Dynamic similarity of oscillatory flows induced by nanomechanical resonators

Abstract

Rarefied gas flows generated by resonating nanomechanical structures pose a significant challenge to theoretical analysis and physical interpretation. The inherent noncontinuum nature of such flows obviates the use of classical theories, such as the Navier-Stokes equations, requiring more sophisticated physical treatments for their characterization. In this Letter, we present a universal dynamic similarity theorem: The quality factor of a nanoscale mechanical resonator at gas pressure P0 is α times that of a scaled-up microscale resonator at a reduced pressure α P0, where α is the ratio of nanoscale and microscale resonator sizes. This holds rigorously for any nanomechanical structure at a..