Dissipation from microscale and nanoscale beam resonators into a surrounding fluid

Simple models for estimating viscous damping, acoustic radiation loss, and loss due to collisions with individual molecules of rarefied gas are presented and examined to show how quality factor of microscale and nanoscale resonators varies with ambient fluid pressure p and resonator geometry. For sufficiently low length to thickness aspect ratios, acoustic radiation loss is the dominant loss mechanism at pressures great enough that the fluid acts as a continuum, and the acoustic loss transitions seamlessly at low pressure to loss due to direct transfer of momentum to individual fluid molecules (both models have loss proportional to fluid pressure). For beams with greater aspect ratio, viscous loss, with loss proportional to root p, dominates over a certain range of pressures, and the width of this region depends on the acoustic radiation efficiency of the beam. The transition between rarefied gas behavior and viscous (continuum) behavior occurs when the mean free path l(mfp), a function of pressure, becomes shorter than the viscous skin depth delta, which is related to beam size but also influenced by aspect ratio. (C) 2008 American Institute of Physics.