In the presence of an applied magnetic field, the viscosity tensor of electron flows exhibits an off-diagonal component. This Hall or odd viscosity has recently been measured in high-mobility devices. It is known that use of the hydrodynamic theory to extract the Hall viscosity from Hall resistivity measurements strongly overestimates its value. We develop a general transport theory, using a matched asymptotic expansion of the kinetic equation in the near-hydrodynamic regime, and thereby investigate the origin of this discrepancy. This reveals that bulk, near-boundary and boundary condition corrections compete with the classical Hall (odd) viscosity. This finding reconciles the above-mentioned disparity and the transport theory we report provides a basis for future measurements.

We experimentally demonstrate a new class of optomechanical nonlinearities in weakly damped micromechanical resonators, arising from the interplay between the Duffing nonlinearity, intermodal coupling, and thermal fluctuations. Within the bistable regime of a single Duffing mode driven by radiation pressure forces, we observe stochastically generated sidebands, originating from thermal fluctuations around equilibrium trajectories in phase space, and exploit these sidebands to induce probabilistic transitions between bistable states using weak secondary acoustic excitation. Extending this framework to multimodal interactions, we show that nonlinear modes coupling within the same resonator leads to similar transitions due to parametric modulation around the noise-excited sidebands as a result of frequency mixing. Simultaneously, abrupt changes in displacements of modes cause their instantaneous energy exchange rates to span five orders of magnitude. These findings open new avenues for reconfigurable optomechanical networks, nonreciprocal energy transport, and precision sensing based on dynamically tunable mechanical nonlinearities.

Recent years have seen explosive growth in miniaturized sensors that can continuously monitor a wide variety of processes, with applications in healthcare, manufacturing, and environmental sensing. The time series generated by these sensors often involves abrupt jumps in the detected signal. One such application uses nanoelectromechanical systems (NEMS) for mass spectrometry, where analyte adsorption produces a quick but finite-time jump in the resonance frequencies of the sensor eigenmodes. This finite-time response can lead to ambiguity in the detection of adsorption events, particularly in high event-rate mass adsorption. Here, we develop a computational algorithm that robustly eliminates this often-encountered ambiguity. A moving-window statistical test together with a feature-based clustering algorithm is proposed to automate the identification of single-event jumps. We validate the method using numerical simulations and demonstrate its application in practice using time-series data that are experimentally generated by molecules adsorbing onto NEMS sensors at a high event rate. This computational algorithm enables new applications, including high-throughput, single-molecule proteomics.

Nanoelectromechanical systems (NEMS)-based mass spectrometry (MS) is an emerging technique that enables determination of the mass of individual adsorbed particles by driving nanomechanical devices at resonance and monitoring the real-time changes in their resonance frequencies induced by each single molecule adsorption event. We incorporate NEMS into an Orbitrap mass spectrometer and report our progress towards leveraging the single-molecule capabilities of the NEMS to enhance the dynamic range of conventional MS instrumentation and to offer new capabilities for performing deep proteomic analysis of clinically relevant samples. We use the hybrid instrument to deliver E. coli GroEL molecules (801 kDa) to the NEMS devices in their native, intact state. Custom ion optics are used to focus the beam down to 40 μm diameter with a maximum flux of 25 molecules/second. The mass spectrum obtained with NEMS-MS shows good agreement with the known mass of GroEL.

Solid particles trapped in an acoustic standing wave have been observed to undergo propulsion. This phenomenon has been attributed to the generation of a steady streaming flow, with a reversal in the propulsion direction at a distinct frequency. We explain the mechanism underlying this reversal by considering the canonical problem of a sphere executing oscillatory rotation in an unbounded fluid that undergoes rectilinear oscillation; these two oscillations occur at identical frequency but with an arbitrary phase difference. Two distinct bifurcations in the flow field occur: (1) a stagnation point first forms with increasing frequency, which (2) splits into a saddle node and a vortex centre. Reversal in the propulsion direction is driven by reversal in the flow far from the sphere, which coincides with the second bifurcation. This flow is identified with that of a Stokeslet whose strength is the net force exerted on the particle, which has implications for studying the flow field around particles of non-spherical geometries and for modelling suspensions of particles in acoustic fields.

A two-dimensional body that moves suddenly in a viscous fluid can instantly generate vortices at its sharp edges. Recent work using inviscid flow theory, based on the Birkhoff–Rott equation and the Kutta condition, predicts that the ‘starting vortices’ generated by the sharp and straight edges of a body – i.e. the vortices formed immediately after motion begins – can be one of three distinct self-similar types. We explore the existence of these starting vortices for a flat plate and two symmetric Joukowski aerofoils immersed in a viscous fluid, using high-fidelity direct numerical simulations (DNS) of the Navier–Stokes equations. A lattice Green's function method is employed and simulations are performed for chord Reynolds numbers ranging from 5040 to 45 255. Vortices generated at the leading and trailing edges of the flat plate show agreement with the derived inviscid theory, for which a detailed assessment is reported. Agreement is also observed for the two symmetric Joukowski aerofoils, demonstrating the utility of the inviscid theory for arbitrary bodies. While this inviscid theory predicts an abrupt transition between the starting-vortex types, DNS shows a smooth transition. This behaviour occurs for all Reynolds numbers and is related to finite-time effects – there is a maximal time for which the (self-similar) starting vortices exist. We confirm the inviscid prediction that the leading-edge starting vortex of a flat plate can be suppressed dynamically. This has implications for the performance of low-speed aircraft such as model aeroplanes, micro air vehicles and unmanned air vehicles.

Fingerprint analysis is a ubiquitous tool for pattern recognition with applications spanning from geolocation and DNA analysis to facial recognition and forensic identification. Central to its utility is the ability to provide accurate identification without an a priori mathematical model for the pattern. We report a data-driven fingerprint approach for nanoelectromechanical systems mass spectrometry that enables mass measurements of particles and molecules using complex, uncharacterized nanoelectromechanical devices of arbitrary specification. Nanoelectromechanical systems mass spectrometry is based on the frequency shifts of the nanoelectromechanical device vibrational modes that are induced by analyte adsorption. The sequence of frequency shifts constitutes a fingerprint of this adsorption, which is directly amenable to pattern matching. Two current requirements of nanoelectromechanical-based mass spectrometry are: (1) a priori knowledge or measurement of the device mode-shapes, and (2) a mode-shape-based model that connects the induced modal frequency shifts to mass adsorption. This may not be possible for advanced nanoelectromechanical devices with three-dimensional mode-shapes and nanometer-sized features. The advance reported here eliminates this impediment, thereby allowing device designs of arbitrary specification and size to be employed. This enables the use of advanced nanoelectromechanical devices with complex vibrational modes, which offer unprecedented prospects for attaining the ultimate detection limits of nanoelectromechanical mass spectrometry. The authors report a data-driven approach that enables mass spectrometry using any nanomechanical device without knowledge of its vibrational modes.

Abstract Microplastic release from semicrystalline plastics threaten the environment and human health. We investigated polypropylene and polyethylene plastics, which together account for 54% of the global market. Mimicking common levels of residual stress found in plastics via cantilever beam experiments, we demonstrated that compressive stress drives nano and microscale segregation of amorphous polymer droplets onto the plastic’s surface. Simulations reveal this stress-driven volumetric flow is consistent with that of a Bingham plastic material, with a temperature-dependent threshold yield stress. Flow is thermally activated and stress dependent, with a reduced energy barrier at higher compressive stresses. Transfer of surface segregated amorphous droplets into the surroundings generates microplastics. Studies with water-containing plastic bottles showed that the highly compressed neck and mouth regions were predominantly responsible for the release of microplastics.

The force and torque on a solid body in a viscous potential flow are often taken to be independent of viscosity. Joseph et al. (Eur. J. Mech. B/Fluids, vol. 12, 1993, pp. 97–106; J. Fluid Mech., vol. 265, 1994, pp. 1–23) proved that this holds for (i) the force (not the torque) in any two-dimensional flow, and (ii) the drag force experienced by a purely translating three-dimensional body. The remaining components of the force and torque, along with general three-dimensional flows, were not considered. Importantly, the flow was assumed to be unbounded and irrotational everywhere. We eliminate this rarely satisfied assumption and consider the viscous force and torque experienced by any closed surface where the flow is irrotational locally; this can include a body's surface. Any vorticity distribution is permitted away from the closed irrotational surface. In so doing, we complete the analysis of Joseph et al. for all components of the viscous force and torque in two and three dimensions and enable application to real flows that inevitably contain regions of vorticity.

The evaluation of epigenetic features such as DNA methylation is becoming increasingly important in many biochemical processes like gene expression and transcription as well as in several diseases like schizophrenia or diabetes. Here, we report that self-assembled nanomechanical resonators entirely composed of DNA molecules can be used to explore gross changes in DNA methylation levels (0-25-50%), while careful control of tensile stress is needed to reduce the variability of resonance frequency for rigorous quantification. The effect of the tensile stress retained by the suspended DNA nanoresonators on the application of the technique is extensively explored using a combination of laser Doppler vibrometry and atomic force spectroscopy. DNA nanoresonators are real-time, label-free sensors and could avoid chemical functionalization and sample amplification. Therefore, they may represent in the future a key complementary routine tool for global DNA methylation analysis needed to evaluate the consequences of environmental stresses on the human genome.

Sensing applications that utilize nanomechanical resonators require careful control of nonlinear effects in their eigenmodes to ensure robust measurement. While the effect of intra- and intermodal nonlinearities on the resonant frequencies of doubly clamped elastic beams have been widely studied using theory and experiment, commensurate studies on cantilevered beams are limited in comparison. Here, we present such a detailed study that includes an explicit and simple formula for the flexural resonant frequencies of slender cantilevered beams that accounts for intra- and intermodal nonlinearities. Using this general theory, numerical results for the modal nonlinear coefficients are tabulated for the first 20 flexural eigenmodes of cantilevered beams possessing uniform cross sections. The accuracy of this theory, and the effect of cantilever aspect ratio (length/width) on these nonlinear coefficients, is explored using high-accuracy laser Doppler vibrometry experiments. We anticipate that these results will find utility in single- and multimode applications, where the effect of finite oscillation amplitude on the cantilever resonant frequencies can significantly impact measurement design and interpretation.

The motion of a finite layer of Bingham material on a solid plate that executes in-plane oscillations was reported previously by Balmforth et al. ( J. Non-Newtonian Fluid Mech. , vol. 158, issue 1–3, 2009, pp. 46–53). There, it was suggested that multiple yielded regions may arise within the material; this contrasts to start-up flow of the same material for which only one yielded region is generated. Here, we explore quantitatively the fluid physics of this oscillatory flow problem through analytical approximations and further numerical computation. Four new key topological properties concerning the generation and termination of the yielded regions are reported. It is shown that the existence of multiple yielded regions is equivalent to the layer never becoming entirely rigid during the periodic motion. For small inertia, the flow is approximately time-reversible with only a single yielded region generated at the plate. For large inertia, shear stress in the material decays rapidly as a function of distance from the plate. A thin zone of yielded material detaches periodically from the plate, and subsequently terminates within the layer. At high oscillation frequency, there can be any number $N$ of distinct rigid regions, satisfying $N= \lfloor 1- {\rm \pi}^{-1} \log B \rfloor$ where $B$ is the Bingham number. It is also shown that for $B>0.5370$ , there are at most one yielded region and one rigid region throughout the motion. These theoretical results can be used as a basis for oscillatory rheometry, allowing for measurement of the yield stress using existing apparatus.

Lithographically prepared plasmonic nanoparticles are ideal mechanical probes, as their vibrational behavior can be precisely tuned through particle size and shape. But these particles exhibit strong intrinsic and extrinsic damping that results in small vibrational quality (Q) factors. Here, we perform single-particle transient transmission microscopy to investigate the effect of substrate-particle binding strength on the vibrational Q-factor of lithographically prepared gold nanodisks on glass. Weak and strong binding is realized through titanium adhesion layers of variable thickness. We find that strong binding leads to the generation of several new acoustic modes with varying Q-factors that depend on the particle aspect ratio and substrate material. Our work proposes an approach to tune enhanced acoustic Q-factors of lithographically prepared nanoparticles and offers a comprehensive description of their damping mechanism.

The flow of an unbounded Newtonian fluid above a flat solid plate, set into motion suddenly with uniform velocity, is a canonical problem investigated by Stokes (On the effect of the internal friction of fluids on the motion of pendulums, Trans. Camb. Phil. Soc., vol. 9, 1851) and Rayleigh (Lond. Edinb. Dubl. Philos. Mag. J. Sci., vol. 21, issue 126, 1911, pp. 697–711). We tackle the same problem but with the fluid replaced by a yield-stress material of finite height with a free surface; the latter ensures both yielded (fluid-like) and rigid behaviour. The interface between the yielded and rigid regions – the so-called ‘yield surface’ – always emerges from the plate at a rate faster than that for momentum diffusion. The rigid region, adjacent to the free surface, is accelerated by the constant yield stress acting at this yield surface. As the velocity of this region increases following start-up, its acceleration climaxes and subsequently diminishes. In this latter period, the thickness of the rigid region increases owing to relaxation of the velocity gradients and the stress. The yield surface eventually collides with the plate in finite time, after which the entire material moves in concert with the plate as a rigid body. Analytical and numerical results are presented that can form the basis for practical applications. This includes the development of a ‘rheological microscope’ to directly detect and measure the yield stress. The analysis focuses on exploring the flow physics of a Bingham material. This is shown to be similar to that of a general Herschel–Bulkley material with shear-thinning or shear-thickening rheology.

Standard continuum assumptions commonly used to describe the fluid mechanics of simple liquids have the potential to break down when considering flows at the nanometer scale. Two common assumptions for simple molecular liquids are that (1) they exhibit a Newtonian response, where the viscosity uniquely specifies the linear relationship between the stress and strain rate, and (2) the liquid moves in tandem with the solid at any solid-liquid interface, known as the no-slip condition. However, even simple molecular liquids can exhibit a non-Newtonian, viscoelastic response at the picosecond time scales that are characteristic of the motion of many nanoscale objects; this viscoelasticity arises because these time scales can be comparable to those of molecular relaxation in the liquid. In addition, even liquids that wet solid surfaces can exhibit nanometer-scale slip at those surfaces. It has recently become possible to interrogate the viscoelastic response of simple liquids and associated nanoscale slip using optical measurements of the mechanical vibrations of metal nanoparticles. Plasmon resonances in metal nanoparticles provide strong optical signals that can be accessed by several spectroscopies, most notably ultrafast transient-absorption spectroscopy. These spectroscopies have been used to measure the frequency and damping rate of acoustic oscillations in the nanoparticles, providing quantitative information about mechanical coupling and exchange of mechanical energy between the solid particle and its surrounding liquid. This information, in turn, has been used to elucidate the rheology of viscoelastic simple liquids at the nanoscale in terms of their constitutive relations, taking into account separate viscoelastic responses for both shear and compressible flows. The nanoparticle vibrations have also been used to provide quantitative measurements of slip lengths on the single-nanometer scale. Viscoelasticity has been shown to amplify nanoscale slip, illustrating the interplay between different aspects of the unconventional fluid dynamics of simple liquids at nanometer length scales and picosecond time scales.

Acoustic vibrations in plasmonic nanostructures provide deep insight into mechanical properties at the nanoscale for potential applications including optomechanical devices. Lithographic fabrication of plasmonic nanostructures allows precise control over shape and size as well as position. Here, we present a summary of our recent ultrafast studies of lithographically fabricated Au and Al nanostructures using single-particle transient extinction spectroscopy to measure the size- and shape-dependent acoustic frequencies and homogeneous damping times. Electronbeam lithography coupling with single-particle measurements necessitate the presence of a substrate, which we found to cause a blue shift in the acoustic vibration frequencies. This frequency shift enables the determination of the binding strength between Au nanostructures and the substrate. The substrate furthermore facilitates vibrational coupling between adjacent Au nanostructures. Electron-beam lithography also makes it possible to explore other plasmonic metals such as Al, which as the Earth's most abundant metal creates a sustainable pathway toward applications. We compared the ultrafast relaxation dynamics and acoustic properties of Al nanodisks to similar Au nanostructures. For both Au and Al nanostructures, we found an acoustic vibration quality factor which we ascribed to internal defects in the polycrystalline nanostructures that dominate the energy dissipation pathway. These findings provide significant insight into the optomechanical properties of nanostructures fabricated by electron-beam lithography.

The motion of a sphere in a viscous gas has been studied since the time of Sir George Gabriel Stokes who explored linear, steady and unsteady flows. While the unsteady Stokes equation is often used to calculate these flows, this continuum treatment cannot capture some key physical phenomena. This includes propulsion of a sphere by temperature gradients on its surface, without convection. Taguchi et al. (J. Fluid Mech., 2021) now calculate the flow generated by the impulsive rotation of a sphere in a gas, a problem first proposed by Stokes, using the linearised Boltzmann-BGK (Bhatnagar, Gross, Krook) equation. This statistical mechanical approach naturally captures continuum through to collisionless flows; the latter occurs even when the gas mean free path is small. The heat flow generated by the sphere is also determined - a non-continuum effect - showing its direction reverses as the flow evolves. The predicted phenomena are yet to be observed in experiment.

Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a ‘viscous flywheel’. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.

Simple liquids are conventionally described by Newtonian fluid mechanics, based on the assumption that relaxation processes in the flow occur much faster than the rate at which the fluid is driven. Nanoscale solids, however, have characteristic mechanical response times on the picosecond scale, which are comparable to mechanical relaxation times in simple liquids; as a result, viscoelastic effects in the liquid must be considered. These effects have been observed using time-resolved optical measurements of vibrating nanoparticles, but interpretation has often been complicated by finite velocity slip at the liquid-solid interface. Here, we use highly spherical gold nanoparticles to drive flows that are theoretically modeled without the use of the no-slip boundary condition at the particle surface. We obtain excellent agreement with this analytical theory that considers both the compression and shear relaxation properties of the liquid.

The resonance frequency of membranes depends on the gas pressure due to the squeeze-film effect, induced by the compression of a thin gas film that is trapped underneath the resonator by the high-frequency motion. This effect is particularly large in low-mass graphene membranes, which makes them promising candidates for pressure-sensing applications. Here, we study the squeeze-film effect in single-layer graphene resonators and find that their resonance frequency is lower than expected from models assuming ideal compression. To understand this deviation, we perform Boltzmann and continuum finite-element simulations and propose an improved model that includes the effects of gas leakage and can account for the observed pressure dependence of the resonance frequency. Thus, this work provides further understanding of the squeeze-film effect and provides further directions into optimizing the design of squeeze-film pressure sensors from 2D materials.