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Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators

Bullard, Elizabeth C. and Li, Jianchang and Lilley, Charles R. and Mulvaney, Paul and Roukes, Michael L. and Sader, John E. (2014) Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators. Physical Review Letters, 112 (1). Art. No. 015501. ISSN 0031-9007. doi:10.1103/PhysRevLett.112.015501.

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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 P_0 is α times that of a scaled-up microscale resonator at a reduced pressure α P_0, 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.

Item Type:Article
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URLURL TypeDescription
Roukes, Michael L.0000-0002-2916-6026
Sader, John E.0000-0002-7096-0627
Additional Information:© 2014 American Physical Society. Received 3 July 2013; published 7 January 2014. We thank D. Chi for assistance in electron beam lithography and A. Naik for helpful discussions. Experimental work at Caltech was supported by the U.S. NSF through Grant No. DBI-0821863, the NIH through Grant No. R01 GM085666-01AIZ, and a NIH Director's Pioneer Award (M. L. R.). Device fabrication was carried out in the Kavli Nanoscience Institute at Caltech. The authors gratefully acknowledge support of the Australian Research Council Grants Scheme and a Caltech's Kavli Nanoscience Institute Distinguished Visiting Professorship (J. E. S.).
Group:Kavli Nanoscience Institute
Funding AgencyGrant Number
NIHR01 GM085666-01AIZ
NIH Director's Pioneer AwardUNSPECIFIED
Australian Research CouncilUNSPECIFIED
Kavli Nanoscience InstituteUNSPECIFIED
Issue or Number:1
Classification Code:PACS: 81.70.-q, 62.25.-g, 81.07.-b
Record Number:CaltechAUTHORS:20140403-162009111
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Official Citation:Bullard, E. C., Li, J., Lilley, C. R., Mulvaney, P., Roukes, M. L., & Sader, J. E. (2014). Dynamic Similarity of Oscillatory Flows Induced by Nanomechanical Resonators. Physical Review Letters, 112(1), 015501.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:44653
Deposited On:04 Apr 2014 14:52
Last Modified:10 Nov 2021 16:54

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