Fluid-structure model for disks vibrating at ultra-high frequency in a compressible viscous fluid

TL;DR

This paper develops an analytical fluid-structure model for disks vibrating at ultra-high frequencies in compressible viscous fluids, enabling better inference of liquid properties from experimental data.

Contribution

The paper introduces a novel analytical model for high-frequency disk vibrations in compressible viscous fluids, addressing a gap in existing fluid-structure interaction models.

Findings

Closed-form expressions for quality factor and frequency shift

Compressibility effects become significant above 1 GHz

Model validated against numerical simulations

Abstract

Radial mechanical modes of miniature disk-shaped resonators are promising candidates for probing the ultra-high-frequency rheological properties of liquids. However, the lack of an analytical fluid-structure model hinders the inference of liquid properties from the experimental measurement of such radial vibrations. Here we develop analytical models for the case of a disk vibrating in a compressible viscous liquid. Closed-form expressions for the mechanical quality factor and resonant frequency shift upon immersion are obtained, which we compare to the results of numerical modeling for a few significant cases. At frequencies above 1 GHz, our model points out the significance of compressibility effects.