Minimal two-sphere model of the generation of fluid flow at low Reynolds numbers

TL;DR

This paper presents a minimal two-sphere model demonstrating that at low Reynolds numbers, flow can be generated with a simple system driven by harmonic potentials, challenging the need for non-reciprocal motion.

Contribution

The study introduces a minimal two-sphere model capable of generating flow at low Reynolds numbers using only harmonic driving, supported by analytical, numerical, and experimental results.

Findings

A time-reversible drive can induce flow at low Reynolds numbers.

The model requires only two degrees of freedom: mean and relative positions.

Flow generation is demonstrated through analytical, numerical, and experimental methods.

Abstract

Locomotion and generation of flow at low Reynolds number are subject to severe limitations due to the irrelevance of inertia: the "scallop theorem" requires that the system have at least two degrees of freedom, which move in non-reciprocal fashion, i.e. breaking time-reversal symmetry. We show here that a minimal model consisting of just two spheres driven by harmonic potentials is capable of generating flow. In this pump system the two degrees of freedom are the mean and relative positions of the two spheres. We have performed and compared analytical predictions, numerical simulation and experiments, showing that a time-reversible drive is sufficient to induce flow.