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Generalized Knudsen number for unsteady fluid flow

By V. Kara, V. Yakhot and K. L. Ekinci

Abstract

We explore the scaling behavior of an unsteady flow that is generated by an oscillating body of finite size in a gas. If the gas is gradually rarefied, the Navier-Stokes equations begin to fail and a kinetic description of the flow becomes more appropriate. The failure of the Navier-Stokes equations can be thought to take place via two different physical mechanisms: either the continuum hypothesis breaks down as a result of a finite size effect or local equilibrium is violated due to the high rate of strain. By independently tuning the relevant linear dimension and the frequency of the oscillating body, we can experimentally observe these two different physical mechanisms. All the experimental data, however, can be collapsed using a single dimensionless scaling parameter that combines the relevant linear dimension and the frequency of the body. This proposed Knudsen number for an unsteady flow is rooted in a fundamental symmetry principle, namely, Galilean invariance

Topics: Physics, General physics, Science & technology, Physical sciences, Physics, multidisciplinary, Nanomechanical resonators, Crystal-oscillator, Vacuum, Air, Physical sciences
Publisher: 'American Physical Society (APS)'
Year: 2017
DOI identifier: 10.1103/PhysRevLett.118.074505
OAI identifier: oai:open.bu.edu:2144/29251
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