A note on the breathing mode of an elastic sphere in Newtonian and complex fluids

TL;DR

This paper investigates the breathing mode vibrations of elastic spheres in Newtonian and viscoelastic fluids, revealing significant effects of fluid properties on vibrational behavior and potential applications in biological sensing.

Contribution

It extends classical continuum mechanics to include viscoelastic effects in the vibrational analysis of elastic spheres, highlighting the importance of fluid properties in acoustic resonance applications.

Findings

Fluid compressibility significantly affects the breathing mode.

Viscoelastic response in water-glycerol mixtures is similar across different vibration modes.

Fluid viscoelasticity influences the effectiveness of virus destruction by acoustic resonance.

Abstract

Experiments on the acoustic vibrations of elastic nanostructures in fluid media have been used to study the mechanical properties of materials, as well as for mechanical and biological sensing. The medium surrounding the nanostructure is typically modeled as a Newtonian fluid. A recent experiment however suggested that high-frequency longitudinal vibration of bipyramidal nanoparticles could trigger a viscoelastic response in water-glycerol mixtures [M. Pelton et al., "Viscoelastic flows in simple liquids generated by vibrating nanostructures," Phys. Rev. Lett. 111, 244502 (2013)]. Motivated by these experimental studies, we first revisit a classical continuum mechanics problem of the purely radial vibration of an elastic sphere, also called the breathing mode, in a compressible viscous fluid, and then extend our analysis to a viscoelastic medium using the Maxwell fluid model. The effects of fluid compressibility and viscoelasticity are discussed. Although in the case of longitudinal vibration of bipyramidal nanoparticles, the effects of fluid compressibility were shown to be negligible, we demonstrate that it plays a significant role in the breathing mode of an elastic sphere. On the other hand, despite the different vibration modes, the breathing mode of a sphere triggers a viscoelastic response in water-glycerol mixtures similar to that triggered by the longitudinal vibration of bipyramidal nanoparticles. We also comment on the effect of fluid viscoelasticity on the idea of destroying virus particles by acoustic resonance.