A Universality in Oscillating Flows

TL;DR

This paper demonstrates that oscillating flows of simple fluids, whether Newtonian or non-Newtonian, can be universally described by a single dimensionless parameter, revealing a fundamental connection across fluid types and flow regimes.

Contribution

The study introduces a universal function based on the dimensionless parameter , applicable to both Newtonian and non-Newtonian oscillating flows, independent of geometry and size.

Findings

Experimental data follow the universal scaling closely across broad ranges.

Flow behavior is governed primarily by the dimensionless parameter .

Suggests a fundamental link between simple and complex fluid 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.