Single-crystal diamond nanomechanical resonators are being developed for countless applications. A number of these applications require that the resonator be operated in a fluid, that is, a gas or a liquid. Here, we investigate the fluid dynamics of single-crystal diamond nanomechanical resonators in the form of nanocantilevers. First, we measure the pressure-dependent dissipation of diamond nanocantilevers with different linear dimensions and frequencies in three gases, He, N2, and Ar. We observe that a subtle interplay between the length scale and the frequency governs the scaling of the fluidic dissipation. Second, we obtain a comparison of the surface accommodation of different gases on the diamond surface by analyzing the dissipation in the molecular flow regime. Finally, we measure the thermal fluctuations of the nanocantilevers in water and compare the observed dissipation and frequency shifts with theoretical predictions. These findings set the stage for developing diamond nanomechanical resonators operable in fluids.
Various nanomechanical movements of bacteria provide a signature of bacterial viability. Most notably, bacterial movements have been observed to subside rapidly and dramatically when the bacteria are exposed to effective antibiotics. Thus, monitoring bacterial movements, if performed with high fidelity, could offer a path to various clinical microbiological applications, including antibiotic susceptibility tests. Here, we introduce a robust and ultrasensitive electrical transduction technique for detecting the nanomechanical movements of bacteria. The technique is based on measuring the electrical fluctuations in a microfluidic channel, which the bacteria populate. The swimming of planktonic bacteria and the random oscillations of surface-immobilized bacteria both cause small but detectable electrical fluctuations. We show that this technique provides enough sensitivity to detect even the slightest movements of a single cell; we also demonstrate an antibiotic susceptibility test in a biological matrix. Given that it lends itself to smooth integration with other microfluidic methods and devices, the technique can be developed into a functional antibiotic susceptibility test, in particular, for urinary tract infections.
We show the dielectrophoretic actuation of single-crystal diamond nanomechanical devices. Gradient radio-frequency electromagnetic forces are used to achieve actuation of both cantilever and doubly clamped beam structures, with operation frequencies ranging from a few MHz to ∼50MHz. Frequency tuning and parametric actuation are also studied.
We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect; or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely Galilean invariance.The Navier-Stokes (NS) equations of hydrodynamics can be obtained perturbatively from the kinetic theory of gases in the limit of small Knudsen number, Kn = λHere, λ is the mean free path in the gas, and L represents a characteristic length scale of the flow. As Kn → 0, it follows from statistical mechanics that density fluctuations in the gas vanish [2], leading to the notion of a "fluid particle." This continuum hypothesis becomes less accurate as Kn grows, eventually leading to the failure of the NS equations for Kn > ∼ 0.1. Likewise, the NS equations break down if the local value of the strain rate,∂xi , becomes so large that the condition τ S ij 1 no longer holds. Here, u i represents the velocity vector, and τ is the relaxation time that characterizes the rate of decay of a perturbation to thermodynamic equilibrium. As τ S ij grows, the fluid particle becomes deformed on shorter and shorter time scales, eventually violating the local equilibrium assumption. For a broad class of flows, breakdown of the continuum hypothesis and violation of local equilibrium can be thought to be equivalent, becauseHere, the Mach number Ma = U c compares the speed of sound c to the characteristic flow velocity U , and it is assumed to remain small and slowly varying. Thus, either Kn or τ S ij emerges as the relevant scaling parameter for determining the crossover from hydrodynamics to kinetic theory.To demonstrate the limitations of the above-described widely-accepted reasoning, we consider the canonical problem of an infinite plate oscillating at a prescribed angular frequency ω 0 in a gas (Stokes Second Problem) [3]. We assume the oscillation amplitude to be small and the geometry to be such that the velocity field is u x (x, y, 0) = U 0 cos ω 0 t, u y = 0, and u z = 0. Since the plate is infinite (l → ∞), the "standard" size-based Knudsen number Kn l = λ l remains zero at all limits and cannot be relevant. The scaling parameter here is the Weissenberg number, Wi = ω 0 τ [4, 5], and one can recover the correct Knudsen number, Kn δ = λ δ , using the boundary lay...
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