Generalized Knudsen Number for Unsteady Fluid Flow

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.

Main article 5 pages, 3 figures, supplementary 15 pages, 10 figures

References in corpus (3)

• High-Frequency Nanofluidics: An Experimental Study using Nanomechanical Resonators
• "Stokes' Second Problem in High Frequency Limit. Application to Micro (Nano)- Resonators
• A Universality in Oscillating Flows

Cited by in corpus (7)

• Pressure-driven Nitrogen Flow in Divergent Microchannels with Isothermal Walls
• Electrothermal Actuation of NEMS Resonators: Modeling and Experimental Validation
• Surface-induced near-field scaling in the Knudsen layer of a rarefied gas
• The dynamics of an externally driven nanoscale beam that is under high tension and immersed in a viscous fluid
• Dynamics of NEMS Resonators across Dissipation Limits
• Multi-mode Brownian Dynamics of a Nanomechanical Resonator in a Viscous Fluid
• Nanomechanical Measurement of the Brownian Force Noise in a Viscous Liquid