A coin vibrational motor swimming at low Reynolds number

TL;DR

This study demonstrates that a coin vibrational motor can swim in a viscous fluid when symmetry is broken, achieving low Reynolds number locomotion that could inspire inexpensive robotic swimmers.

Contribution

It reveals that breaking rotational symmetry enables vibrational motors to swim, providing a novel approach to low-cost robotic propulsion at low Reynolds numbers.

Findings

Motor swims at 3 mm/s in glycerin

Swim speed depends on steady streaming velocity

Breaking symmetry enables swimming in viscous fluids

Abstract

Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its vibrations induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. The swim speed puts the vibrational motor in a low Reynolds number regime similar to bacterial motility, but because of the vibration it is not analogous to biological organisms. Rather the swimming vibrational motor may inspire small inexpensive robotic swimmers that are robust as they contain no external moving parts. A time dependent Stokes equation planar sheet model suggests that the swim speed depends on a steady streaming velocity $V_{stream} \sim Re_s^{1/2} U_0$ where $U_0$ is the velocity of surface vibrations, and streaming Reynolds number $Re_s = U_0^2/(\omega \nu)$ for angular vibrational frequency $\omega$ and fluid kinematic viscosity $\nu$.