A Universality in Oscillating Flows

Abstract

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 $<\omega /2\pi <10^8$ Hz) range. Our results suggest a deep connection between flows of simple and complex fluids.

To be published in Physical Review Letters

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