Energy dissipation in microfluidic beam resonators: Dependence on mode number

Sader, John E.; Lee, Jungchul; Manalis, Scott R.

doi:10.1063/1.3514100

Cited by 22 publications

(37 citation statements)

References 28 publications

(53 reference statements)

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“…In previous studies, energy dissipation has been attributed to environmental factors, such as viscosity, temperature, clamping loss, intrinsic defects, and the change of the elastic energy. 11,15,16,[37][38][39][40][41][42] Here, we take advantage of the in situ technique to directly measure and calculate the input and output energies. The input energy can be assumed as the energy of a capacitor, between the free end of the Si NW and the W probe.…”

Section: Resultsmentioning

confidence: 99%

“…However, it is still challenging to realize high-order resonances at high frequencies due to the large energy dissipation and strict resonant conditions. 15,16 By using the top-down approach, high-order normal and parametric resonances were demonstrated, 17,18 with a resonant frequency of several MHz. 17 Bottom-up grown nanowires (NWs) are attractive as high frequency resonators because of their high crystallinity and small mass.…”

Section: Introductionmentioning

confidence: 99%

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Realization and direct observation of five normal and parametric modes in silicon nanowire resonators by in situ transmission electron microscopy

et al. 2019

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Mechanical resonators have wide applications in sensing bio-chemical substances, and provide an accurate method to measure the intrinsic elastic properties of oscillating materials. A high resonance order with high response frequency and a small resonator mass are critical for enhancing the sensitivity and precision. Here, we report on the realization and direct observation of high-order and high-frequency silicon nanowire (Si NW) resonators. By using an oscillating electric-field for inducing a mechanical resonance of singlecrystalline Si NWs inside a transmission electron microscope (TEM), we observed resonance up to the 5 th order, for both normal and parametric modes at $100 MHz frequencies. The precision of the resonant frequency was enhanced, as the deviation reduced from 3.14% at the 1 st order to 0.25% at the 5 th order, correlating with the increase of energy dissipation. The elastic modulus of Si NWs was measured to be $169 GPa in the [110] direction, and size scaling effects were found to be absent down to the $20 nm level.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Realization and direct observation of five normal and parametric modes in silicon nanowire resonators by in situ transmission electron microscopy

et al. 2019

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“…Overall, an NSR would have relatively increased sensitivity, by two orders of magnitude, and as a consequence, could detect pressure variations with improved resolution relative to the presented micro-scale prototype. A previous study 25 showed that Q decreases with a decrease in length (mode number) of a resonator. In the case of an NSR, and as evidenced by previous work, an appropriate combination of aspect ratio 26 (Ch w , t, F w , L, Ch h ) could help in retaining high Q.…”

Section: A)mentioning

confidence: 97%

Pressure modulated changes in resonance frequency of microchannel string resonators

Khan

Knowles

Dennison

et al. 2014

Applied Physics Letters

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Resonating strings have shown promise in a variety of applications including micron-scale mass and temperature sensors. We present microchannel string resonators (MSRs) which have resonance frequency modulated by the internal gauge pressure of silicon nitride microchannels sitting atop the strings. We present an analytical model to predict the pressure sensitivity (Hz/kPa) of the first resonance frequency as well as experimental results for three identical MSRs. While the highest experimental sensitivity of one of the resonators is 5.19 Hz/kPa (0.5 Hz/mbar), the analytical model suggests sensitivity could increase by two orders of magnitude if the microchannels are fabricated at nanometer scale with a length of 10 μm, a channel width of 600 nm, and a channel thickness of 50 nm. The average pressure resolution of the sensors is 0.4 kPa. These results are for a calibrated range of pressure from 50 kPa to 100 kPa (500 mbar to 1000 mbar). However, the analytical model shows that resonance frequency is a linear function of pressure over a range of several MPa, suggesting that the microchannel resonators could have a pressure sensing range (dynamic range) suitable for many applications.

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“…Each prong can be individually considered as a clamped-free cantilever beam, and the symmetrical prongs of QTF reduce the number of possible modes. Since the length L of each prong of the tuning fork is much larger than its width l and thickness e, according to the beam theory of Euler-Bernoulli, the governing differential equation for the deflection w(x, t) of the beam [35][36][37] is given by…”

Section: Hydrodynamic Modelmentioning

confidence: 99%

A Hydrodynamic Model for Measuring Fluid Density and Viscosity by Using Quartz Tuning Forks

Zhang

Chen

et al. 2019

Sensors

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A hydrodynamic model of using quartz tuning forks (QTFs) for density and viscosity sensing, by measuring the resonance frequency and quality factor, has been established based on the cantilever beam theory applied to the atomic force microscope (AFM). Two examples are presented to verify the usability of this model. Then, the Sobol index method is chosen for explaining quantitatively how the resonance frequency and quality factor of the QTFs are affected by the fluid density and viscosity, respectively. The results show that the relative mean square error in viscosity of the eight solutions evaluated by the hydrodynamic model is reduced by an order of magnitude comparing with Butterworth-Van Dyke equivalent circuit method. When the measured resonance frequency and quality factor of the QTFs vary from 25,800-26,100 Hz and 28-41, the sensitivities of the quality factor affected by the fluid density increase. This model provides an idea for improving the accuracy of fluid component recognition in real time, and lays a foundation for the application of miniaturized and cost-effective downhole fluid density and viscosity sensors.Sensors 2020, 20, 198 2 of 12 lithium niobate tuning fork were 10.48% and 2.89%, respectively. Although it is a physical fact for tuning fork sensors that the error on density is smaller than that on viscosity [22], we can still reduce the viscosity error to meet the measurement requirements.Tuning fork sensors, microcantilever beam, AlN resonator, torsional resonators and so on, can all be used as sensitive components for the D-V sensor [23][24][25]. On the one hand, quartz tuning forks (QTFs) studied in this paper have high Curie temperature, good stability and high accuracy, which is suitable for downhole high temperature and high pressure environment, and, on the other hand, a millimeter-sized QTF can be integrated in small-scale measurement platforms for downhole deployment. In addition, the QTFs are low-cost and commercially used as frequency standards in watches, working at 32.768 kHz. The QTF is widely used in gas sensing based on photoacoustic spectroscopy and photothermal spectroscopy [26][27][28], and scanning probe microscopy applications such as atomic force microscopy (AFM) [29][30][31] and near-field scanning optical microscopy (NSOM) [32][33][34]. In order to estimate the density and viscosity of a liquid at the same time, the hydrodynamic model based on the work of Sader, J.E. [35] for the atomic force microscope (AFM) is established, and two examples are verified by using this model.

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Energy dissipation in microfluidic beam resonators: Dependence on mode number

Cited by 22 publications

References 28 publications

Realization and direct observation of five normal and parametric modes in silicon nanowire resonators by in situ transmission electron microscopy

Realization and direct observation of five normal and parametric modes in silicon nanowire resonators by in situ transmission electron microscopy

Pressure modulated changes in resonance frequency of microchannel string resonators

A Hydrodynamic Model for Measuring Fluid Density and Viscosity by Using Quartz Tuning Forks

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