An analytical framework to determine flow velocities within nanotubes from their vibration frequencies

Abstract

We develop a theoretical framework to determine fluid velocities within nanotubes. We demonstrate that the fluid/tube dynamic coupling could be exploited to determine flow velocities based on knowledge of the bending frequency spectrum of a single nanotube. We develop an analytical methodology that allows one to associate any of the frequencies in the spectrum with a single value of the fluid velocity. We discuss the feasibility of experiments by state-of-the-art atomic force microscopy and perform numerical simulations to determine uncertainties in fluid velocities. These are below 5% for common nanotube sizes, which are considerably smaller than the ones reported in the literature for conventional methods.