Journal article

Variational method enabling simplified solutions to the linearized Boltzmann equation for oscillatory gas flows

Daniel R Ladiges, John E Sader

PHYSICAL REVIEW FLUIDS | AMER PHYSICAL SOC | Published : 2018

Abstract

Nanomechanical resonators and sensors, operated in ambient conditions, often generate low-Mach-number oscillating rarefied gas flows. Cercignani [C. Cercignani, J. Stat. Phys. 1, 297 (1969)JSTPBS0022-471510.1007/BF01007482] proposed a variational principle for the linearized Boltzmann equation, which can be used to derive approximate analytical solutions of steady (time-independent) flows. Here we extend and generalize this principle to unsteady oscillatory rarefied flows and thus accommodate resonating nanomechanical devices. This includes a mathematical approach that facilitates its general use and allows for systematic improvements in accuracy. This formulation is demonstrated for two can..

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University of Melbourne Researchers

Grants

Awarded by Australian Research Council Centre of Excellence in Exciton Science


Funding Acknowledgements

This research was supported by the Australian Research Council Centre of Excellence in Exciton Science (CE170100026) and the Australian Research Council Grants Scheme.