Dynamic similarity of oscillatory flows induced by nanomechanical resonators.
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 all degrees of rarefaction, from continuum through to transition and free molecular flows. The theorem is demonstrated for a series of nanomechanical cantilever devices of different size, for which precise universal behavior is observed. This result is of significance for research aimed at probing the fundamental nature of rarefied gas flows and gas-structure interactions at nanometer length scales.
Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA.
Elizabeth C
EC
Bullard
School of Chemistry and Bio21 Institute, The University of Melbourne, Victoria 3010, Australia.
Jianchang
J
Li
Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia.
Charles R
CR
Lilley
School of Chemistry and Bio21 Institute, The University of Melbourne, Victoria 3010, Australia.
Paul
P
Mulvaney
Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA.
Michael L
ML
Roukes
Kavli Nanoscience Institute and Departments of Physics, Applied Physics, and Bioengineering, California Institute of Technology, Pasadena, California 91125, USA and Department of Mathematics and Statistics, The University of Melbourne, Victoria 3010, Australia.
John E
JE
Sader
D005740:Gases; D055617:Micro-Electrical-Mechanical Systems / Q000295:instrumentation / Q000379:methods*; D008962:Models, Theoretical; D036103:Nanotechnology / Q000295:instrumentation / Q000379:methods*
D005740:Gases