrelation and the heat-flux–temperature-gradient relation are approximately linear if the flow is ... Hypothesis for a Newtonian, 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, ...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 4 pps

... Microchannels,” in The Handbook of MEMS, M. Gad- el- Hak, ed., CRC Press, Boca Raton, Florida.Shih, J.C., Ho, C M., Liu, J., and Tai, Y C. (1995) “Non-Linear Pressure Distribution in UniformMicrochannels,” ... Smoluchowski, M. (1898) “Ueber Wärmeleitung in verdünnten Gasen,” Ann. Phys. Chem. 64, pp. 101–30.Went, F.W. (1968) The Size of Man,” Am. Sci. 56, pp. 40 0 41 3. 4- 3 6 MEMS: Introduction and Fundamentals â ... speed-up can be obtained using the graph-based algorithm.5.3.3 The Structural Simulator The membrane of the micropump is modeled using the linear string-beam equation as given by the fol-lowing...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 5 ppsx

... applied elec-tric field4. Sedimentation potential: electric field created by the motion of charged particles relative to a sta-tionary liquid (opposite of electrophoresis).6.3.2 The Electro-Osmotic ... reason, the model with b ϭ Ϫ1 results in 10% error in the slip velocity 6-1 4 MEMS: Introduction and Fundamentals BoltzmannDSMC datab = 0b = −10 .5 00.01 0. 05 0.1 0 .5 Kn1 5 1011 .5 U* (y,Kn)FIGURE ... of the ions close to the wall, keep-ing the bulk of the liquid far away from the wall electrically neutral. The distance from the wall at which the electric potential energy is equal to the thermal...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 6 potx

... Equation IncludingThermal Creep Flow,” J. Tribol. 110, p. 253. Gad- el- Hak, M. (2002) “Flow Physics,” in Handbook of MEMS, 1st ed., M. Gad- el- Hak, ed., CRC Press,Boca Raton.Gallis, M.A., Rader, D.J., ... gas, the ther-mophoretic force can be calculated by integrating the momentum flux imparted by the molecules strik-ing the particle. The particle can be considered sufficiently small when the ... of Small-Scale Internal Gaseous Flows 7-1 7−0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.24.855.25.45 .6 5.8 6 6.2 6. 4 6. 6BrNutFIGURE 7.7 Variation of the fully developed Nusselt number...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 7 pdf

... between the Navier–Stokes solutions and the augmented Burnett solu-tions at the entrance, but as the local Knudsen number increases toward the exit of the channel, the dif-ference between the Navier–Stokes ... compute the super-sonic flow in a microchannel. The geometry and grid of the microchannel are shown in Figure 8.29. As the flow enters the channel, the tangential velocity component to the wall is ... 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 MEMS: Introduction and Fundamentals y/ymax0.00.51.00.0...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 9 ppsx

... B. (2004) “Electrokinetically Driven Micro FlowCytometers with Integrated Fiber Optics for On-Line Cell/Particle Detection,” Anal. Chim. Acta507, pp. 163– 69. Gad- el- Hak, M. ( 199 9) The Fluid ... 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 high conductivity regions. The seminal ... E is the electric field driving the fluid. Since we have assumedthat the EDL is thin, the electric field at the slip surface can be approximated by the electric field at the wall. The electric...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 10 pps

... in MEMS 1 1-1 5 10 0 10 −1 10 −2 10 −3 10 −4 10 −5 10 −1 10 0 10 1␨Λ␧ = 0.8␧ = 0.6␧ = 0.4␧ = 0.2Λ90705030 10 10−1 10 0 10 10φ (deg)␧ = 0.8␧ = 0.8␧ = 0.9FIGURE 11 .10 ... 701)Continuum flowSlip flowMolecular flow 10 10 10 8 10 6 10 4 10 2 10 −2 10 0 10 0 10 2 10 4 10 6FIGURE 11.2 (See color insert following page 1 0-3 4.) Theory and measurements of Couette damping ... the boundarycondition is relaxed from the standard non-slip condition to that of a slip-flow condition where the velocity at the wall is related to the Knudsen number and the gradient of velocity...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 11 ppsx

... problem, the dimensionless fluid velocities in the x- and y- directions are defined asU ϭ , V ϭ . (12.8d)Then the continuity Equation (12.2) requires that the z-component of the velocity field w ... energy in the thicker part of the film is greater than in its thin-ner part. Thus, the interfacial temperature at the depression is lower than at the crest of the interface, and the thermocapillary ... on the fact that lateral gradients of the electric fieldapplied in the vicinity of the film interface induce variations of surface tension and thus lead to the elec-trocapillary effect. The electrocapillary...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 12 doc

... and thermal conductivity of the vapor with respect to the respective prop-erties of the liquid. The vapor dynamics are ignored in the one-sided model, and only the mass conser-vation and the ... respectively, the densities of the vapor and the liquid; vυand vfare the vapor and liquid velocities at z ϭ h; and viis the velocity of the interface. Equation (12. 79a) provides the relationship ... includes: the qualitative nature of any transient response of the system, the reference signal tracking properties of the system, and the long-term or steady-state per-formance of the system. The...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 13 pptx

... 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 solution of the previous ... 1948, 1950]. Because the real part of the pole corresponds to exponentialsolutions, if all the poles are in the left-half plane, the poles closest to the jω-axis will dominate the system response. ... curves. The first curve is the logarithm of the magnitude of the responseof the open-loop transfer function with respect to unit sinusoidal inputs of frequency ω. The second1 4-1 2 MEMS: Introduction...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 14 doc

... refer to several other chapters in this handbook and to the recent reviews of Ho and Tai (1996, 1998), McMichael (1996), Gad- el- Hak (1996),and Löfdahl and Gad- el- Hak (1999). For a mathematical perspective, ... downstream. The estimation convolution kernels shown in Figure 15.9, on the other hand,extend well downstream of the measurement point. This accounts for the delay between the motions of the convecting ... are the nonzero part of the ωˆ component of the eigenvectors (solid) and the nonzero part of the vˆcomponent of the eigenvectors (dashed) as a function of y from the lower wall (bottom) to the...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 15 pps

... reviewed the applications of MEMS to flow con-trol. Gad- el- Hak (1999) discussed the fluid mechanics of microdevices, and Löfdahl and Gad- el- Hak (1999)provided an overview of the applications of MEMS ... Gradient The identity Equation (15. 13) is now simplified using the equations defining the state field Equation (15. 11), the perturbation field Equation (15. 12), and the adjoint field Equation (15. 14). ... than the dynamics of the open-loop (uncontrolled) system. Thus, development of simulation-based reduced-order models for turbulent flows should probably be coordinated with the design of the control...

The MEMS Handbook Introduction & Fundamentals (2nd Ed) - M. Gad el Hak Part 16 potx

... 16. 26 and 16. 27.Figure 16. 26 illustrates the response of the pendulum angle, and Figure 16. 27 illustrates the velocity of the pendulum. Figure 16. 28 illustrates the control effort. Because the ... V.V., and Vellekoop, M.J. (1997) “Design and Fabrication ofWireless Remotely Readable MEMS Based Microaccelerometers,” Smart Mater. Struct. 6(6), pp. 7308.1 6-3 4 MEMS: Introduction and Fundamentals â ... the pendulum angle is Ϫ20°and the angular velocity is ϩ22.5°/s. The fuzzy state of the angle of the system is determined according to1 6-2 0 MEMS: Introduction and Fundamentals positivesmallpositivelarge0−30...

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