Vibration of Nanoparticles in Viscous Fluids

The dynamics of mechanical structures can be strongly affected by the fluid in which they are immersed. Ultrafast laser spectroscopy has recently provided fundamental insight into this fluid-structure interaction for nanoparticles immersed in a range of viscous fluids. In this article, we present results of a rigorous finite-element analysis and commensurate scaling theory that enable interpretation and analysis of these experiments, for the extensional vibrational modes of axisymmetric nanoparticles immersed in viscous fluids. Right circular, conical, and bipyramidal axisymmetric cylinder geometries are considered. We also develop an approximate analytical model that accounts for finite viscous penetration depth, which displays excellent agreement with finite-element results for particles of large aspect ratio. The finite-element results agree well with available measurements for particles in low viscosity fluids such as water, but significant discrepancies exist at higher viscosities. Possible mechanisms for these differences are discussed.