High-frequency nanofluidics: an experimental study using nanomechanical resonators

Here we apply nanomechanical resonators to the study of oscillatory fluid dynamics. A high-resonance-frequency nanomechanical resonator generates a rapidly oscillating flow in a surrounding gaseous environment; the nature of the flow is studied through the flow-resonator interaction. Over the broad frequency and pressure range explored, we observe signs of a transition from Newtonian to non-Newtonian flow at omega tau approximately 1, where tau is a properly defined fluid relaxation time. The obtained experimental data appear to be in close quantitative agreement with a theory that predicts a purely elastic fluid response as omega tau --> infinity.     

Fiber-optic, cantilever-type acoustic motion velocity hydrophone

The interaction between fluid loaded fiber-optic cantilevers and a low frequency acoustic wave is investigated as the basis for an acoustic vector sensor. The displacements of the prototype cantilevers are measured with an integrated fiber laser strain sensor. A theoretical model predicting the frequency dependent shape of acoustically driven planar and cylindrical fiber-optic cantilevers incorporating effects of fluid viscosity is presented. The model demonstrates good agreement with the measured response of two prototype cantilevers, characterized with a vibrating water column, in the regime of Re ≥ 1. The performance of each cantilever geometry is also analyzed. Factors affecting the sensor performance such as fluid viscosity, laser mode profile, and support motion are considered. The planar cantilever is shown to experience the largest acoustically induced force and hence the highest acoustic responsivity. However, the cylindrical cantilever exhibits the smoothest response in water, due to the influence of viscous fluid damping, and is capable of two axis particle velocity measurement. These cantilevers are shown to be capable of achieving acoustic resolutions approaching the lowest sea-state ocean noise.     

Frequency shifts of cantilever in AFM

The frequency shift and frequency shift image of cantilever in AFM have been studied by numerical integration of the equation of motion of cantilever for silicon tip with rutile TiO₂(0 0 1) surface in UHV conditions and by the Hamaker summation method for the tip-surface interaction forces. The effects of the excitation frequency at the cantilever base and the equilibrium position of the tip on the frequency shift have been calculated and the results showed the same phenomena as those measured, e.g., the frequency shift increased dramatically or rapidly before the contact point and was then almost level off after the contact point. The effects of scanning speed and the initial closest distance of tip to the contact point have been calculated at different excitation frequencies at the cantilever base and the results showed that proper frequency shift image could be obtained either by noncontact mode at the excitation frequency slightly less than the resonance frequency of free cantilever, or by tapping mode at the excitation frequency a few times smaller than the resonance frequency of free cantilever.     

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler–Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.     

原子力显微镜高次谐波幅度对样品弹性性质表征的研究

轻敲模式下原子力显微镜微悬臂探针在接近其基态共振频率的外加驱动下振荡, 其末端针尖周期性靠近、远离样品, 产生于针尖与样品非线性相互作用过程中的高次谐波信号包含更多的待测样品表面纳米力学特性等方面的信息. 通过理论分析、计算, 系统地研究了针尖与样品接触时间受样品弹性模量的影响, 以及高次谐波幅度与接触时间的关系, 获得了通过高次谐波幅度区分待测样品表面弹性性质差异的规律. 并在自制的高次谐波成像实验装置上, 得到了与理论预期一致的实验结果. 关键词： 轻敲模式原子力显微镜 接触时间 高次谐波幅度 弹性模量     

Micro-Gas Flow Induced Stochastic Resonance of a Nonlinear Nanomechanical Resonator

Fluidics is one of the most historic subjects that are well-established over centuries on the macroscopic scale.In recent years,fluid detection using a number of micro/nano scale devices has been achieved.However,the interaction of microfluid and solid devices on micro/nano-meter scale still lacks in-depth research.We demonstrate a practical nanomechanical detector for microfluidics via a string resonator with high Q-factor,suspended over a hole.This device is placed under a jet nozzle with several microns of diameter,and the interaction between the micro-gas flow and the resonator is observed by monitoring the variation of the fundamental frequency and the quality factor.Moreover,we manage to measure the fluctuations of the micro-gas flow on the nanomechanical resonator by means of stochastic resonance.This work manifests a potential platform for detecting dynamical fluid behaviors at microscopic scale for novel fluid physics.     

品质因子可调的石墨烯纳米机械振子

纳米机械振子尺寸小,质量轻,可以用来制作探测力、质量等微小物理量的超灵敏探测器.石墨烯拥有质量轻、密度低和杨氏模量高等特性,被认为是制作纳米机械振子的理想材料.石墨烯纳米机械振子因其具有的谐振频率高、品质因子高和谐振频率可调性高等优势,近年来得到了人们的广泛关注.作为表征纳米机械振子性能的一个重要指标,品质因子越高,意味着纳米机械振子耗散越低,纳米机械振子的灵敏度越高.本文通过微纳加工的工艺制备出一种谐振频率随栅压可调(调节的范围为73 MHz～90 MHz)的石墨烯纳米机械振子样品,研究其在极低温高真空环境下的品质因子与栅极电压之间的关系.实验表明通过栅压调节振子的内部应力,能够使石墨烯纳米机械振子品质因子从220提高到1000.我们的结果为二维材料纳米机械振子的耗散研究提供了一种新的研究思路.     

Effect of tip mass on frequency response and sensitivity of AFM cantilever in liquid

The effect of tip mass on the frequency response and sensitivity of atomic force microscope (AFM) cantilever in the liquid environment is investigated. For this purpose, using Euler–Bernoulli beam theory and considering tip mass and hydrodynamic functions in a liquid environment, an expression for the resonance frequencies of AFM cantilever in liquid is derived. Then, based on this expression, the effect of the surface contact stiffness on the flexural mode of a rectangular AFM cantilever in fluid is investigated and compared with the case where the AFM cantilever operates in the air. The results show that in contrast with an air environment, the tip mass has no significant impact on the resonance frequency and sensitivity of the AFM cantilever in the liquid. Hence, analysis of AFM behaviour in liquid environment by neglecting the tip mass is logical.     

Influence of nanomechanical force on the electronic structure of InAs/GaAs quantum dots

We show nanomechanical force is useful to dynamically control the optical response of self-assembled quantum dots, giving a method to shift electron and heavy hole levels, interval of electron and heavy hole energy levels, and the emission wavelength of quantum dots (QDs). The strain, the electron energy levels, and heavy hole energy levels of InAs/GaAs(001) quantum dots with vertical nanomechanical force are investigated. Both the lattice mismatch and nanomechanical force are considered at the same time. The results show that the hydrostatic and the biaxial strains inside the QDs subjected to nanomechanical force vary with nanomechanical force. That gives the control for tailoring band gaps and optical response. Moreover, due to strain-modified energy, the band edge is also influenced by nanomechanical force. The nanomechanical force is shown to influence the band edge. As is well known, the band offset affects the electronic structure, which shows that the nanomechanical force is proven to be useful to tailor the emission wavelength of QDs. Our research helps to better understand how the nanomechanical force can be used to dynamically control the optics of quantum dots.     

Single-spin measurements for quantum computation using magnetic resonance force microscopy

The quantum theory of a single-spin measurement using magnetic resonance force microscopy is presented. We use an oscillating cantilever-driven adiabatic reversal technique. The frequency shift of the cantilever vibrations is estimated. We show that the frequency shift causes the formation of a Schrödinger cat state for the cantilever. The interaction between the cantilever and the environment quickly destroys the coherence between the two cantilever trajectories. It is shown that using partial adiabatic reversals one can obtain a significant increase in the frequency shift. We discuss the possibility of sub-magneton spin density detection in molecules using magnetic resonance force microscopy.     

Interplay between nonlinearity,scan speed,damping, and electronics in frequency modulation atomic-force microscopy

Numerical simulations of the frequency modulation atomic force microscope, including the whole dynamical regulation by the electronics, show that the cantilever dynamics is conditionally stable and that there is a direct link between the frequency shift and the conservative tip-sample interaction. However, a soft coupling between the electronics and the nonlinearity of the interaction may significantly affect the damping. A resonance between the scan speed and the response time of the system can provide a simple explanation for the spatial shift and contrast inversion between topographical and damping images, and for the extreme sensitivity of the damping to a tip change.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Interferometric profiling of microcantilevers in liquid

Silicon micro cantilevers are used as highly sensitive transducers for a wide range of physical, chemical and biochemical stimuli. Vibrating the cantilevers at higher-order resonant modes can achieve extra sensitivity, but the difficulty lies in determining exactly which modes are excited in the cantilever. This problem is exacerbated for cantilever sensors operating in liquid where the computational analysis of the resonance modes is very challenging. Using strobed interferometric microscopy, we are able to image the dynamic behavior of individual (100×500×1 μm³) cantilevers in an eight cantilever array over frequencies from 0–1 MHz. We show how some modifications to the interferometric microscope allow for the spatial visualization of 16 longitudinal modes of cantilevers working in liquid with nanometer-scale amplitudes. We also compare the shift in frequency response and reduction in quality factor for cantilevers resonating in liquid versus in air and simulations in vacuum. Because the resonant frequency spectrum is fairly complex and does not follow simple intuition, our work maps the actual behavior of cantilevers without having any specific knowledge of the sample and environment parameters and without the necessity of involved simulations and calculations.     

Calculation of the optimal imaging parameters for frequency modulation atomic force microscopy

True atomic resolution of conductors and insulators is now routinely obtained in vacuum by frequency modulation atomic force microscopy. So far, the imaging parameters (i.e., eigenfrequency, stiffness and oscillation amplitude of the cantilever, frequency shift) which result in optimal spatial resolution for a given cantilever and sample have been found empirically. Here, we calculate the optimal set of parameters from first principles as a function of the tip–sample system. The result shows that the either the acquisition rate or the signal-to-noise ratio could be increased by up to two orders of magnitude by using stiffer cantilevers and smaller amplitudes than are in use today.     

Behavior of nonlinear fluid viscous dampers for control of shock vibrations

Fluid viscous dampers have been widely used for suppression of high velocity shocks. While linear fluid viscous dampers have been used for a long time, nonlinear fluid viscous dampers show considerable promise due to their superior energy dissipation characteristics and significant reduction in the damper force compared to a linear fluid viscous damper for the same peak displacement. This paper presents results from experimental study to characterize fluid viscous dampers when subjected to half-cycle sine shock excitation. The mathematical formulation and a numerical study to evaluate the relative performance of structures with fluid viscous dampers subjected to short-duration shock (impulse) loading are also discussed. The influence of damper nonlinearity (α) and the supplemental damping ratio (ξ_sd) on response has been investigated. The supplemental damping ratio of nonlinear fluid viscous dampers when subjected to shock excitation is found by equivalent linearization using the concept of equal energy dissipation. The paper also presents some design charts, which can be used for preliminary decisions on parameters of nonlinear dampers to be used in design.     

Nonlinear effects in the dynamics of clouds of bubbles

This paper presents a spectral analysis of the response of a fluid containing bubbles to the motions of a wall oscillating normal to itself. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear effects in the oscillation of a single bubble in an infinite fluid. This is used in the approximate solution of the oscillating wall problem, and the resulting expressions are evaluated numerically in order to examine the nonlinear effects. Harmonic generation results from the nonlinearity. It is observed that the bubble natural frequency remains the dominant natural frequency in the volume oscillations of the bubbles near the wall. On the other hand, the pressure perturbations near the wall are dominated by the first and second harmonics present at twice the natural frequency while the pressure perturbation at the natural frequency of the bubble is inhibited. The response at the forcing frequency and its harmonics is explored along with the variation with amplitude of wall oscillation, void fraction, and viscous and surface tension effects. Splitting and cancellation of frequencies of maximum and minimum response due to enhanced nonlinear effects are also observed.     

Some exact solutions of magnetized viscous model in string cosmology

In this paper, we study anisotropic Bianchi-V Universe with magnetic field and bulk viscous fluid in string cosmology. Exact solutions of the field equations are obtained by using the equation of state (EoS) for a cloud of strings, and a relationship between bulk viscous coefficient and scalar expansion. The bulk viscous coefficient is assumed to be inversely proportional to the expansion scalar. It is interesting to examine the effects of magnetized bulk viscous string model in early and late stages of evolution of the Universe. This paper presents different string models like geometrical (Nambu string), Takabayasi (p-string) and Reddy string models by taking certain physical conditions. We discuss the nature of classical potential for viscous fluid with and without magnetic field. The presence of bulk viscosity stops the Universe from becoming empty in its future evolution. It is observed that the Universe expands with decelerated rate in the presence of viscous fluid with magnetic field whereas, it expands with marginal inflation in the presence of viscous fluid without magnetic field. The other physical and geometrical aspects of each string model are discussed in detail.     

Effect of viscosity on ultrasound wave reflection from a solid/liquid interface

A study of the simulated reflection of a wideband ultrasound shear wave from the solid/viscous fluid interface is presented. Various parameters affecting reflection factors including the material properties of the solid, fluid properties like density and viscosity, and the operating frequency are discussed. Simulated ultrasonic response waveforms are compared with the experimentally obtained data for NIST traceable calibration standards of viscosity. A good agreement was observed between the simulated and experimental waveforms at various viscosities and for different solid substrates.     

Passive cooling of a micromechanical oscillator with a resonant electric circuit

We cool the fundamental mode of a miniature cantilever by capacitively coupling it to a driven rf resonant circuit. Cooling results from the rf capacitive force, which is phase shifted relative to the cantilever motion. We demonstrate the technique by cooling a 7 kHz cantilever from room temperature to 45 K, obtaining reasonable agreement with a model for the cooling, damping, and frequency shift. Extending the method to higher frequencies in a cryogenic system could enable ground state cooling and may prove simpler than related optical experiments in a low temperature apparatus.