Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P ^–r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h ₀/L<0.01). As this ratio increases, the range of validity decreases.     

Generalized mean-square amplitudes of vibration in some XY4 type ions (II)

The generalized mean-square amplitudes of vibration and mean amplitudes of vibration have been computed for CrO^3-₄, Mn¹⁸O^-₄, MoSe^2-₄ and WSe^2-₄ ions at three temperatures, T = 0°K, T = 298°K, T = 500°K, employing Cyvin's method. The results have been discussed in the light of atomic weight and electronegativity of the atom in the ionic system.     

Spectroscopic investigations in molecularly organized solvent media. Part 3. Examination of the nitromethane selective quenching rule in aqueous anionic + cationic and anionic + nonionic mixed surfactant solutions

Applicability of the nitromethane selective quenching rule for discriminating between alternant versus nonalternant polycyclic aromatic hydrocarbons (PAHs) is examined for 20 representative PAH solutes dissolved in micellar sodium dodecylsulfate (SDS) + cetyltrimethylammonium bromide (CTAB), SDS + dodecyltrimethylammonium bromide (DTAB), SDS + Brij-35, and SDS + sodium octanoate (SO) mixed surfactant solvent media. Experimental results show that nitromethane quenched fluorescence of all 8 alternant PAHs studied in the four different solvent systems. Unexpected quenching behavior was observed, however, in the case of nonalternant PAHs. Nitromethane quenched fluorescence emission of nonalternant PAHs dissolved in the SDS + SO solvent media, which is contrary to the selective quenching rule. In the case of the mixed anionic + cationic surfactant solvent media, nitromethane quenching selectivity was restored at concentration ratios of approximately 4 : 1 (anionic:cationic) or less. Received: 22 May 1997 / Revised: 29 September 1997 / Accepted: 3 October 1997     

Force constants,coriolis coupling constants and mean amplitudes of vibration of GaF63− and FeF63−

The force constants, Coriolis coupling constants and mean amplitudes of vibration at 0, 298.16 and 500 K for GaF₆^3?FeF₆^3? have been reported for the first time employing recent vibrational data. The results are discussed in the light of available information.     

Synthesis of Mannich type products via a three-component coupling reaction

The reactions of alkyl nitriles, acetyl chloride, aldehydes and β-ketoesters or simple ketones was studied for the one-pot synthesis of β-acetamido carbonyl compounds. It was observed that the reaction proceeds in the absence of Lewis acids. However, a Lewis acid catalyzes the reaction and several were tested. It was found that whereas Cu(OTf)₂ is suitable for the coupling of β-ketoesters with aldehydes, Sc(OTf)₃ is the best for ketones. A possible mechanism is proposed based on the isolation and characterization of an intermediate.     

Recovery of Band-Limited Functions on Locally Compact Abelian Groups from Irregular Samples

Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group G. The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek's work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative reconstruction algorithms apply simultaneously to families of Banach spaces.     

Intensification of the reaction between Udaipur rock phosphate and sulphuric acid by means of ultrasound

The solid-liquid reaction between Udaipur rock phosphate and different concentrations of sulphuric acid is found to be greatly enhanced when the reaction is carried out in the presence of high intensity ultrasound (800 kHz and 80 W cm^?2). Even coarser rock particles up to 50 mesh (BSS) can be effectively decomposed in the presence of ultrasound to such an extent that is suitable for utilization in a commercial phosphatic fertilizer plant, which is not otherwise possible. The ultrasound helps the diffusion of reactants on to the solid rock particles and also inhibits the coating of calcium sulphate, formed during the reaction, on the unreacted solid rock particles. The decomposition curve of Udaipur rock phosphate at 80°C with different concentrations of sulphuric acid contains two maxima and two minima which are controlled by the concentration of H₃O⁺, HSO₄^? and SO₄^2? ions in the medium as the reaction proceeds. It is found that the presence of ultrasound reduces the difference between these maxima and minima and the decomposition is increased in all cases.     

Crystallographic and microstructural aspects of the superconductor YBa2Cu3O7-y —an overview

Crystal structures and structural inhomogeneities observed in YBa₂Cu₃O_7-y are reviewed. It is brought out that a proper understanding of the nature of the structural inhomogeneities is essential for exploiting the technological potential of this material. The need for an adequate characterization of specimens used for experiments is emphasized. Practical implications of the ferroelastic nature of the material are discussed.