Fluid density sensor based on resonance vibration

Enoksson, Peter; Stemme, Göran; Stemme, E.

doi:10.1016/0924-4247(94)00915-5

Cited by 67 publications

(36 citation statements)

References 5 publications

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“…Andrews and Harris [13] have described a device with two parallel plates, each supported by beams, that are oscillated normal to each other to determine the viscosity of gases while Martin et al [14] presented a flexural plate wave resonator, fabricated on a silicon nitride membrane, to determine density. There are also fluid-filled vibrating U-tube densimeters fabricated with MEMS albeit with a square rather than the traditional circular cross section [15][16][17]. In addition to these devices, there are numerous applications of cantilever beams (developed from the devices used in atomic force microscopy [18]) to the measurement of density and viscosity [19][20][21][22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

et al. 2006

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In the petroleum industry, measurements of the density and viscosity of petroleum reservoir fluids are required to determine the value of the produced fluid and the production strategy. Measurements of the density and viscosity of petroleum fluids require a transducer that can operate at reservoir conditions, and results with an uncertainty of about ±1% in density and ±10% in viscosity are needed to guide value and exploitation calculations with sufficient rigor. Necessarily, these specifications place robustness as a superior priority to accuracy for the design. A vibrating plate, with dimensions of the order of 1 mm and a mass of about 0.12 mg, clamped along one edge, has been fabricated, with the methods of Microelectromechanical (MEMS) technology, to provide measurements of both density and viscosity of fluids in which it is immersed. The resonance frequency (at pressure p = 0 is about 12 kHz) and quality factor (at p = 0 is about 2 800) of the first order bending (flexural) mode of the plate are combined with semi-empirical working equations, coefficients obtained by calibration, and the mechanical properties of the plate to provide the density and viscosity of the fluid into which it is immersed. When the device was surrounded by argon at temperatures between 348 and 423 K and at pressures between 20 and 68 MPa, the density and viscosity were determined with an expanded (k = 2) uncertainty, including the calibration, of about ±0.35% and ±3%, respectively. These results, when compared with accepted correlations for argon reported in the literature, were found to lie within ±0.8% for density and less than ±5% for viscosity of literature values, which are within a reasonable multiple of the relative combined expanded (k = 2) uncertainty.

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Section: Introductionmentioning

confidence: 99%

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

et al. 2006

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“…This concept has been used for years in macroscopic U-tube density meters. More recently, micro and nanomechanical U-tube resonators, also called suspended microchannel resonators, have been successfully used for weighing of biomolecules [12] and nanoparticles [13], and for density [11,14,15] and viscosity [16] measurements. The viscosity detection is non-trivial because the quality factor has been shown to be a nonmonotonic function of the liquids viscosity [17,18].…”

Section: Liquid Inside the Resonatormentioning

confidence: 99%

Quality Factor

Schmid¹,

Villanueva²,

Roukes³

2016

Fundamentals of Nanomechanical Resonators

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The quality factor defines the rate with which a nanomechanical resonator dissipates energy. Low energy loss, i.e. a high quality factor, is desirable for most applications of nanomechanical resonators. In this chapter, the three main sources of energy loss in nanomechanical resonators are presented. Energy can be lost (1) to the surrounding medium, which can be a liquid or a gas, (2) through the clamping to the substrate via elastic waves, or (3) through dissipation mechanisms that are intrinsic to the resonator. Medium interaction losses can readily be circumvented by operation in vacuum, and clamping losses can be minimized by an optimized resonator design. This typically leaves intrinsic losses as the limiting mechanism defining the maximal obtainable quality factor. Intrinsic losses consist of material friction and fundamental loss mechanisms such as thermoelastic loss and phonon-phonon interaction loss. Generally, intrinsic losses can be reduced by decreasing the temperature. Damping dilution reduces the effect of intrinsic loss in resonators under tensile stress, resulting in quality factors up to several million even at room temperature.

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“…As reported by Rinaldi et al (2010), the design parameters of microstructures would meet requirements of several aspects, such as the material properties, size, geometry, boundary conditions, and modal properties. In this article, we focus on a class of microstructures that may be characterized as micromachined pipes containing internal fluid flow (see, e.g., Enoksson et al 1995Enoksson et al , 1997Westberg et al 1999;Burg et al 2007;Najmzadeh et al 2007;Sparks et al 2009). …”

Section: Introductionmentioning

confidence: 99%

Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory

Xia

Wang

2010

Microfluid Nanofluid

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The problem of microfluid-induced vibration and instability in the walls of the micro-channels containing internal fluid is now of considerable interest for potential micro-fluidics device applications. In this article, we have studied a non-viscous and incompressible fluid through microstructures. Based on a modified couple stress theory, a non-classical Timoshenko beam model is developed for the free vibration of microstructures containing internal fluid flow, modeled as micromachined pipes conveying fluid. Compared with the classical pipe models, this new model contains a material length scale parameter which can describe the microstructure-dependent vibration characteristics of the microscale pipes. By considering the effect of the microfluid flow, the equations of motion are derived using Hamiltonian approach. Based on the newly developed Timoshenko model, the effects of material length scale parameter and Poisson ratio on the vibration characteristics and the critical flow velocity are discussed. When the outside diameter of the pipe becomes comparable to the material length scale parameter, it is found that the natural frequencies increase remarkably and that the critical flow velocities predicted by the non-classical Timoshenko beam theory are much higher than that predicted by the classical beam theory. The size effects, however, are almost diminishing as the diameter of the pipe is far greater than the material length scale parameter. This study might be helpful to characterize the dynamical behavior of microscale pipes conveying fluid or design microfluidic and nanofluidic devices in a wide range of applications.Keywords Microscale pipes conveying fluid Á Vibration Á Non-classical Timoshenko beam model Á Size effect Á Microfluidic device 1 Introduction

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Fluid density sensor based on resonance vibration

Cited by 67 publications

References 5 publications

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

A Vibrating Plate Fabricated by the Methods of Microelectromechanical Systems (MEMS) for the Simultaneous Measurement of Density and Viscosity: Results for Argon at Temperatures Between 323 and 423K at Pressures up to 68 MPa

Quality Factor

Microfluid-induced vibration and stability of structures modeled as microscale pipes conveying fluid based on non-classical Timoshenko beam theory

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