# Generalized Knudsen Number for Unsteady Fluid Flow

## TL;DR

This paper introduces a generalized Knudsen number for unsteady gas flows generated by oscillating bodies, unifying different physical mechanisms of flow failure through a single dimensionless parameter based on Galilean invariance.

## Contribution

It proposes a new unsteady flow Knudsen number that captures both size and frequency effects, unifying flow regimes under a common scaling law.

## Key findings

- Experimental data collapse using the new Knudsen number
- Identification of two physical mechanisms of flow failure
- Validation of the scaling parameter across different conditions

## 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.