A Universality in Oscillating Flows

We show that oscillating flow of a simple fluid in both the Newtonian and the non-Newtonian regime can be described by a universal function of a single dimensionless scaling parameter $\omega \tau$, where $\omega$ is the oscillation (angular) frequency and $\tau$ is the fluid relaxation-time; geometry and linear dimension bear no effect on the flow. Experimental energy dissipation data of mechanical resonators in a rarefied gas follow this universality closely in a broad linear dimension (${10}^{-6}$ m$<L<{10}^{-2}$ m) and frequency (${10}^5$ Hz $<\omega \mathrm{/}2\pi <{10}^8$ Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.