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

In the present paper we theoretically study the shear force exerted on an infinite horizontal plane undergoing fast lateral oscillations in presence of a rigid particle suspended in the viscous liquid above the plate. The study is largely motivated by Quartz Crystal Microbalance (QCM-D) technique which relies on analyzing response (complex impedance) of fast oscillating (in MHz range) quartz crystal disk in the liquid medium due to small substances adsorbed at its surface. In...

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform ...

This paper presents an efficient coupling of the 3D Stokes flow interacting with an effective perforated periodic heterogeneous anisotropic 2D plate. The effective model was obtained by the asymptotic analysis in earlier works and here an effective numerical algorithm is given. By $Q_3$ or bi-cubic spacial interpolation the time-dependent problem was reduced to an algebraic system of ordinary differential equation in time. Different examples were given, demonstrating the infl...

Dynamics of a deformable capsule in an oscillatory flow of a Newtonian fluid in a microchannel has been studied numerically. The effects of oscillation frequency, capsule deformability, and channel flow rate have been explored by simulating the capsule within a microchannel. In addition, the simulation captures the effect of the type of imposed pressure oscillations on the migration pattern of the capsule. An oscillatory channel flow enables the focusing of extremely small bi...

An analytical model of open-cavity second sound resonators is presented and validated against simulations and experiments in superfluid helium using a new resonator design that achieves unprecedented resolution. The model incorporates diffraction, geometrical misalignments, and flow through the cavity, and is validated using cavities with aspect ratios close to unity, operated up to their 20th resonance in superfluid helium.An important finding of this study is that resonator...

We consider incompressible flows between two transversely vibrating solid walls and construct an asymptotic expansion of solutions of the Navier-Stokes equations in the limit when both the amplitude of vibrations and the thickness of the Stokes layer are small and have the same order of magnitude. Our asymptotic expansion is valid up to the flow boundary. In particular, we derive equations and boundary conditions, for the averaged flow. In the leading order, the averaged flow...

In this paper we investigate the interaction of fluid flow with a thin porous elastic layer. We consider two fluid-filled bulk domains which are separated by a thin periodically perforated layer consisting of a fluid and an elastic solid part. Thickness and periodicity of the layer are of order $\epsilon$, where $\epsilon$ is small compared to the size of the bulk domains. The fluid flow is described by an instationary Stokes equation and the solid via linear elasticity. The ...

Non-linear effects of the Navier-Stokes equations disappear under the Stokes regime of Newtonian fluid flows disallowing the fluid flow rectification. Here we show mathematically and experimentally that passive flow rectification of Newtonian fluids is obtainable under the Stokes regime of both compressible and incompressible flows by introducing nonlinearity into the otherwise linear Stokes equations. Asymmetric flow resistances arise in shallow nozzle/diffuser microchannels...

Vibrating nano- and micromechanical resonators have been the subject of research aiming at ultrasensitive mass sensors for mass spectrometry, chemical analysis and biomedical diagnosis. Unfortunately, their merits diminish dramatically in liquids due to dissipative mechanisms like viscosity and acoustic losses. A push towards faster and lighter miniaturized nanodevices would enable improved performances, provided dissipation was controlled and novel techniques were available ...

It is well known that a boundary layer develops along an infinite plate under oscillatory motion in a Newtonian fluid. In this work, this oscillatory boundary layer theory is generalized to the case of linear viscoelastic(LVE) flow. We demonstrate that the dynamics in LVE are generically different than those for flow of similar settings in Newtonian fluids, in several aspects. These new discoveries are expected to have consequences on related engineering applications. Mimicki...