"Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators

The recent development of opto-mechano-fluidic resonators has provided -- by harnessing photon radiation pressure -- a new microfluidics platform for the optical sensing of fluid density and bulk modulus. Here we show that fluid viscosity can also be determined through optomechanical measurement of the vibrational noise spectrum of the resonator mechanical modes. A linear relationship between the spectral linewidth and root-viscosity is predicted and experimentally verified i...

Describing effects of small but finite inertia on suspended particles is a fundamental fluid dynamical problem that has never been solved in full generality. Modern microfluidics has turned this academic problem into a practical challenge through the use of high-frequency oscillatory flows, perhaps the most efficient way to take advantage of inertial effects at low Reynolds numbers, to precisely manipulate particles, cells and vesicles without the need for charges or chemistr...

The well-known problem of unidirectional plane flow of a fluid in a half-space due to the impulsive motion of the plate it rests upon is discussed in the context of the second-grade and the Oldroyd-B non-Newtonian fluids. The governing equations are derived from the conservation laws of mass and momentum and three correct known representations of their exact solutions given. Common mistakes made in the literature are identified. Simple numerical schemes that corroborate the a...

It has been shown recently [PRL 102, 254503 (2009)] that in the plane-plane configuration a mechanical resonator vibrating close to a rigid wall in a simple fluid can be overdamped to a frozen regime. Here, by solving analytically the Navier Stokes equations with partial slip boundary conditions at the solid fluid interface, we develop a theoretical approach justifying and extending these earlier findings. We show in particular that in the perfect slip regime the above mentio...

Turbulent motions in a fluid relax at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the relaxation rate is not generally known. This paper concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reached higher Reynolds numbers than ever before and covered a wide range of them ($10^4 < Re = UM/\nu < 5\times10^6$), we measured the ...

An elastic sheet that deforms near a solid substrate in a viscous fluid is a situation relevant to various dynamical processes in biology, geophysics and engineering. Here, we study the relaxation dynamics of an elastic plate resting on a thin viscous film that is supported by a solid substrate. By combining scaling analysis, numerical simulations and experiments, we identify asymptotic regimes for the elastohydrodynamic leveling of a surface perturbation of the form of a bum...

We report a novel technique capable of measuring the kinematic shear viscosity of Newtonian liquids with steady streaming in microfluidic devices. This probe-free microrheological method utilizes sub-kilohertz liquid oscillation frequencies around a cylindrical obstacle, ensuring that the inner streaming layer is comparable in size to the cylinder radius. To calibrate the viscometer, the evolution of the inner streaming layer as a function of oscillation frequency for a liqui...

We report (semi-)analytical solutions of a problem involving a visco-hyperelastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics are rationalized, based on fluid viscosity and solid elasticity, via wave and boundary-layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomen...

We show that full-image micro-PIV analysis in combination with images of transient particle motion is a powerful tool for experimental studies of acoustic radiation forces and acoustic streaming in microfluidic chambers under piezo-actuation in the MHz range. The measured steady-state motion of both large 5 um and small 1 um particles can be understood in terms of the acoustic eigenmodes or standing ultra-sound waves in the given experimental microsystems. This interpretation...

Relaxation of single defects in a nanometer sized resonator is observed by coupling surface acoustic waves to a freely suspended beam. The surface waves act on the resonator as driving forces being able to modify the internal friction in the beam. In analogy to classical experiments on internal friction in macroscopic samples, we perform frequency, amplitude, and temperature dependent experiments on the nano resonator and find a scenario which is consistent with the observati...